************************************************************************************************************************************ ************************************************************************************************************************************ **** **** **** **** **** ParaMonte **** **** Plain Powerful Parallel **** **** Monte Carlo Library **** **** **** **** Version 1.5.1 **** **** **** **** Build: Sun Jan 03 05:28:35 2021 **** **** **** **** Department of Physics **** **** Computational & Data Science Lab **** **** Data Science Program, College of Science **** **** The University of Texas at Arlington **** **** **** **** originally developed at **** **** **** **** Multiscale Modeling Group **** **** Center for Computational Oncology (CCO) **** **** Oden Institute for Computational Engineering and Sciences **** **** Department of Aerospace Engineering and Engineering Mechanics **** **** Department of Neurology, Dell-Seton Medical School **** **** Department of Biomedical Engineering **** **** The University of Texas at Austin **** **** **** **** For questions and further information, please contact: **** **** **** **** Amir Shahmoradi **** **** **** **** shahmoradi@utexas.edu **** **** amir.shahmoradi@uta.edu **** **** ashahmoradi@gmail.com **** **** **** **** cdslab.org/pm **** **** **** **** https://www.cdslab.org/paramonte/ **** **** **** **** **** ************************************************************************************************************************************ ************************************************************************************************************************************ ************************************************************************************************************************************ **** **** **** ParaMonte library interface specifications **** **** **** ************************************************************************************************************************************ Python 3.7.6 (default, Jan 8 2020, 20:23:39) [MSC v.1916 64 bit (AMD64)] ************************************************************************************************************************************ **** **** **** ParaMonte library compiler version **** **** **** ************************************************************************************************************************************ Intel(R) Visual Fortran Intel(R) 64 Compiler for applications running on Intel(R) 64, Version 19.1.1.216 Build 20200306 ************************************************************************************************************************************ **** **** **** ParaMonte library compiler options **** **** **** ************************************************************************************************************************************ /I:D:\Dropbox\Projects\20180101_ParaMonte\git\build\winx64\intel\19.1.1.216\release\shared\heap\serial\Python\mod /I:. /nologo /stan dard-semantics /F0x1000000000 /O3 /Qip /Qipo /Qunroll /Qunroll-aggressive /heap-arrays /fpp /define:PARAMONTE_VERSION='1.5.1' /defin e:CFI_ENABLED /define:PYTHON_ENABLED /define:OS_IS_WINDOWS /define:INTEL_COMPILER_ENABLED /define:DLL_ENABLED /threads /libs:static /module:D:\Dropbox\Projects\20180101_ParaMonte\git\build\winx64\intel\19.1.1.216\release\shared\heap\serial\Python\mod /c ************************************************************************************************************************************ **** **** **** Runtime platform specifications **** **** **** ************************************************************************************************************************************ Host Name: PHYS-125112 OS Name: Microsoft Windows 10 Enterprise OS Version: 10.0.18363 N/A Build 18363 OS Manufacturer: Microsoft Corporation OS Configuration: Member Workstation OS Build Type: Multiprocessor Free Registered Owner: uta Registered Organization: university of texas @ arlington Product ID: 00329-00000-00003-AA203 Original Install Date: 6/14/2020, 12:08:39 PM System Boot Time: 1/3/2021, 8:20:23 PM System Manufacturer: Dell Inc. System Model: Precision 7520 System Type: x64-based PC Processor(s): 1 Processor(s) Installed. [01]: Intel64 Family 6 Model 94 Stepping 3 GenuineIntel ~2901 Mhz BIOS Version: Dell Inc. 1.17.0, 1/9/2020 Windows Directory: C:\WINDOWS System Directory: C:\WINDOWS\system32 Boot Device: \Device\HarddiskVolume2 System Locale: en-us;English (United States) Input Locale: en-us;English (United States) Time Zone: (UTC-06:00) Central Time (US & Canada) Total Physical Memory: 65,385 MB Available Physical Memory: 36,276 MB Virtual Memory: Max Size: 75,113 MB Virtual Memory: Available: 42,929 MB Virtual Memory: In Use: 32,184 MB Page File Location(s): C:\pagefile.sys Domain: uta.edu Logon Server: \\DC-OSS-ARDC-1 Hotfix(s): 10 Hotfix(s) Installed. [01]: KB4576484 [02]: KB4517245 [03]: KB4560959 [04]: KB4561600 [05]: KB4565554 [06]: KB4569073 [07]: KB4576751 [08]: KB4580325 [09]: KB4586863 [10]: KB4592449 Network Card(s): 6 NIC(s) Installed. [01]: Cisco AnyConnect Secure Mobility Client Virtual Miniport Adapter for Windows x64 Connection Name: Ethernet 2 Status: Hardware not present [02]: ExpressVPN TAP Adapter Connection Name: Ethernet 3 Status: Media disconnected [03]: Intel(R) Ethernet Connection (5) I219-LM Connection Name: Ethernet Status: Media disconnected [04]: Qualcomm QCA61x4A 802.11ac Wireless Adapter Connection Name: Wi-Fi DHCP Enabled: Yes DHCP Server: 192.168.0.1 IP address(es) [01]: 192.168.0.177 [02]: fe80::f094:d1d8:e71d:50a3 [05]: Bluetooth Device (Personal Area Network) Connection Name: Bluetooth Network Connection Status: Media disconnected [06]: Hyper-V Virtual Ethernet Adapter Connection Name: vEthernet (WSL) DHCP Enabled: No IP address(es) [01]: 192.168.3.81 [02]: fe80::cc5b:c197:1790:c2be Hyper-V Requirements: A hypervisor has been detected. Features required for Hyper-V will not be displayed. ************************************************************************************************************************************ **** **** **** Setting up the ParaDRAM simulation environment **** **** **** ************************************************************************************************************************************ ParaDRAM - NOTE: Interfacing Python with ParaDRAM... ParaDRAM - NOTE: Variable outputFileName detected among the input variables to ParaDRAM: ParaDRAM - NOTE: ./out/mvn_serial ParaDRAM - NOTE: ParaDRAM - NOTE: Absolute path to the current working directory: ParaDRAM - NOTE: D:\Dropbox\Projects\20180101_ParaMonte\git\paramontex\Python\Jupyter\sampling_multivariate_normal_distribution_via_paradram ParaDRAM - NOTE: ParaDRAM - NOTE: Generating the requested directory for the ParaDRAM output files: ParaDRAM - NOTE: .\out\ ParaDRAM - NOTE: ParaDRAM - NOTE: ParaDRAM output files will be prefixed with: ParaDRAM - NOTE: .\out\mvn_serial ParaDRAM - NOTE: Generating the output progress file: ParaDRAM - NOTE: .\out\mvn_serial_process_1_progress.txt ParaDRAM - NOTE: Generating the output chainfile: ParaDRAM - NOTE: .\out\mvn_serial_process_1_chain.txt ************************************************************************************************************************************ **** **** **** ParaDRAM simulation specifications **** **** **** ************************************************************************************************************************************ ndim 4 ParaDRAM - NOTE: ndim is a 32-bit positive integer, representing the number of dimensions of the domain of the objective ParaDRAM - NOTE: function. It is the only simulation specification variable that the user must always provide along ParaDRAM - NOTE: with the objective function, separately from the rest of the simulation specifications. The variable ParaDRAM - NOTE: ndim must be always provided directly to the ParaMonte routines, along with the objective function. ParaDRAM - NOTE: If specified within an input file, its value will be ignored and not used. The variable ndim has no ParaDRAM - NOTE: default value as it is the only mandatory piece of information that must be provided by the user. description UNDEFINED ParaDRAM - NOTE: The variable 'description' contains general information about the specific ParaDRAM simulation that ParaDRAM - NOTE: is going to be performed. It has no effects on the simulation and serves only as a general description ParaDRAM - NOTE: of the simulation for future reference. The ParaDRAM parser automatically recognizes the C-style '\n' ParaDRAM - NOTE: escape sequence as the new-line character, and '\\' as the backslash character '\' if they used in ParaDRAM - NOTE: the description. For example, '\\n' will be converted to '\n' on the output, while '\n' translates ParaDRAM - NOTE: to the new-line character. Other C escape sequences are neither supported nor needed. The default ParaDRAM - NOTE: value for description is 'UNDEFINED'. inputFileHasPriority F ParaDRAM - NOTE: A logical (boolean) variable. If TRUE (or .true. or true or .t. from within an input file), then the ParaDRAM - NOTE: input specifications of the sampler will be read from the input file provided by the user, and the ParaDRAM - NOTE: simulation specification assignments from within the programming language environment (if any are ParaDRAM - NOTE: made) will be completely ignored. If inputFileHasPriority is FALSE, then all simulation specifications ParaDRAM - NOTE: of the ParaDRAM sampler that are taken from the user-specified input file will be overwritten by ParaDRAM - NOTE: their corresponding input values that are set from within the user's programming environment (if any ParaDRAM - NOTE: is provided). Note that this feature is useful when, for example, some simulation specifications have ParaDRAM - NOTE: to computed and specified at runtime and therefore, cannot be specified before the program execution. ParaDRAM - NOTE: Currently, this functionality (i.e., prioritizing the input file values to input-procedure-argument ParaDRAM - NOTE: values) is available only in the Fortran-interface to the ParaMonte