{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "hummingage -- a fast and transparent Bayesian Age Depth Model\n",
    "=================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Age-depth models are used in paleoclimate analyses in the field of reconstructing past climate environments. Vertical sediment profiles (cores) contain information about past environmental conditions at every depth. However, the relation between the depth in a sediment core and the corresponding age of the material is not given at any depth, because of the limited sampling rate (e.g. every 20 cm). To draw age conclusions also from depths inbetween sampling points a way of interpolating the samples is needed, hence the need for age-depth models. Additionally, and similar important (maybe even more) is a good estimation of the errors of the interpolated age-depth relation.\n",
    "\n",
    "Similar to other methods we apply restrictions to our model, e.g. that age must increase monotonically with depth (e.g. Blaauw and Christen 2005). Further we adopt the idea of an underlying physical accumulation process of the sediment according to a sedimenatation rate (Blaauw and Christen, 2011). The evolution or change of the sedimentation rate over time is responsible for the shape of the age-depth curve.\n",
    "\n",
    "If there are some good age-depth model on the market, the question arises, why do we need another one. The answer is twofold. (i) our aim is to provide a simple age-depth model, where the user can really get into the source code and adjust it to his/her needs. We don't want a black-box, where the user cannot interact with, unless being a programming and statistics expert. This includes a clear, simple and transparent error estimation, which is crucial. (ii) we apply a new Bayesian step (borrowed from astro-physics), not used yet in this way in age-depth modelling, which finally gives a very attractive answer to the essential question of finding the best fitting curve for the data given the physical basis and restrictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Input data\n",
    "--------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As input data for our method we require a strict text format:\n",
    "\n",
    "\"labID\",\"age\",\"error\",\"depth\"<br>\n",
    "1,2.385,1.231,3<br>\n",
    "2,9.960,1.346,43<br>\n",
    "3,13.258,1.158,67<br>\n",
    "4,15.391,1.140,93<br>\n",
    "5,16.857,1.158,149<br>\n",
    "6,20.172,1.254,203<br>\n",
    "7,18.314,1.236,249<br>\n",
    "8,19.498,1.369,313<br>\n",
    "9,22.724,1.292,491<br>\n",
    "10,25.007,1.379,515<br>\n",
    "11,26.612,1.524,662<br>\n",
    "12,27.054,2.436,740<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first line must contain the names (exactly as seen in the above example) of the columns, whereas \"labID\" is simply a running number, \"age\" is the age of the data (in ka), the \"error\" is interpreted as a standard deviation and finally we have the depth (in cm). The units must not be ka and cm, however the plots are expecting these units. If you have other units, just change the labels of the plot axes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The source code of the pure R script and the here shown R code (in Jupyter Notebook) is synchronized. However, the only difference is that we use the script as a function in pure R and as a script here in the Jupyter Notebook. Thus the pure R scripts start like below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "hummingage <- function(path,infile,segments,DiscardOutliers,EstimateNullRate,token,plot_format) {\n",
    "    ##                                                                                                                                          \n",
    "    ## usage:                                                                                                                                   \n",
    "    ## hummingage(\"/home/user/data/\",\"myfile.csv\",c(NaN),TRUE,\"estimate\",\"KJmpmGgQ\",\"png,pdf\")                                                  \n",
    "    ## hummingage(\"/home/user/data/\",\"myfile.csv\",c(124),FALSE,\"estimate\",\"KJmpmGgQ\",\"png\")                                                     \n",
    "    ## hummingage(\"/home/user/data/\",\"myfile.csv\",c(334,856,1223),TRUE,\"estimate\",\"KJmpmGgQ\",\"pdf\")                                             \n",
    "    ## segments in cm                                                                                                                           \n",
    "\n",
    "    ## path: (string): is the path to the infile                                                                                                \n",
    "    ## infile: (string): is the data file according to a certain format                                                                         \n",
    "    ## segments: (integer array): is an array indicating roughly the positions of the segments, use c(NaN) for no segments                      \n",
    "    ## DiscardOutliers: (boolean): can be TRUE or FALSE. If true, a simple algorithm is applied to identify outliers                            \n",
    "    ## EstimateNullRate: (string or integer): possible values are                                                                               \n",
    "    ##                   \"estimate\": the x-axis offset is estimated from the data                                                               \n",
    "    ##                   \"null\": the x-axis offset is set to 0                                                                                  \n",
    "    ##                   negative or positive integer: x-axis offset is set to the inserted value, e.g. -42, 14, ... (in cm)                    \n",
    "    ## token: (string): this is a random string, which can be choosen arbitrarily                                                               \n",
    "    ## plot_format (string): this can be \"png,pdf\", \"png\" or \"pdf\" and defines what kinds of images are written to disk                         \n",
    "    ##                       both, png and pdf or only png or pdf                                                                               \n",
    "    ##  \n",