library routines. The default ParaDRAM - NOTE: value is FALSE. silentModeRequested F ParaDRAM - NOTE: A logical (boolean) variable. If TRUE (or .true. or true or .t. from within an input file), then the ParaDRAM - NOTE: following contents will not be printed in the output report file of ParaDRAM: ParaDRAM - NOTE: ParaDRAM - NOTE: + ParaDRAM interface, compiler, and platform specifications. ParaDRAM - NOTE: + ParaDRAM simulation specification-descriptions. ParaDRAM - NOTE: ParaDRAM - NOTE: Setting this variable to true may break the functionality of the report-file parser methods of the ParaDRAM - NOTE: ParaMonte library in high-level languages (e.g., MATLAB, Python, R, ...). The default value is FALSE. domainLowerLimitVec -.1797693134862316E+308 -.1797693134862316E+308 -.1797693134862316E+308 -.1797693134862316E+308 ParaDRAM - NOTE: domainLowerLimitVec represents the lower boundaries of the cubical domain of the objective function ParaDRAM - NOTE: to be sampled. It is an ndim-dimensional vector of 64-bit real numbers, where ndim is the number of ParaDRAM - NOTE: variables of the objective function. It is also possible to assign only select values of domainLowerLimitVec ParaDRAM - NOTE: and leave the rest of the components to be assigned the default value. This is POSSIBLE ONLY when ParaDRAM - NOTE: domainLowerLimitVec is defined inside the input file to ParaDRAM. For example, having the following ParaDRAM - NOTE: inside the input file, ParaDRAM - NOTE: ParaDRAM - NOTE: domainLowerLimitVec(3:5) = -100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the lower limits of the third, fourth, and the fifth dimensions to -100, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: domainLowerLimitVec(1) = -100, domainLowerLimitVec(2) = -1.e6 ParaDRAM - NOTE: ParaDRAM - NOTE: will set the lower limit on the first dimension to -100, and 1.e6 on the second dimension, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: domainLowerLimitVec = 3*-2.5e100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the lower limits on the first, second, and the third dimensions to -2.5*10^100, ParaDRAM - NOTE: while the rest of the lower limits for the missing dimensions will be automatically set ParaDRAM - NOTE: to the default value. ParaDRAM - NOTE: ParaDRAM - NOTE: The default value for all elements of domainLowerLimitVec is: -1.797693134862316E+307. domainUpperLimitVec .1797693134862316E+308 .1797693134862316E+308 .1797693134862316E+308 .1797693134862316E+308 ParaDRAM - NOTE: domainUpperLimitVec represents the upper boundaries of the cubical domain of the objective function ParaDRAM - NOTE: to be sampled. It is an ndim-dimensional vector of 64-bit real numbers, where ndim is the number of ParaDRAM - NOTE: variables of the objective function. It is also possible to assign only select values of domainUpperLimitVec ParaDRAM - NOTE: and leave the rest of the components to be assigned the default value. This is POSSIBLE ONLY when ParaDRAM - NOTE: domainUpperLimitVec is defined inside the input file to ParaDRAM. For example, ParaDRAM - NOTE: ParaDRAM - NOTE: domainUpperLimitVec(3:5) = 100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the upper limits of the third, fourth, and the fifth dimensions to 100, or, ParaDRAM - NOTE: ParaDRAM - NOTE: domainUpperLimitVec(1) = 100, domainUpperLimitVec(2) = 1.e6 ParaDRAM - NOTE: ParaDRAM - NOTE: will set the upper limit on the first dimension to 100, and 1.e6 on the second dimension, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: domainUpperLimitVec = 3*2.5e100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the upper limits on the first, second, and the third dimensions to 2.5*10^100, ParaDRAM - NOTE: while the rest of the upper limits for the missing dimensions will be automatically set ParaDRAM - NOTE: to the default value. ParaDRAM - NOTE: ParaDRAM - NOTE: The default value for all elements of domainUpperLimitVec is: 1.797693134862316E+307. variableNameList SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 ParaDRAM - NOTE: variableNameList contains the names of the variables to be sampled by ParaDRAM. It is used to construct ParaDRAM - NOTE: the header of the output sample file. Any element of variableNameList that is not set by the user ParaDRAM - NOTE: will be automatically assigned a default name. The default value is 'SampleVariablei' where integer ParaDRAM - NOTE: 'i' is the index of the variable. parallelizationModel singleChain ParaDRAM - NOTE: parallelizationModel is a string variable that represents the parallelization method to be used in ParaDRAM - NOTE: ParaDRAM. The string value must be enclosed by either single or double quotation marks when provided ParaDRAM - NOTE: as input. Two options are currently supported: ParaDRAM - NOTE: ParaDRAM - NOTE: parallelizationModel = 'multiChain' ParaDRAM - NOTE: ParaDRAM - NOTE: This method uses the Prefect Parallelism scheme in which multiple MCMC chains are generated ParaDRAM - NOTE: independently of each other. In this case, multiple output MCMC chain files will also be ParaDRAM - NOTE: generated. ParaDRAM - NOTE: ParaDRAM - NOTE: parallelizationModel = 'singleChain' ParaDRAM - NOTE: ParaDRAM - NOTE: This method uses the fork-style parallelization scheme. A single MCMC chain file will be ParaDRAM - NOTE: generated in this case. At each MCMC step multiple proposal steps will be checked in ParaDRAM - NOTE: parallel until one proposal is accepted. ParaDRAM - NOTE: ParaDRAM - NOTE: Note that in serial mode, there is no parallelism. Therefore, this option does not affect non-parallel ParaDRAM - NOTE: simulations and its value is ignored. The serial mode is equivalent to either of the parallelism ParaDRAM - NOTE: methods with only one simulation image (processor, core, or thread). The default value is ParaDRAM - NOTE: parallelizationModel = 'singleChain'. Note that the input values are case-insensitive and white-space ParaDRAM - NOTE: characters are ignored. mpiFinalizeRequested T ParaDRAM - NOTE: In parallel ParaDRAM simulations via MPI communication libraries, if mpiFinalizeRequested = true (or ParaDRAM - NOTE: T, both case-insensitive), then a call will be made to the MPI_Finalize() routine from inside ParaDRAM ParaDRAM - NOTE: at the end of the simulation to finalize the MPI communications. Set this variable to false (or f, ParaDRAM - NOTE: both case-insensitive) if you do not want ParaDRAM to finalize the MPI communications for you. This ParaDRAM - NOTE: is a low-level simulation specification variable, relevant to simulations that directly involve MPI ParaDRAM - NOTE: parallelism. If you do not have any MPI-routine calls in your main program, you can safely ignore ParaDRAM - NOTE: this variable with its default value. Note that in non-MPI-enabled simulations, such as serial and ParaDRAM - NOTE: Coarray-enabled simulations, the value of this variable is completely ignored. The default value is ParaDRAM - NOTE: TRUE. outputFileName .\out\mvn_serial ParaDRAM - NOTE: outputFileName contains the path and the base of the filename for ParaDRAM output files. If not ParaDRAM - NOTE: provided by the user, the default outputFileName is constructed from the current date and time: ParaDRAM - NOTE: ParaDRAM - NOTE: ParaDRAM_run_yyyymmdd_hhmmss_mmm ParaDRAM - NOTE: ParaDRAM - NOTE: where yyyy, mm, dd, hh, mm, ss, mmm stand respectively for the current year, month, day, hour, minute, ParaDRAM - NOTE: second, and millisecond. In such a case, the default directory for the output files will be the ParaDRAM - NOTE: current working directory of ParaDRAM. If outputFileName is provided, but ends with a separator ParaDRAM - NOTE: character '/' or '\' (as in Linux or Windows OS), then its value will be used as the directory to ParaDRAM - NOTE: which ParaDRAM output files will be written. In this case, the output file naming convention described ParaDRAM - NOTE: above will be used. Also, the given directory will be automatically created if it does not exist ParaDRAM - NOTE: already. overwriteRequested T ParaDRAM - NOTE: A logical (boolean) variable. If true (or .true. or TRUE or .t. from within an input file), then any ParaDRAM - NOTE: existing old simulation files with the same name as the current simulation will be overwritten with ParaDRAM - NOTE: the new simulation output files. Note that if overwriteRequested is set to TRUE, then the restart ParaDRAM - NOTE: functionality is automatically turned off and any existing old simulation output files with the same ParaDRAM - NOTE: name as the current simulation will be overwritten by ParaDRAM. The default value is FALSE. targetAcceptanceRate UNDEFINED ParaDRAM - NOTE: targetAcceptanceRate sets an optimal target for the ratio of the number of accepted objective function ParaDRAM - NOTE: calls to the total number of function calls by the ParaDRAM sampler. It is a real-valued array of ParaDRAM - NOTE: length 2, whose elements determine the upper and lower bounds of the desired acceptance rate. When ParaDRAM - NOTE: the acceptance rate of the sampler is outside the specified limits, the sampler's settings will be ParaDRAM - NOTE: automatically adjusted to bring the overall acceptance rate to within the specified limits by the ParaDRAM - NOTE: input variable targetAcceptanceRate. When assigned from within a dynamic-language programming ParaDRAM - NOTE: environment, such as MATLAB or Python, or from within an input file, targetAcceptanceRate can also ParaDRAM - NOTE: be a single real number between 0 and 1. In such case, the ParaDRAM sampler will constantly attempt ParaDRAM - NOTE: (with no guarantee of success) to bring the average acceptance ratio of the sampler as close to the ParaDRAM - NOTE: user-provided target ratio as possible. The success of ParaDRAM in keeping the average acceptance ParaDRAM - NOTE: ratio close to the requested target value depends heavily on: ParaDRAM - NOTE: ParaDRAM - NOTE: 1) the value of adaptiveUpdatePeriod; the larger, the easier. ParaDRAM - NOTE: 2) the value of adaptiveUpdateCount; the larger, the easier. ParaDRAM - NOTE: ParaDRAM - NOTE: Note that the acceptance ratio adjustments will only occur every adaptiveUpdatePeriod