    "    ...\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "whereas here in the Notebook we start with the code below. The \"path\" is simply the path to our data and \"infile\" holds the name of our data file. \"segments\" is crucial, while it defines in how many segments we split our data. More details are given later, here we just need to know that segments is an array. We use \"c(NaN)\" if do not want to split the data. We use \"c(103)\" if we want to split the data between the sample point before depth=103 cm and after depth=103 cm. The same would be accomplished by \"c(105)\", so segments do not need to be exact. If we would have used \"c(103,345,564)\" we would have split the data into four segments, i.e. cutting three times. As said above, we restrict the age data to increase monotonically with depth, thus negative accumulation rates are not allowed. A simple algorithm can be used to remove negative rates, i.e. outliers from the data by setting \"DiscardOutliers=TRUE\". It is important to note that it is recommended to quality control the data before to remove data by expert knowledge. In order to calculate back from the rates to the ages we need to estimate the rate at depth $0$. Set \"EstimateNullRate\" to \"estimate\" to let the algorithm estimate the nullrate or use \"null\" to set it to $0$ or set it to an integer defining the depth-axis crossing. We use a \"token\" value as a prefix for the output data. For instance the png figure for the rates is named \"KHzvfrTgfX_rates.png\" etc. The parameter \"plot_format\" is used to define the output format of the plots, whereas plot_format=\"png,pdf\" yields both png and pdf, other possibilities are plot_format=\"png\", plot_format=\"pdf\" and plot_format=\"jupyter\", which enables the plotting on the default device, e.g. here in the Jupyter Notebook or X11 on a Linux system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "path <- \"/home/jovyan/work/hummingage/\"\n",
    "infile <- \"my_test_data_1.csv\"\n",
    "segments <- c(420)\n",
    "DiscardOutliers <- TRUE\n",
    "EstimateNullRate <- \"estimate\"\n",
    "token <- \"KHzvfrTgfX\"\n",
    "#plot_format <- \"png,pdf\"\n",
    "plot_format <- \"jupyter\"                                                                                                                   \n",
    "#plot_format <- \"\"\n",
    "\n",
    "    ## path: (string): is the path to the infile                                                                                                \n",
    "    ## infile: (string): is the data file according to a certain format                                                                         \n",
    "    ## segments: (integer array): is an array indicating roughly the positions of the segments, use c(NaN) for no segments                      \n",
    "    ## DiscardOutliers: (boolean): can be TRUE or FALSE. If true, a simple algorithm is applied to identify outliers                            \n",
    "    ## EstimateNullRate: (string or integer): possible values are                                                                               \n",
    "    ##                   \"estimate\": the x-axis offset is estimated from the data                                                               \n",
    "    ##                   \"null\": the x-axis offset is set to 0                                                                                  \n",
    "    ##                   negative or positive integer: x-axis offset is set to the inserted value, e.g. -42, 14, ... (in cm)                    \n",
    "    ## token: (string): this is a random string, which can be choosen arbitrarily                                                               \n",
    "    ## plot_format (string): this can be \"png,pdf\", \"png\" or \"pdf\" and defines what kinds of images are written to disk                         \n",
    "    ##                       both, png and pdf or only png or pdf                                                                               \n",
    "    ##  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we load the data and define some setting. Additionally we calculate the sedimentation rates $accRatesOrig$. Token is {{token}}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "## full file-path                                                                                                                                                                        \n",
    "    xfile <- paste(path,infile,sep=\"\");\n",
    "\n",
    "    ## transform plot_format to array                                                                                                                                                        \n",
    "    plot_format_tmp <- strsplit(plot_format,\",\")\n",
    "    plot_format <- plot_format_tmp[[1]]\n",
    "\n",
    "\n",
    "    ## load the infile and save as ageDataOrig                                                                                                                                               \n",
    "    ageDataOrig <- read.table(xfile, header = TRUE,sep=\",\")\n",
    "\n",
    "    ## if no segment will be used set it to empty                                                                                                                                            \n",
    "    if (is.nan(segments)){\n",
    "        segments = c()\n",
    "    }\n",
    "\n",
    "    ## calculate length and estimate rates                                                                                                                                                   \n",
    "    lengthData <- length(ageDataOrig$depth)\n",
    "    diffDepths <- diff(ageDataOrig$depth)\n",
    "    accRatesOrig <- diff(ageDataOrig$age)/diffDepths\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We implemented a simple method to exclude negative rates from the analysis, which is executed if $DiscardOuliers \\; \\mbox{<-} \\; true$. The method simply searches for negative rates. If a negative rate has been found the method must decide, which age value is the outlier, the value at depth $i$ or $i+1$. Therefore we calculate the mean of the age values at $i-1$ and $i+2$. Then we evaluate which of the values at $i$ and $i+1$ is farther away from the mean, which means that this value is the outlier. If the age value at $i$ is the outlier, it's fine. If it is $i+1$ we we set $negRatesIndex[m] \\; \\mbox{<-} \\; negRatesIndex[m]+1$, because we want to remove the age data at $i+1$.\n",
    "It is important to note that this is a very simple approach and that it must used with caution. For instance removing age points can yield to the introduction of new negative rates. An improvement would be to extend the method to check the data recursively until no negative rate is left. Therefore we recomment to quality control your data before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "##--------------------------------------------------------------------------------------------##                                                                                         \n",
    "    ## this block is only executed if DiscardOutliers == TRUE                                                                                                                                \n",
    "    ## identify negative rates, i.e. outliers                                                                                                                                                \n",
    "    ## the difficulty is to identify the outlier                                                                                                                                             \n",