sampling steps ParaDRAM - NOTE: for a total number of adaptiveUpdateCount. There is no default value for targetAcceptanceRate, as ParaDRAM - NOTE: the acceptance ratio is not directly adjusted during sampling. sampleSize -1 ParaDRAM - NOTE: The variable sampleSize is an integer that dictates the number of (hopefully, independent and ParaDRAM - NOTE: identically distributed [i.i.d.]) samples to be drawn from the user-provided objective function. ParaDRAM - NOTE: Three ranges of values are possible. If ParaDRAM - NOTE: ParaDRAM - NOTE: sampleSize < 0, ParaDRAM - NOTE: ParaDRAM - NOTE: then, the absolute value of sampleSize dictates the sample size in units of the effective ParaDRAM - NOTE: sample size. The effective sample is by definition i.i.d., and free from duplicates and ParaDRAM - NOTE: residual autocorrelation. The effective sample size is automatically determined by ParaDRAM ParaDRAM - NOTE: toward the end of the simulation. For example: ParaDRAM - NOTE: ParaDRAM - NOTE: sampleSize = -1 yields the effective i.i.d. sample drawn from the objective ParaDRAM - NOTE: function. ParaDRAM - NOTE: ParaDRAM - NOTE: sampleSize = -2 yields a (potentially non-i.i.d.) sample twice as big as the ParaDRAM - NOTE: effective sample. ParaDRAM - NOTE: ParaDRAM - NOTE: sampleSize > 0, ParaDRAM - NOTE: ParaDRAM - NOTE: then, the sample size is assumed to be in units of the number of points to be sampled. ParaDRAM - NOTE: If sampleSize turns out to be less than effectiveSampleSize, the resulting sample will ParaDRAM - NOTE: be i.i.d.. If sampleSize turns out to be larger than effectiveSampleSize, the resulting ParaDRAM - NOTE: sample will be potentially non-i.i.d.. The larger this difference, the more non-i.i.d. ParaDRAM - NOTE: the resulting final refined sample will be. For example: ParaDRAM - NOTE: ParaDRAM - NOTE: sampleSize = 1000 yields a 1000-points sample from the objective function. ParaDRAM - NOTE: ParaDRAM - NOTE: sampleSize = 0, ParaDRAM - NOTE: ParaDRAM - NOTE: then, no sample file will be generated. ParaDRAM - NOTE: ParaDRAM - NOTE: The default value is sampleSize = -1. randomSeed 3751 ThisProcessID RandomSeedVectorSize RandomSeedVectorValues 1 2 1421007875 1697917846 OtherProcessID RandomSeedVectorSize RandomSeedVectorValues No other processor exists. ParaDRAM - NOTE: randomSeed is a scalar 32bit integer that serves as the seed of the random number generator. When it ParaDRAM - NOTE: is provided, the seed of the random number generator will be set in a specific deterministic manner ParaDRAM - NOTE: to enable future replications of the simulation with the same configuration and input specifications. ParaDRAM - NOTE: The default value for randomSeed is an integer vector of processor-dependent size and value that will ParaDRAM - NOTE: vary from one simulation to another. However, enough care has been taken to assign unique random seed ParaDRAM - NOTE: values to the random number generator on each of the parallel threads (or images, processors, cores, ParaDRAM - NOTE: ...) at all circumstances. outputColumnWidth 0 ParaDRAM - NOTE: The variable outputColumnWidth is a non-negative integer number that determines the width of the data ParaDRAM - NOTE: columns in ParaDRAM formatted output files that have tabular structure. If it is set to zero, ParaDRAM ParaDRAM - NOTE: will ensure to set the width of each output element to the minimum possible width without losing the ParaDRAM - NOTE: requested output precision. In other words, setting outputColumnWidth = 0 will result in the ParaDRAM - NOTE: smallest-size for the formatted output files that are in ASCII format. The default value is 0. outputDelimiter , ParaDRAM - NOTE: outputDelimiter is a string variable, containing a sequence of one or more characters (excluding ParaDRAM - NOTE: digits, the period symbol '.', and the addition and subtraction operators: '+' and '-'), that is used ParaDRAM - NOTE: to specify the boundary between separate, independent information elements in the tabular output ParaDRAM - NOTE: files of ParaDRAM. The string value must be enclosed by either single or double quotation marks when ParaDRAM - NOTE: provided as input. To output in Comma-Separated-Values (CSV) format, set outputDelimiter = ','. If ParaDRAM - NOTE: the input value is not provided, the default delimiter ',' will be used when input outputColumnWidth ParaDRAM - NOTE: = 0, and a single space character, ',' will be used when input outputColumnWidth > 0. A value of '\t' ParaDRAM - NOTE: is interpreted as the TAB character. To avoid this interpretation, use '\\t' to yield '\t' without ParaDRAM - NOTE: being interpreted as the TAB character. The default value is ','. outputRealPrecision 8 ParaDRAM - NOTE: The variable outputRealPrecision is a 32-bit integer number that determines the precision - that is, ParaDRAM - NOTE: the number of significant digits - of the real numbers in the output files of ParaDRAM. Any positive ParaDRAM - NOTE: integer is acceptable as the input value of outputRealPrecision. However, any digits of the output ParaDRAM - NOTE: real numbers beyond the accuracy of 64-bit real numbers (approximately 16 digits of significance) ParaDRAM - NOTE: will be meaningless and random. Set this variable to 16 (or larger) if full reproducibility of the ParaDRAM - NOTE: simulation is needed in the future. But keep in mind that larger precisions will result in larger-size ParaDRAM - NOTE: output files. This variable is ignored for binary output (if any occurs during the simulation). The ParaDRAM - NOTE: default value is 8. chainFileFormat compact ParaDRAM - NOTE: chainFileFormat is a string variable that represents the format of the output chain file(s) of ParaDRAM ParaDRAM - NOTE: simulation. The string value must be enclosed by either single or double quotation marks when provided ParaDRAM - NOTE: as input. Three values are possible: ParaDRAM - NOTE: ParaDRAM - NOTE: chainFileFormat = 'compact' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the ASCII (text) file format which is human-readable but does not preserve the ParaDRAM - NOTE: full accuracy of the output values. It is also a significantly slower mode of chain file ParaDRAM - NOTE: generation, compared to the binary file format (see below). If the compact format is ParaDRAM - NOTE: specified, each of the repeating MCMC states will be condensed into a single entry (row) ParaDRAM - NOTE: in the output MCMC chain file. Each entry will be then assigned a sample-weight that is ParaDRAM - NOTE: equal to the number of repetitions of that state in the MCMC chain. Thus, each row in ParaDRAM - NOTE: the output chain file will represent a unique sample from the objective function. This ParaDRAM - NOTE: will lead to a significantly smaller ASCII chain file and faster output size compared to ParaDRAM - NOTE: the verbose chain file format (see below). ParaDRAM - NOTE: ParaDRAM - NOTE: chainFileFormat = 'verbose' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the ASCII (text) file format which is human-readable but does not preserve the ParaDRAM - NOTE: full accuracy of the output values. It is also a significantly slower mode of chain file ParaDRAM - NOTE: generation, compared to both compact and binary chain file formats (see above and below). ParaDRAM - NOTE: If the verbose format is specified, all MCMC states will have equal sample-weights of 1 ParaDRAM - NOTE: in the output chain file. The verbose format can lead to much larger chain file sizes ParaDRAM - NOTE: than the compact and binary file formats. This is especially true if the target objective ParaDRAM - NOTE: function has a very high-dimensional state space. ParaDRAM - NOTE: ParaDRAM - NOTE: chainFileFormat = 'binary' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the binary file format which is not human-readable, but preserves the exact values ParaDRAM - NOTE: in the output MCMC chain file. It is also often the fastest mode of chain file generation. ParaDRAM - NOTE: If the binary file format is chosen, the chain will be automatically output in the compact ParaDRAM - NOTE: format (but as binary) to ensure the production of the smallest-possible output chain ParaDRAM - NOTE: file. Binary chain files will have the .bin file extensions. Use the binary format if ParaDRAM - NOTE: you need full accuracy representation of the output values while having the smallest-size ParaDRAM - NOTE: output chain file in the shortest time possible. ParaDRAM - NOTE: ParaDRAM - NOTE: The default value is chainFileFormat = 'compact' as it provides a reasonable trade-off between speed ParaDRAM - NOTE: and output file size while generating human-readable chain file contents. Note that the input values ParaDRAM - NOTE: are case-insensitive. restartFileFormat ascii ParaDRAM - NOTE: restartFileFormat is a string variable that represents the format of the output restart file(s) which ParaDRAM - NOTE: are used to restart an interrupted ParaDRAM simulation. The string value must be enclosed by either ParaDRAM - NOTE: single or double quotation marks when provided as input. Two values are possible: ParaDRAM - NOTE: ParaDRAM - NOTE: restartFileFormat = 'binary' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the binary file format which is not human-readable, but preserves the exact values ParaDRAM - NOTE: of the specification variables required for the simulation restart. This full accuracy ParaDRAM - NOTE: representation is required to exactly reproduce an interrupted simulation. The binary ParaDRAM - NOTE: format is also normally the fastest mode of restart file generation. Binary restart files ParaDRAM - NOTE: will have the .bin file extensions. ParaDRAM - NOTE: ParaDRAM - NOTE: restartFileFormat = 'ASCII' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the ASCII (text) file format which is human-readable but does not preserve the ParaDRAM - NOTE: full accuracy of the specification variables required for the simulation restart. It is ParaDRAM - NOTE: also a significantly slower mode of restart file generation, compared to the binary ParaDRAM - NOTE: format. Therefore, its usage should be limited to situations where the user wants to ParaDRAM - NOTE: track the dynamics of simulation specifications throughout the simulation time. ASCII ParaDRAM - NOTE: restart file(s) will have the .txt file extensions. ParaDRAM - NOTE: ParaDRAM - NOTE: The default value is restartFileFormat = 'binary'. Note that the input values are case-insensitive. progressReportPeriod 1000 ParaDRAM - NOTE: Every progressReportPeriod calls to the objective function, the sampling progress will be reported ParaDRAM - NOTE: to the log file. Note that progressReportPeriod must be a positive integer. The default value is 1000. maxNumDomainCheckToWarn 1000 ParaDRAM - NOTE: maxNumDomainCheckToWarn is an integer number beyond which the user will be warned about the newly-proposed ParaDRAM - NOTE: points being excessively proposed outside the domain of the objective function. For every ParaDRAM - NOTE: maxNumDomainCheckToWarn consecutively-proposed new points that fall outside the domain of the objective ParaDRAM - NOTE: function, the user will be warned until maxNumDomainCheckToWarn = maxNumDomainCheckToStop, in which ParaDRAM - NOTE: case the sampler returns a fatal error and the program stops globally. The counter for this warning ParaDRAM - NOTE: message is reset after a proposal sample from within the domain of the objective function is obtained. ParaDRAM - NOTE: When out-of-domain sampling happens frequently, it is a strong indication of something fundamentally ParaDRAM - NOTE: wrong in the simulation. It is, therefore, important to closely inspect and monitor for such frequent ParaDRAM - NOTE: out-of-domain samplings. This can be done by setting maxNumDomainCheckToWarn to an appropriate value ParaDRAM - NOTE: determined by the user. The default value is 1000. maxNumDomainCheckToStop 10000 ParaDRAM - NOTE: maxNumDomainCheckToStop is an integer number beyond which the program will stop globally with a fatal ParaDRAM - NOTE: error message declaring that the maximum number of proposal-out-of-domain-bounds has reached. The ParaDRAM - NOTE: counter for this global-stop request is reset after a proposal point is accepted as a sample from ParaDRAM - NOTE: within the domain of the objective function. When out-of-domain sampling happens frequently, it is ParaDRAM - NOTE: a strong indication of something fundamentally wrong in the simulation. It is, therefore, important ParaDRAM - NOTE: to closely inspect and monitor for such frequent out-of-domain samplings. This can be done by setting ParaDRAM - NOTE: maxNumDomainCheckToStop to an appropriate value determined by the user. The default value is 10000. chainSize 30000 ParaDRAM - NOTE: chainSize determines the number of non-refined, potentially auto-correlated, but unique, samples ParaDRAM - NOTE: drawn by the MCMC sampler before stopping ParaDRAM. For example, if you specify chainSize = 10000, ParaDRAM - NOTE: then 10000 unique sample points (with no duplicates) will be drawn from the target objective function ParaDRAM - NOTE: that the user has provided. The input value for chainSize must be a positive integer of a minimum ParaDRAM - NOTE: value ndim+1 or larger, where ndim is the number of variables that define the domain of the objective ParaDRAM - NOTE: function to be sampled. The default value is 100000. randomStartPointDomainLowerLimitVec -.1797693134862316E+309 -.1797693134862316E+309 -.1797693134862316E+309 -.1797693134862316E+309 ParaDRAM - NOTE: RandomStartPointDomainLowerLimitVec represents the lower boundaries of the cubical domain from which ParaDRAM - NOTE: the starting point(s) of the MCMC chain(s) will be initialized randomly (only if requested via the ParaDRAM - NOTE: input variable randomStartPointRequested. This happens only when some or all of the elements of the ParaDRAM - NOTE: input variable StartPoint are missing. In such cases, every missing value of input StartPoint will ParaDRAM - NOTE: be set to the center point between RandomStartPointDomainLowerLimitVec and RandomStartPointDomainUpperLimit ParaDRAM - NOTE: in the corresponding dimension. If RandomStartPointRequested=TRUE (or True, true, t, all case-insensitive), ParaDRAM - NOTE: then the missing elements of StartPoint will be initialized to values drawn randomly from within the ParaDRAM - NOTE: corresponding ranges specified by the input variable RandomStartPointDomainLowerLimitVec. As an input ParaDRAM - NOTE: variable, RandomStartPointDomainLowerLimitVec is an ndim-dimensional vector of 64-bit real numbers, ParaDRAM - NOTE: where ndim is the number of variables of the objective function. It is also possible to assign only ParaDRAM - NOTE: select values of RandomStartPointDomainLowerLimitVec and leave the rest of the components to be ParaDRAM - NOTE: assigned the default value. This is POSSIBLE ONLY when RandomStartPointDomainLowerLimitVec is defined ParaDRAM - NOTE: inside the input file to ParaDRAM. For example, having the following inside the input file, ParaDRAM - NOTE: ParaDRAM - NOTE: RandomStartPointDomainLowerLimitVec(3:5) = -100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the lower limits of the third, fourth, and the fifth dimensions to -100, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: RandomStartPointDomainLowerLimitVec(1) = -100, RandomStartPointDomainLowerLimitVec(2) = -1.e6 ParaDRAM - NOTE: ParaDRAM - NOTE: will set the lower limit on the first dimension to -100, and 1.e6 on the second dimension, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: RandomStartPointDomainLowerLimitVec = 3*-2.5e100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the lower limits on the first, second, and the third dimensions to -2.5*10^100, ParaDRAM - NOTE: while the rest of the lower limits for the missing dimensions will be automatically set ParaDRAM - NOTE: to the default value. ParaDRAM - NOTE: ParaDRAM - NOTE: The default values for all elements of RandomStartPointDomainLowerLimitVec are taken from the ParaDRAM - NOTE: corresponding values in the input variable domainLowerLimitVec. randomStartPointDomainUpperLimitVec -.1797693134862316E+309 -.1797693134862316E+309 -.1797693134862316E+309 -.1797693134862316E+309 ParaDRAM - NOTE: randomStartPointDomainUpperLimitVec represents the upper boundaries of the cubical domain from which ParaDRAM - NOTE: the starting point(s) of the MCMC chain(s) will be initialized randomly (only if requested via the ParaDRAM - NOTE: input variable randomStartPointRequested. This happens only when some or all of the elements of the ParaDRAM - NOTE: input variable StartPoint are missing. In such cases, every missing value of input StartPoint will ParaDRAM - NOTE: be set to the center point between randomStartPointDomainUpperLimitVec and randomStartPointDomainLowerLimitVec ParaDRAM - NOTE: in the corresponding dimension. If RandomStartPointRequested=TRUE (or True, true, t, all case-insensitive), ParaDRAM - NOTE: then the missing elements of StartPoint will be initialized to values drawn randomly from within the ParaDRAM - NOTE: corresponding ranges specified by the input variable randomStartPointDomainUpperLimitVec. As an input ParaDRAM - NOTE: variable, randomStartPointDomainUpperLimitVec is an ndim-dimensional vector of 64-bit real numbers, ParaDRAM - NOTE: where ndim is the number of variables of the objective function. It is also possible to assign only ParaDRAM - NOTE: select values of randomStartPointDomainUpperLimitVec and leave the rest of the components to be ParaDRAM - NOTE: assigned the default value. This is POSSIBLE ONLY when randomStartPointDomainUpperLimitVec is defined ParaDRAM - NOTE: inside the input file to ParaDRAM. For example, having the following inside the input file, ParaDRAM - NOTE: ParaDRAM - NOTE: randomStartPointDomainUpperLimitVec(3:5) = -100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the upper limits of the third, fourth, and the fifth dimensions to -100, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: randomStartPointDomainUpperLimitVec(1) = -100, randomStartPointDomainUpperLimitVec(2) = -1.e6 ParaDRAM - NOTE: ParaDRAM - NOTE: will set the upper limit on the first dimension to -100, and 1.e6 on the second dimension, ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: randomStartPointDomainUpperLimitVec = 3*-2.5e100 ParaDRAM - NOTE: ParaDRAM - NOTE: will only set the upper limits on the first, second, and the third dimensions to -2.5*10^100, ParaDRAM - NOTE: while the rest of the upper limits for the missing dimensions will be automatically set ParaDRAM - NOTE: to the default value. ParaDRAM - NOTE: ParaDRAM - NOTE: The default values for all elements of randomStartPointDomainUpperLimitVec are taken from the ParaDRAM - NOTE: corresponding values in the input variable domainUpperLimitVec. startPointVec -.1797693134862316E+309 -.1797693134862316E+309 -.1797693134862316E+309 -.1797693134862316E+309 ParaDRAM - NOTE: startPointVec is a 64bit real-valued vector of length ndim (the dimension of the domain of the input ParaDRAM - NOTE: objective function). For every element of startPointVec that is not provided as input, the default ParaDRAM - NOTE: value will be the center of the domain of startPointVec as specified by domainLowerLimitVec and ParaDRAM - NOTE: domainUpperLimitVec input variables. If the input variable randomStartPointRequested=TRUE (or true ParaDRAM - NOTE: or t, all case-insensitive), then the missing elements of startPointVec will be initialized to values ParaDRAM - NOTE: drawn randomly from within the corresponding ranges specified by the input variables ParaDRAM - NOTE: randomStartPointDomainLowerLimitVec and randomStartPointDomainUpperLimitVec. randomStartPointRequested F ParaDRAM - NOTE: A logical (boolean) variable. If true (or .true. or TRUE or .t. from within an input file), then the ParaDRAM - NOTE: variable startPointVec will be initialized randomly for each MCMC chain that is to be generated by ParaDRAM - NOTE: ParaDRAM. The random values will be drawn from the specified or the default domain of startPointVec, ParaDRAM - NOTE: given by RandomStartPointDomain variable. Note that the value of startPointVec, if provided, has ParaDRAM - NOTE: precedence over random initialization. In other words, for every