    "    ## i.e. which age is the outlier, because the rate is calculated from two ages                                                                                                           \n",
    "    ## thus we take the ages left and right to the two ages which make the negative rate                                                                                                     \n",
    "    ## and then we calculate which age is further away from the mean of the two left                                                                                                         \n",
    "    ## and rights                                                                                                                                                                            \n",
    "    if (DiscardOutliers==TRUE){\n",
    "        ## find negative rates                                                                                                                                                               \n",
    "        negRatesIndex <- which(accRatesOrig < 0)\n",
    "    } else {\n",
    "        ## set this to empty                                                                                                                                                                 \n",
    "        negRatesIndex <- integer(0)\n",
    "    }\n",
    "    ## make a copy of the indices of the negative rates                                                                                                                                      \n",
    "    negRatesIndexCopy <- negRatesIndex\n",
    "\n",
    "    ## go through the negative rates and decide which age is the outlier, left or right                                                                                                      \n",
    "    m <- 1\n",
    "    for (i in negRatesIndexCopy) {\n",
    "        ## skip the first                                                                                                                                                                    \n",
    "        if (i==1){\n",
    "            next\n",
    "        }\n",
    "        ## calculate the mean between the left and right age next to the two                                                                                                                 \n",
    "        ## ages, which where used to calculate the rate                                                                                                                                      \n",
    "        TheMean <- (ageDataOrig$age[(i-1)]+ageDataOrig$age[(i+2)])/2\n",
    "        ## distance of the left age to the mean                                                                                                                                              \n",
    "        dist1 <- abs(ageDataOrig$age[(i)]-TheMean)\n",
    "        ## distance of the right age to the mean                                                                                                                                             \n",
    "        dist2 <- abs(ageDataOrig$age[(i+1)]-TheMean)\n",
    "        ## if the right is further away then this is the outlier                                                                                                                             \n",
    "        ## so increment the index                                                                                                                                                            \n",
    "        ## otherwise it's the left and leave the index                                                                                                                                       \n",
    "        if (dist2>dist1){\n",
    "            negRatesIndex[m] <- negRatesIndex[m]+1\n",
    "        }\n",
    "        m <- m+1\n",
    "    }\n",
    "    ##--------------------------------------------------------------------------------------------##  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next step we remove the outliers from the age data. Accordingly we again calculate the sedimentation rates $accRates$ and the corresponding standard deviations, where we use the Gaussian error propagation for the standard deviation of a difference. For simplicity we assume independence of the age data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "## remove extreme rates and exclude the first                                                                                                                                            \n",
    "    ## because the first must be estimated later below                                                                                                                                       \n",
    "    ## remove outliers from original data                                                                                                                                                    \n",
    "    ## or copy data as they are, if there are no outliers                                                                                                                                    \n",
    "    LnegRatesIndex <- length(negRatesIndex)\n",
    "    if (LnegRatesIndex>0){\n",
    "        ## remove data                                                                                                                                                                       \n",
    "        ageData <- ageDataOrig[-negRatesIndex,]\n",
    "    } else {\n",
    "        ## leave data as they are                                                                                                                                                            \n",
    "        ageData <- ageDataOrig\n",
    "    }\n",
    "\n",
    "    ## now, outliers have been removed calculate again length, rates etc.                                                                                                                    \n",
    "    lengthData <- length(ageData$depth)\n",
    "    diffDepths <- diff(ageData$depth)\n",
    "    accRates <- diff(ageData$age)/diffDepths\n",
    "    sigmaRates <- sqrt((ageData$error[2:lengthData]^2+ageData$error[1:(lengthData-1)]^2))/diffDepths\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have to find the position of the above defined segments. Since we have defined the positions of the segments in cm, we have to find now the corresponding indices in the $depth$ vector. Finally we add $0$ and $lengthData$ to the $segPos$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    " ## convert segments from depth to point number                                                                                                                                           \n",
    "    ## find the position, i.e. between the two closest points                                                                                                                                \n",