element of startPointVec that is ParaDRAM - NOTE: not provided as input only that element will initialized randomly if randomStartPointRequested=TRUE. ParaDRAM - NOTE: Also, note that even if startPointVec is randomly initialized, its random value will be deterministic ParaDRAM - NOTE: between different independent runs of ParaDRAM if the input variable randomSeed is provided by the ParaDRAM - NOTE: user. The default value is FALSE. sampleRefinementCount 1073741823 ParaDRAM - NOTE: When sampleSize < 0, the integer variable sampleRefinementCount dictates the maximum number of times ParaDRAM - NOTE: the MCMC chain will be refined to remove the autocorrelation within the output MCMC sample. For ParaDRAM - NOTE: example, ParaDRAM - NOTE: ParaDRAM - NOTE: if sampleRefinementCount = 0, ParaDRAM - NOTE: ParaDRAM - NOTE: no refinement of the output MCMC chain will be performed, the resulting MCMC sample will ParaDRAM - NOTE: simply correspond to the full MCMC chain in verbose format (i.e., each sampled state has ParaDRAM - NOTE: a weight of one). ParaDRAM - NOTE: ParaDRAM - NOTE: if sampleRefinementCount = 1, ParaDRAM - NOTE: ParaDRAM - NOTE: the refinement of the output MCMC chain will be done only once if needed, and no more, ParaDRAM - NOTE: even though there may still exist some residual autocorrelation in the output MCMC sample. ParaDRAM - NOTE: In practice, only one refinement of the final output MCMC Chain should be enough to remove ParaDRAM - NOTE: the existing autocorrelations in the final output sample. Exceptions occur when the ParaDRAM - NOTE: Integrated Autocorrelation (IAC) of the output MCMC chain is comparable to or larger than ParaDRAM - NOTE: the length of the chain. In such cases, neither the BatchMeans method nor any other method ParaDRAM - NOTE: of IAC computation will be able to accurately compute the IAC. Consequently, the samples ParaDRAM - NOTE: generated based on the computed IAC values will likely not be i.i.d. and will still be ParaDRAM - NOTE: significantly autocorrelated. In such scenarios, more than one refinement of the MCMC ParaDRAM - NOTE: chain will be necessary. Very small sample size resulting from multiple refinements of ParaDRAM - NOTE: the sample could be a strong indication of the bad mixing of the MCMC chain and the output ParaDRAM - NOTE: chain may not contain true i.i.d. samples from the target objective function. ParaDRAM - NOTE: ParaDRAM - NOTE: if sampleRefinementCount > 1, ParaDRAM - NOTE: ParaDRAM - NOTE: the refinement of the output MCMC chain will be done for a maximum sampleRefinementCount ParaDRAM - NOTE: number of times, even though there may still exist some residual autocorrelation in the ParaDRAM - NOTE: final output MCMC sample. ParaDRAM - NOTE: ParaDRAM - NOTE: if sampleRefinementCount >> 1 (e.g., comparable to or larger than the length of the MCMC chain), ParaDRAM - NOTE: ParaDRAM - NOTE: the refinement of the output MCMC chain will continue until the integrated autocorrelation ParaDRAM - NOTE: of the resulting final sample is less than 2, virtually implying that an independent ParaDRAM - NOTE: identically-distributed (i.i.d.) sample has finally been obtained. ParaDRAM - NOTE: ParaDRAM - NOTE: Note that to obtain i.i.d. samples from a multidimensional chain, ParaDRAM will, by default, use the ParaDRAM - NOTE: maximum of Integrated Autocorrelation (IAC) among all dimensions of the chain to refine the chain. ParaDRAM - NOTE: Note that the value specified for sampleRefinementCount is used only when the variable sampleSize < ParaDRAM - NOTE: 0, otherwise, it will be ignored. The default value is sampleRefinementCount = 1073741823. sampleRefinementMethod BatchMeans ParaDRAM - NOTE: sampleRefinementMethod is a string variable that represents the method of computing the Integrated ParaDRAM - NOTE: Autocorrelation Time (IAC) to be used in ParaDRAM for refining the final output MCMC chain and sample. ParaDRAM - NOTE: The string value must be enclosed by either single or double quotation marks when provided as input. ParaDRAM - NOTE: Options that are currently supported include: ParaDRAM - NOTE: ParaDRAM - NOTE: sampleRefinementMethod = 'BatchMeans' ParaDRAM - NOTE: ParaDRAM - NOTE: This method of computing the Integrated Autocorrelation Time is based on the approach ParaDRAM - NOTE: described in SCHMEISER, B., 1982, Batch size effects in the analysis of simulation output, ParaDRAM - NOTE: Oper. Res. 30 556-568. The batch sizes in the BatchMeans method are chosen to be int(N^(2/3)) ParaDRAM - NOTE: where N is the length of the MCMC chain. As long as the batch size is larger than the ParaDRAM - NOTE: IAC of the chain and there are significantly more than 10 batches, the BatchMeans method ParaDRAM - NOTE: will provide reliable estimates of the IAC. Note that the refinement strategy involves ParaDRAM - NOTE: two separate phases of sample decorrelation. At the first stage, the Markov chain is ParaDRAM - NOTE: decorrelated recursively (for as long as needed) based on the IAC of its compact format, ParaDRAM - NOTE: where only the the uniquely-visited states are kept in the (compact) chain. Once the ParaDRAM - NOTE: Markov chain is refined such that its compact format is fully decorrelated, the second ParaDRAM - NOTE: phase of the decorrelation begins during which the Markov chain is decorrelated based on ParaDRAM - NOTE: the IAC of the chain in its verbose (Markov) format. This process is repeated recursively ParaDRAM - NOTE: for as long as there is any residual autocorrelation in the refined sample. ParaDRAM - NOTE: ParaDRAM - NOTE: sampleRefinementMethod = 'BatchMeans-compact' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the same as the first case in the above, except that only the first phase of the ParaDRAM - NOTE: sample refinement described in the above will be performed, that is, the (verbose) Markov ParaDRAM - NOTE: chain is refined only based on the IAC computed from the compact format of the Markov ParaDRAM - NOTE: chain. This will lead to a larger final refined sample. However, the final sample will ParaDRAM - NOTE: likely not be fully decorrelated. ParaDRAM - NOTE: ParaDRAM - NOTE: sampleRefinementMethod = 'BatchMeans-verbose' ParaDRAM - NOTE: ParaDRAM - NOTE: This is the same as the first case in the above, except that only the second phase of ParaDRAM - NOTE: the sample refinement described in the above will be performed, that is, the (verbose) ParaDRAM - NOTE: Markov chain is refined only based on the IAC computed from the verbose format of the ParaDRAM - NOTE: Markov chain. While the resulting refined sample will be fully decorrelated, the size of ParaDRAM - NOTE: the refined sample may be smaller than the default choice in the first case in the above. ParaDRAM - NOTE: ParaDRAM - NOTE: Note that in order to obtain i.i.d. samples from a multidimensional chain, ParaDRAM will use the ParaDRAM - NOTE: average of IAC among all dimensions of the chain to refine the chain. If the maximum, minimum, or ParaDRAM - NOTE: the median of IACs is preferred add '-max' (or '-maximum'), '-min' (or '-minimum'), '-med' (or ParaDRAM - NOTE: '-median'), respectively, to the value of sampleRefinementMethod. For example, ParaDRAM - NOTE: ParaDRAM - NOTE: sampleRefinementMethod = 'BatchMeans-max' ParaDRAM - NOTE: ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: sampleRefinementMethod = 'BatchMeans-compact-max' ParaDRAM - NOTE: ParaDRAM - NOTE: or, ParaDRAM - NOTE: ParaDRAM - NOTE: sampleRefinementMethod = 'BatchMeans-max-compact' ParaDRAM - NOTE: ParaDRAM - NOTE: Also, note that the value specified for sampleRefinementCount is used only when the variable sampleSize ParaDRAM - NOTE: < 0, otherwise, it will be ignored. The default value is sampleRefinementMethod = 'BatchMeans'. Note ParaDRAM - NOTE: that the input values are case-insensitive and white-space characters are ignored. scaleFactor gelman ParaDRAM - NOTE: scaleFactor is a real-valued positive number (which must be given as string), by the square of which ParaDRAM - NOTE: the covariance matrix of the proposal distribution of the MCMC sampler is scaled. In other words, ParaDRAM - NOTE: the proposal distribution will be scaled in every direction by the value of scaleFactor. It can also ParaDRAM - NOTE: be given in units of the string keyword 'gelman' (which is case-INsensitive) after the paper: ParaDRAM - NOTE: ParaDRAM - NOTE: Gelman, Roberts, and Gilks (1996): 'Efficient Metropolis Jumping Rules'. ParaDRAM - NOTE: ParaDRAM - NOTE: The paper finds that the optimal scaling factor for a Multivariate Gaussian proposal distribution ParaDRAM - NOTE: for the Metropolis-Hastings Markov Chain Monte Carlo sampling of a target Multivariate Normal ParaDRAM - NOTE: Distribution of dimension ndim is given by: ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = 2.38/sqrt(ndim) , in the limit of ndim -> Infinity. ParaDRAM - NOTE: ParaDRAM - NOTE: Multiples of the gelman scale factors are also acceptable as input and can be specified like the ParaDRAM - NOTE: following examples: ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = '1' ParaDRAM - NOTE: ParaDRAM - NOTE: multiplies the ndim-dimensional proposal covariance matrix by 1, essentially no change ParaDRAM - NOTE: occurs to the covariance matrix. ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = "1" ParaDRAM - NOTE: ParaDRAM - NOTE: same as the previous example. The double-quotation marks act the same way as single-quotation ParaDRAM - NOTE: marks. ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = '2.5' ParaDRAM - NOTE: ParaDRAM - NOTE: multiplies the ndim-dimensional proposal covariance matrix by 2.5. ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = '2.5*Gelman' ParaDRAM - NOTE: ParaDRAM - NOTE: multiplies the ndim-dimensional proposal covariance matrix by 2.5 * 2.38/sqrt(ndim). ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = "2.5 * gelman" ParaDRAM - NOTE: ParaDRAM - NOTE: same as the previous example, but with double-quotation marks. space characters are ParaDRAM - NOTE: ignored. ParaDRAM - NOTE: ParaDRAM - NOTE: scaleFactor = "2.5 * gelman*gelman*2" ParaDRAM - NOTE: ParaDRAM - NOTE: equivalent to gelmanFactor-squared multiplied by 5. ParaDRAM - NOTE: ParaDRAM - NOTE: Note, however, that the result of Gelman et al. paper applies only to multivariate normal proposal ParaDRAM - NOTE: distributions, in the limit of infinite dimensions. Therefore, care must be taken when using Gelman's ParaDRAM - NOTE: scaling factor with non-Gaussian proposals and target objective functions. Note that only the product ParaDRAM - NOTE: symbol (*) can be parsed in the string value of scaleFactor. The presence of other mathematical ParaDRAM - NOTE: symbols or multiple appearances of the product symbol will lead to a simulation crash. Also, note ParaDRAM - NOTE: that the prescription of an acceptance range specified by the input variable 'targetAcceptanceRate' ParaDRAM - NOTE: will lead to dynamic modification of the initial input value of scaleFactor throughout sampling for ParaDRAM - NOTE: adaptiveUpdateCount times. The default scaleFactor string-value is 'gelman' (for all proposals), ParaDRAM - NOTE: which is subsequently converted to 2.38/sqrt(ndim). proposalModel normal ParaDRAM - NOTE: proposalModel is a string variable containing the name of the proposal distribution for the MCMC ParaDRAM - NOTE: sampler. The string value must be enclosed by either single or double quotation marks when provided ParaDRAM - NOTE: as input. One option is currently supported: ParaDRAM - NOTE: ParaDRAM - NOTE: proposalModel = 'normal' ParaDRAM - NOTE: ParaDRAM - NOTE: This is equivalent to the multivariate normal distribution, which is the most widely-used ParaDRAM - NOTE: proposal model along with MCMC samplers. ParaDRAM - NOTE: ParaDRAM - NOTE: proposalModel = 'uniform' ParaDRAM - NOTE: ParaDRAM - NOTE: The proposals will be drawn uniformly from within a ndim-dimensional ellipsoid whose ParaDRAM - NOTE: covariance matrix and scale are initialized by the user and optionally adaptively updated ParaDRAM - NOTE: throughout the simulation. ParaDRAM - NOTE: ParaDRAM - NOTE: The default value is 'normal'. proposalStartStdVec 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 ParaDRAM - NOTE: proposalStartStdVec is a real-valued positive vector of length ndim, where ndim is the dimension of ParaDRAM - NOTE: the sampling space. It serves as the best-guess starting Standard Deviation of each of the components ParaDRAM - NOTE: of the proposal distribution. If the initial covariance matrix (ProposalStartCovMat) is missing as ParaDRAM - NOTE: an input variable to ParaDRAM, then proposalStartStdVec (along with the input variable ProposalStartCorMat) ParaDRAM - NOTE: will be used to construct the initial covariance matrix of the proposal distribution of the MCMC ParaDRAM - NOTE: sampler. However, if ProposalStartCovMat is present as an input argument to ParaDRAM, then the input ParaDRAM - NOTE: proposalStartStdVec along with the input ProposalStartCorMat will be completely ignored and the input ParaDRAM - NOTE: value for ProposalStartCovMat will be used to construct the initial covariance matrix of the proposal ParaDRAM - NOTE: distribution of ParaDRAM. The default value of proposalStartStdVec is a vector of unit values (i.e., ParaDRAM - NOTE: ones) of length ndim. proposalStartCorMat 1.000000000000000 .000000000000000 .000000000000000 .000000000000000 .000000000000000 1.000000000000000 .000000000000000 .000000000000000 .000000000000000 .000000000000000 1.000000000000000 .000000000000000 .000000000000000 .000000000000000 .000000000000000 1.000000000000000 ParaDRAM - NOTE: proposalStartCorMat is a real-valued positive-definite matrix of size (ndim,ndim), where ndim is the ParaDRAM - NOTE: dimension of the sampling space. It serves as the best-guess starting correlation matrix of the ParaDRAM - NOTE: proposal distribution used by ParaDRAM. It is used (along with the input vector ProposalStartStdVec) ParaDRAM - NOTE: to construct the covariance matrix of the proposal distribution when the input covariance matrix is ParaDRAM - NOTE: missing in the input list of variables. If the covariance matrix is given as input to ParaDRAM, any ParaDRAM - NOTE: input values for proposalStartCorMat, as well as ProposalStartStdVec, will be automatically ignored ParaDRAM - NOTE: by ParaDRAM. As input to ParaDRAM, the variable proposalStartCorMat along with ProposalStartStdVec ParaDRAM - NOTE: is especially useful in situations where obtaining the best-guess covariance matrix is not trivial. ParaDRAM - NOTE: The default value of proposalStartCorMat is an ndim-by-ndim Identity matrix. proposalStartCovMat 1.000000000000000 .000000000000000 .000000000000000 .000000000000000 .000000000000000 1.000000000000000 .000000000000000 .000000000000000 .000000000000000 .000000000000000 1.000000000000000 .000000000000000 .000000000000000 .000000000000000 .000000000000000 1.000000000000000 ParaDRAM - NOTE: proposalStartCovMat is a real-valued positive-definite matrix of size (ndim,ndim), where ndim is the ParaDRAM - NOTE: dimension of the sampling space. It serves as the best-guess starting covariance matrix of the proposal ParaDRAM - NOTE: distribution. To bring the sampling efficiency of ParaDRAM to within the desired requested range, ParaDRAM - NOTE: the covariance matrix will be adaptively updated throughout the simulation, according to the user's ParaDRAM - NOTE: requested schedule. If proposalStartCovMat is not provided by the user or it is completely missing ParaDRAM - NOTE: from the input file, its value will be automatically computed via the input variables proposalStartCorMat ParaDRAM - NOTE: and proposalStartStdVec (or via their default values, if not provided). The default value of ParaDRAM - NOTE: proposalStartCovMat is an ndim-by-ndim Identity matrix. adaptiveUpdatePeriod 16 ParaDRAM - NOTE: Every adaptiveUpdatePeriod calls to the objective function, the parameters of the proposal distribution ParaDRAM - NOTE: will be updated. The variable adaptiveUpdatePeriod must be a positive integer (>0). The smaller the ParaDRAM - NOTE: value of adaptiveUpdatePeriod, the easier it will be for the ParaDRAM kernel to adapt the proposal ParaDRAM - NOTE: distribution to the covariance structure of the objective function. However, this will happen at the ParaDRAM - NOTE: expense of slower simulation runtime as the adaptation process can become computationally expensive, ParaDRAM - NOTE: in particular, for very high dimensional objective functions (ndim>>1). The larger the value of ParaDRAM - NOTE: adaptiveUpdatePeriod, the easier it will be for the ParaDRAM kernel to keep the sampling efficiency ParaDRAM - NOTE: close to the requested target acceptance rate range (if specified via the input variable ParaDRAM - NOTE: targetAcceptanceRate). However, too large values for adaptiveUpdatePeriod will only delay the adaptation ParaDRAM - NOTE: of the proposal distribution to the global structure of the objective function that is being sampled. ParaDRAM - NOTE: If adaptiveUpdatePeriod>=chainSize, then no adaptive updates to the proposal distribution will be ParaDRAM - NOTE: made. The default value is 4 * ndim, where ndim is the dimension of the domain of the objective ParaDRAM - NOTE: function to be sampled. In this particular ParaDRAM simulation, this corresponds to the value 16. adaptiveUpdateCount 1073741823 ParaDRAM - NOTE: adaptiveUpdateCount represents the total number of adaptive updates that will be made to the parameters ParaDRAM - NOTE: of the proposal distribution to increase the efficiency of the sampler thus increasing the overall ParaDRAM - NOTE: sampling efficiency of ParaDRAM. Every adaptiveUpdatePeriod number of calls to the objective function, ParaDRAM - NOTE: the parameters of the proposal distribution will be updated until either the total number of adaptive ParaDRAM - NOTE: updates reaches the value of adaptiveUpdateCount. This variable must be a non-negative integer. As ParaDRAM - NOTE: a rule of thumb, it may be appropriate to set the input variable chainSize > 2 * adaptiveUpdatePeriod ParaDRAM - NOTE: * adaptiveUpdateCount, to ensure ergodicity and stationarity of the MCMC sampler. If adaptiveUpdateCount=0, ParaDRAM - NOTE: then the proposal distribution parameters will be fixed to the initial input values throughout the ParaDRAM - NOTE: entire MCMC sampling. The default value is 1073741823. greedyAdaptationCount 0 ParaDRAM - NOTE: If greedyAdaptationCount is set to a positive integer then the first greedyAdaptationCount number of ParaDRAM - NOTE: the adaptive updates of the sampler will be made using only the 'unique' accepted points in the MCMC ParaDRAM - NOTE: chain. This is useful, for example, when the function to be sampled by ParaDRAM is high dimensional, ParaDRAM - NOTE: in which case, the adaptive updates to ParaDRAM's sampler distribution will less likely lead to ParaDRAM - NOTE: numerical instabilities, for example, a singular covariance matrix for the multivariate proposal ParaDRAM - NOTE: sampler. The variable greedyAdaptationCount must be a non-negative integer, and not larger than the ParaDRAM - NOTE: value of adaptiveUpdateCount. If it is larger, it will be automatically set to adaptiveUpdateCount ParaDRAM - NOTE: for the simulation. The default value is 0. burninAdaptationMeasure 1.000000000000000 ParaDRAM - NOTE: burninAdaptationMeasure is a 64-bit real number between 0 and 1, representing the adaptation measure ParaDRAM - NOTE: threshold below which the simulated Markov chain will be used to generate the output ParaDRAM sample. ParaDRAM - NOTE: In other words, any point in the output Markov Chain that has been sampled during significant adaptation ParaDRAM - NOTE: of the proposal distribution (as determined by burninAdaptationMeasure) will not be included in the ParaDRAM - NOTE: construction of the final ParaDRAM output sample. This is to ensure that the generation of the output ParaDRAM - NOTE: sample will be based on the part of the simulated chain that is practically guaranteed to be Markovian ParaDRAM - NOTE: and ergodic. If this variable is set to 0, then the output sample will be generated from the part of ParaDRAM - NOTE: the chain where no proposal adaptation has occurred. This non-adaptive or minimally-adaptive part of ParaDRAM - NOTE: the chain may not even exist if the total adaptation period of the simulation (as determined by ParaDRAM - NOTE: adaptiveUpdateCount and adaptiveUpdatePeriod input variables) is longer than the total length of the ParaDRAM - NOTE: output MCMC chain. In such cases, the resulting output sample may have a zero size. In general, when ParaDRAM - NOTE: good mixing occurs (e.g., when the input variable chainSize is very large) any specific value of ParaDRAM - NOTE: burninAdaptationMeasure becomes practically irrelevant. The default value for burninAdaptationMeasure ParaDRAM - NOTE: is 1.00000000000000, implying that the entire chain (with the exclusion of an initial automatically-determined ParaDRAM - NOTE: burnin period) will be used to generate the final output sample. delayedRejectionCount 0 ParaDRAM - NOTE: 0 <= delayedRejectionCount <= 1000 is an integer that represents the total number of stages for which ParaDRAM - NOTE: rejections of new proposals will be tolerated by ParaDRAM before going back to the previously accepted ParaDRAM - NOTE: point (state). Possible values are: ParaDRAM - NOTE: ParaDRAM - NOTE: delayedRejectionCount = 0 ParaDRAM - NOTE: ParaDRAM - NOTE: indicating no deployment of the delayed rejection algorithm. ParaDRAM - NOTE: ParaDRAM - NOTE: delayedRejectionCount > 0 ParaDRAM - NOTE: ParaDRAM - NOTE: which implies a maximum delayedRejectionCount number of rejections will be tolerated. ParaDRAM - NOTE: ParaDRAM - NOTE: For example, delayedRejectionCount = 1, means that at any point during the sampling, if a proposal ParaDRAM - NOTE: is rejected, ParaDRAM will not go back to the last sampled state. Instead, it will continue to propose ParaDRAM - NOTE: a new state from the last rejected proposal. If the new state is again rejected based on the rules ParaDRAM - NOTE: of ParaDRAM, then the algorithm will not tolerate further rejections, because the maximum number of ParaDRAM - NOTE: rejections to be tolerated has been set by the user to be delayedRejectionCount = 1. The algorithm ParaDRAM - NOTE: then goes back to the original last-accepted state and will begin proposing new states from that ParaDRAM - NOTE: location. The default value is delayedRejectionCount = 0. delayedRejectionScaleFactorVec UNDEFINED ParaDRAM - NOTE: delayedRejectionScaleFactorVec is a real-valued positive vector of length (1:delayedRejectionCount) ParaDRAM - NOTE: by which the covariance matrix of the proposal distribution of ParaDRAM sampler is scaled when the ParaDRAM - NOTE: Delayed Rejection (DR) scheme is activated (by setting delayedRejectionCount>0). At each ith stage ParaDRAM - NOTE: of the DR process, the proposal distribution from the last stage is scaled by the factor ParaDRAM - NOTE: delayedRejectionScaleFactorVec(i). Missing elements of the delayedRejectionScaleFactorVec in the ParaDRAM - NOTE: input to ParaDRAM will be set to the default value. The default value at all stages is 0.5^(1/ndim) ParaDRAM - NOTE: = 0.840896415253715, which reduces the volume of the covariance matrix of the proposal from the last ParaDRAM - NOTE: DR stage by one half. The variable ndim represents the number of dimensions of the Domain of the ParaDRAM - NOTE: objective function. ************************************************************************************************************************************ **** **** **** Starting the ParaDRAM sampling - 2021/01/08 - 01:17:31 **** **** **** ************************************************************************************************************************************ ************************************************************************************************************************************ **** **** **** Exiting the ParaDRAM sampling - 2021/01/08 - 01:17:33 **** **** **** ************************************************************************************************************************************ stats.numFuncCall.accepted 30000 ParaDRAM - NOTE: This is the total number of accepted function calls (unique samples). stats.numFuncCall.acceptedRejected 101916 ParaDRAM - NOTE: This is the total number of accepted or rejected function calls. stats.numFuncCall.acceptedRejectedDelayed 101916 ParaDRAM - NOTE: This is the total number of accepted or rejected or delayed-rejection (if any requested) function ParaDRAM - NOTE: calls. stats.numFuncCall.acceptedRejectedDelayedUnused 101916 ParaDRAM - NOTE: This is the total number of accepted or rejected or unused function calls (by all processes, including ParaDRAM - NOTE: delayed rejections, if any requested). stats.chain.verbose.efficiency.meanAcceptanceRate .2947811553851852 ParaDRAM - NOTE: This is the average MCMC acceptance rate. stats.chain.verbose.efficiency.acceptedOverAcceptedRejected .2943600612268927 ParaDRAM - NOTE: This is the MCMC sampling efficiency given the accepted and rejected function calls, that is, the ParaDRAM - NOTE: number of accepted function calls divided by the number of (accepted + rejected) function calls. stats.chain.verbose.efficiency.acceptedOverAcceptedRejectedDelayed .2943600612268927 ParaDRAM - NOTE: This is the MCMC sampling efficiency given the accepted, rejected, and delayed-rejection (if any ParaDRAM - NOTE: requested) function calls, that is, the number of accepted function calls divided by the number of ParaDRAM - NOTE: (accepted + rejected + delayed-rejection) function calls. stats.chain.verbose.efficiency.acceptedOverAcceptedRejectedDelayedUnused .2943600612268927 ParaDRAM - NOTE: This is the MCMC sampling efficiency given the accepted, rejected, delayed-rejection (if any requested), ParaDRAM - NOTE: and unused function calls, that is, the number of accepted function calls divided by the number of ParaDRAM - NOTE: (accepted + rejected + delayed-rejection + unused) function calls. stats.time.total 1.848000049591064 ParaDRAM - NOTE: This is the total runtime in seconds. stats.time.perFuncCallAccepted .6160000165303548E-04 ParaDRAM - NOTE: This is the average effective time cost of each accepted function call, in seconds. stats.time.perFuncCallAcceptedRejected .1813258025816422E-04 ParaDRAM - NOTE: This is the average effective time cost of each accepted or rejected function call, in seconds. stats.time.perFuncCallAcceptedRejectedDelayed .1813258025816422E-04 ParaDRAM - NOTE: This is the average effective time cost of each accepted or rejected function call (including ParaDRAM - NOTE: delayed-rejections, if any requested), in seconds. stats.time.perFuncCallAcceptedRejectedDelayedUnused .1813258025816422E-04 ParaDRAM - NOTE: This is the average effective time cost of each accepted or rejected or unused function call (including ParaDRAM - NOTE: delayed-rejections, if any requested), in seconds. stats.time.perInterProcessCommunication UNDEFINED ParaDRAM - NOTE: This is the average time cost of inter-process communications per used (accepted or rejected or ParaDRAM - NOTE: delayed-rejection) function call, in seconds. stats.time.perFuncCall .1036144368731530E-04 ParaDRAM - NOTE: This is the average pure time cost of each function call, in seconds. stats.parallelism.current.numProcess 1 ParaDRAM - NOTE: This is the number of processes (images) used in this simulation. stats.parallelism.processContribution 30000 ParaDRAM - NOTE: These are contributions of individual processes to the construction of the MCMC chain. Essentially, ParaDRAM - NOTE: they represent the total number of accepted states by the corresponding processor, starting from the ParaDRAM - NOTE: first processor to the last. This information is mostly informative in parallel Fork-Join (singleChain) ParaDRAM - NOTE: simulations. stats.parallelism.processContribution.geometricFit.successProbNormFac UNDEFINED ParaDRAM - NOTE: These are the parameters of the Geometric fit to the distribution of the processor contributions to ParaDRAM - NOTE: the construction of the MCMC chain (the processor contributions are reported in the first column of ParaDRAM - NOTE: the output chain file. The fit has the following form: ParaDRAM - NOTE: ParaDRAM - NOTE: ProcessConstribution(i) = successProbNormFac(1) * successProbNormFac(2) * (1-successProbNormFac(1))^(i-1) ParaDRAM - NOTE: / (1 - (1 - successProbNormFac(1))^numProcess) ParaDRAM - NOTE: ParaDRAM - NOTE: where i is the ID of the processor (starting from index 1), numProcess is the total number of processes ParaDRAM - NOTE: used in the simulation, and successProbNormFac(1) is equivalent to an effective MCMC sampling efficiency ParaDRAM - NOTE: computed from contributions of individual processes to the MCMC chain and successProbNormFac(2) is ParaDRAM - NOTE: a normalization constant. stats.parallelism.current.speedup 1.000000000000000 ParaDRAM - NOTE: This is the estimated maximum speedup gained via singleChain parallelization model compared to serial ParaDRAM - NOTE: mode. stats.parallelism.optimal.current.numProcess UNDEFINED ParaDRAM - NOTE: This is the predicted optimal number of physical computing processes for singleChain parallelization ParaDRAM - NOTE: model, given the current MCMC sampling efficiency. stats.parallelism.optimal.current.speedup UNDEFINED ParaDRAM - NOTE: This is the predicted optimal maximum speedup gained via singleChain parallelization model, given ParaDRAM - NOTE: the current MCMC sampling efficiency.This is the predicted optimal number of physical computing ParaDRAM - NOTE: processes for singleChain parallelization model, given the current MCMC sampling efficiency. stats.parallelism.optimal.current.scaling.strong.speedup UNDEFINED ParaDRAM - NOTE: This is the predicted strong-scaling speedup behavior of the singleChain parallelization model, given ParaDRAM - NOTE: the current MCMC sampling efficiency, for increasing numbers of processes, starting from a single ParaDRAM - NOTE: process. stats.parallelism.optimal.absolute.numProcess UNDEFINED ParaDRAM - NOTE: This is the predicted absolute optimal number of physical computing processes for singleChain ParaDRAM - NOTE: parallelization model, under any MCMC sampling efficiency. stats.parallelism.optimal.absolute.speedup UNDEFINED ParaDRAM - NOTE: This is the predicted absolute optimal maximum speedup gained via singleChain parallelization model, ParaDRAM - NOTE: under any MCMC sampling efficiency. This simulation will likely NOT benefit from any additional ParaDRAM - NOTE: computing processors beyond the predicted absolute optimal number, 1, in the above. This is true for ParaDRAM - NOTE: any value of MCMC sampling efficiency. Keep in mind that the predicted absolute optimal number of ParaDRAM - NOTE: processors is just an estimate whose accuracy depends on many runtime factors, including the topology ParaDRAM - NOTE: of the communication network being used, the number of processors per node, and the number of tasks ParaDRAM - NOTE: to each processor or node. stats.parallelism.optimal.absolute.scaling.strong.speedup UNDEFINED ParaDRAM - NOTE: This is the predicted absolute strong-scaling speedup behavior of the singleChain parallelization ParaDRAM - NOTE: model, under any MCMC sampling efficiency, for increasing numbers of processes, starting from a single ParaDRAM - NOTE: process. stats.chain.compact.burnin.location.likelihoodBased 25 ParaDRAM - NOTE: This is the burnin location in the compact chain, based on the occurrence likelihood. stats.chain.compact.burnin.location.adaptationBased 1 ParaDRAM - NOTE: This is the burnin location in the compact chain, based on the value of burninAdaptationMeasure ParaDRAM - NOTE: simulation specification. stats.chain.verbose.burnin.location.likelihoodBased 189 ParaDRAM - NOTE: This is the burnin location in the verbose (Markov) chain, based on the occurrence likelihood. stats.chain.verbose.burnin.location.adaptationBased 1 ParaDRAM - NOTE: This is the burnin location in the verbose (Markov) chain, based on the value of burninAdaptationMeasure ParaDRAM - NOTE: simulation specification. stats.chain.verbose.logFunc.max -2.580565408927936 ParaDRAM - NOTE: This is the maximum logFunc value (the maximum of the user-specified objective function). stats.chain.compact.logFunc.max.location 1385 ParaDRAM - NOTE: This is the location of the first occurrence of the maximum logFunc in the compact chain. stats.chain.verbose.logFunc.max.location 7765 ParaDRAM - NOTE: This is the location of the first occurrence of the maximum logFunc in the verbose (Markov) chain. stats.chain.verbose.logFunc.max.state SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 -0.99827939E+001 0.15045671E+002 0.20149802E+002 0.11925233E+000 ParaDRAM - NOTE: This is the coordinates, within the domain of the user-specified objective function, where the maximum ParaDRAM - NOTE: logFunc occurs. ************************************************************************************************************************************ **** **** **** The statistical properties of the Markov chain **** **** **** ************************************************************************************************************************************ stats.chain.verbose.length.burninExcluded 101728 ParaDRAM - NOTE: This is the length of the verbose (Markov) Chain excluding burnin. stats.chain.verbose.avgStd variableName Mean Standard Deviation SampleVariable1 -0.10010854E+002 0.10034321E+001 SampleVariable2 0.14994500E+002 0.99855267E+000 SampleVariable3 0.20002189E+002 0.10071184E+001 SampleVariable4 -0.35036258E-002 0.10065693E+001 ParaDRAM - NOTE: This is the mean and standard deviation of the verbose (Markov) chain variables. stats.chain.verbose.covmat SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 SampleVariable1 0.10068759E+001 0.45972795E+000 -0.29972107E+000 -0.31336684E-002 SampleVariable2 0.45972795E+000 0.99710744E+000 0.29127800E+000 -0.19728929E+000 SampleVariable3 -0.29972107E+000 0.29127800E+000 0.10142875E+001 0.62179484E+000 SampleVariable4 -0.31336684E-002 -0.19728929E+000 0.62179484E+000 0.10131817E+001 ParaDRAM - NOTE: This is the covariance matrix of the verbose (Markov) chain. stats.chain.verbose.cormat SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 SampleVariable1 0.10000000E+001 0.45881958E+000 -0.29658471E+000 -0.31025686E-002 SampleVariable2 0.45881958E+000 0.10000000E+001 0.28963842E+000 -0.19628579E+000 SampleVariable3 -0.29658471E+000 0.28963842E+000 0.10000000E+001 0.61337052E+000 SampleVariable4 -0.31025686E-002 -0.19628579E+000 0.61337052E+000 0.10000000E+001 ParaDRAM - NOTE: This is the correlation matrix of the verbose (Markov) chain. stats.chain.verbose.quantile Quantile SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 Q0 -0.14056097E+002 0.10961355E+002 0.16184642E+002 -0.41501984E+001 Q5 -0.11654115E+002 0.13344897E+002 0.18345707E+002 -0.16704988E+001 Q10 -0.11292723E+002 0.13719612E+002 0.18695664E+002 -0.13038679E+001 Q25 -0.10697403E+002 0.14315088E+002 0.19323026E+002 -0.66998773E+000 Q50 -0.10020048E+002 0.14999895E+002 0.20005545E+002 0.10415275E-002 Q75 -0.93378186E+001 0.15676014E+002 0.20671093E+002 0.67093764E+000 Q90 -0.87162798E+001 0.16259453E+002 0.21297418E+002 0.12950173E+001 Q95 -0.83483504E+001 0.16625782E+002 0.21653550E+002 0.16427705E+001 Q100 -0.57026443E+001 0.19753492E+002 0.24118269E+002 0.38578196E+001 ParaDRAM - NOTE: This is the quantiles table of the variables of the verbose (Markov) chain. stats.chain.refined.iac RefinementStage SampleSize IAC_SampleLogFunc IAC_SampleVariable1 IAC_SampleVariable2 IAC_SampleVariable3 IAC_SampleVariable4 0 101916 0.42520544E+001 0.47080992E+001 0.25659400E+001 0.32811403E+001 0.41125184E+001 1 26884 0.28925776E+001 0.37166557E+001 0.24447023E+001 0.28581786E+001 0.31490495E+001 2 8924 0.13679641E+001 0.21937744E+001 0.11944795E+001 0.13312027E+001 0.12226444E+001 ParaDRAM - NOTE: This is the table of the Integrated Autocorrelation (IAC) of individual variables in the verbose ParaDRAM - NOTE: (Markov) chain, at increasing stages of chain refinements. stats.chain.refined.ess 8924 ParaDRAM - NOTE: This is the estimated Effective (decorrelated) Sample Size (ESS) of the final refined chain. stats.chain.refined.efficiency.essOverAccepted .2974666666666667 ParaDRAM - NOTE: This is the effective MCMC sampling efficiency given the accepted function calls, that is, the final ParaDRAM - NOTE: refined effective sample size (ESS) divided by the number of accepted function calls. stats.chain.refined.efficiency.essOverAcceptedRejected .8756230621295970E-01 ParaDRAM - NOTE: This is the effective MCMC sampling efficiency given the accepted and rejected function calls, that ParaDRAM - NOTE: is, the final refined effective sample size (ESS) divided by the number of (accepted + rejected) ParaDRAM - NOTE: function calls. stats.chain.refined.efficiency.essOverAcceptedRejectedDelayed .8756230621295970E-01 ParaDRAM - NOTE: This is the effective MCMC sampling efficiency given the accepted, rejected, and delayed-rejection ParaDRAM - NOTE: (if any requested) function calls, that is, the final refined effective sample size (ESS) divided by ParaDRAM - NOTE: the number of (accepted + rejected + delayed-rejection) function calls. stats.chain.refined.efficiency.essOverAcceptedRejectedDelayedUnused .8756230621295970E-01 ParaDRAM - NOTE: This is the effective MCMC sampling efficiency given the accepted, rejected, delayed-rejection (if ParaDRAM - NOTE: any requested), and unused function calls, that is, the final refined effective sample size (ESS) ParaDRAM - NOTE: divided by the number of (accepted + rejected + delayed-rejection + unused) function calls. ParaDRAM - NOTE: Generating the output sample file: ParaDRAM - NOTE: .\out\mvn_serial_process_1_sample.txt ************************************************************************************************************************************ **** **** **** The statistical properties of the final refined sample **** **** **** ************************************************************************************************************************************ stats.chain.refined.length 8924 ParaDRAM - NOTE: This is the final output refined sample size. stats.chain.refined.avgStd variableName Mean Standard Deviation SampleVariable1 -0.10013841E+002 0.99949866E+000 SampleVariable2 0.14988699E+002 0.10076150E+001 SampleVariable3 0.19994788E+002 0.10016795E+001 SampleVariable4 -0.69434037E-002 0.10061002E+001 ParaDRAM - NOTE: This is the Mean and standard deviation table of the final output refined sample. stats.chain.refined.covmat SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 SampleVariable1 0.99899756E+000 0.46478705E+000 -0.28859420E+000 -0.25609472E-002 SampleVariable2 0.46478705E+000 0.10152880E+001 0.29741583E+000 -0.20325495E+000 SampleVariable3 -0.28859420E+000 0.29741583E+000 0.10033618E+001 0.61459823E+000 SampleVariable4 -0.25609472E-002 -0.20325495E+000 0.61459823E+000 0.10122376E+001 ParaDRAM - NOTE: This is the covariance matrix of the final output refined sample. stats.chain.refined.cormat SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 SampleVariable1 0.10000000E+001 0.46150581E+000 -0.28825484E+000 -0.25466965E-002 SampleVariable2 0.46150581E+000 0.10000000E+001 0.29467323E+000 -0.20049580E+000 SampleVariable3 -0.28825484E+000 0.29467323E+000 0.10000000E+001 0.60984758E+000 SampleVariable4 -0.25466965E-002 -0.20049580E+000 0.60984758E+000 0.10000000E+001 ParaDRAM - NOTE: This is the correlation matrix of the final output refined sample. stats.chain.refined.quantile Quantile SampleVariable1 SampleVariable2 SampleVariable3 SampleVariable4 Q0 -0.13558018E+002 0.10992699E+002 0.16534873E+002 -0.41501984E+001 Q5 -0.11649990E+002 0.13318408E+002 0.18326434E+002 -0.16667877E+001 Q10 -0.11288734E+002 0.13696897E+002 0.18694033E+002 -0.13131435E+001 Q25 -0.10703673E+002 0.14300506E+002 0.19330867E+002 -0.67518996E+000 Q50 -0.10035943E+002 0.14987778E+002 0.20001356E+002 -0.94853874E-002 Q75 -0.93384733E+001 0.15684804E+002 0.20655911E+002 0.66457993E+000 Q90 -0.87273095E+001 0.16272959E+002 0.21291152E+002 0.12975707E+001 Q95 -0.83683730E+001 0.16641198E+002 0.21643570E+002 0.16226315E+001 Q100 -0.62213057E+001 0.18829987E+002 0.23608027E+002 0.35109434E+001 ParaDRAM - NOTE: This is the quantiles table of the variables of the final output refined sample. ParaDRAM - NOTE: Mission Accomplished.