    "    Lsegments <- length(segments)\n",
    "    if (Lsegments == 0) {\n",
    "        segPos = c()\n",
    "    } else {\n",
    "        segPos <- rep(0,Lsegments)\n",
    "        for (i in seq(1,Lsegments)){\n",
    "            ## difference between depth variable and a sequence position (in cm)                                                                                                             \n",
    "            Xdiff <- ageData$depth-segments[i]\n",
    "            ## find the indices smaller than the segment position                                                                                                                            \n",
    "            a <- which(Xdiff<0)\n",
    "            ## set the position at the last negative                                                                                                                                         \n",
    "            segPos[i] <- max(a)\n",
    "        }\n",
    "    }\n",
    "\n",
    "    ## copy of segPos                                                                                                                                                                        \n",
    "    segPosPlot <- segPos\n",
    "    ## add left and right boundaries to segPos                                                                                                                                               \n",
    "    segPos <- c(0,segPos,lengthData)\n",
    "    segPosLength <- length(segPos)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A crucial point in using the segmentation rates as basis for the regression of the original age data is that the  we have $N-1$ data points for the rates (if we had $N$ data points for the ages), simply because of the differential quotient used to estimate the rates. Thus we need to estimate the \"null\" rate at depth $0$, i.e. the depth-axis crossing. This is needed to convert back later from the rates to the ages to calculate the first age value. If \"EstimateNullRate\" is set to \"estimate\" we apply a linear regression to the first three age values to find the depth-axis crossing. If it is set to \"null\" we choose $0$ as depth-crossing or if the user gives an integer value, this is used as the depth-crossing value. Finally we calculate the $NullRate$ and $NullError$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "##--------------------------------------------------------------------------------------------##                                                                                         \n",
    "    ##  estimate the x-axis crossing to estimate the first rate                                                                                                                              \n",
    "    ##  if we would take the origin 0,0 than the first rate will be wrong                                                                                                                    \n",
    "    ##  because there is an offset                                                                                                                                                           \n",
    "    ##                                                                                                                                                                                       \n",
    "    ##  so, we fit the first segment and estimate the x-crossing                                                                                                                             \n",
    "    ##  cut out first segment                                                                                                                                                                \n",
    "    xcrossing <- 0\n",
    "    if (EstimateNullRate == \"estimate\"){\n",
    "        N <- 3\n",
    "        Lu <- length(1:N)\n",
    "        u <- ageData$age[1:N]\n",
    "        X <- replicate(2,rep(1,Lu))\n",
    "        X[,2] <- ageData$depth[1:N]\n",
    "        ##  print(X)                                                                                                                                                                         \n",
    "        beta <- solve(t(X) %*% X) %*% t(X) %*% u\n",
    "        ##  print(beta)                                                                                                                                                                      \n",
    "        ##  only if slope is positive                                                                                                                                                        \n",
    "        if (beta[2]>0){\n",
    "            xcrossing <- beta[1]/beta[2]*(-1)\n",
    "            ##  print(xcrossing)                                                                                                                                                             \n",
    "        } else {\n",
    "            xcrossing <- 0\n",
    "        }\n",
    "    }\n",
    "    if (EstimateNullRate == \"null\"){\n",
    "        xcrossing <- 0\n",
    "    }\n",
    "    if (is.numeric(EstimateNullRate) == TRUE){\n",
    "        ##  then this is xcrossing                                                                                                                                                           \n",
    "        xcrossing <- EstimateNullRate\n",
    "    }\n",
    "    NullDiff <- ageData$depth[1]-xcrossing\n",
    "    NullRate <- ageData$age[1]/NullDiff\n",
    "    NullError <- ageData$error[1]/NullDiff\n",
    "    ##--------------------------------------------------------------------------------------------##    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can add the $NullRate$ and the $NullError$ to the rates and errors, respectively. Additionally \n",
    "we initialise arrays for the folling fit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "## now we have the first rate and add it to the rates                                                                                                                                    \n",
    "    accRates <- c(NullRate,accRates)\n",
    "    ## print(accRates)                                                                                                                                                                       \n",
    "    ## add also a std for the first                                                                                                                                                          \n",
    "    sigmaRates <- c(NullError,sigmaRates)\n",
    "\n",
    "    ## initialise arrays for the fits                                                                                                                                                        \n",
    "    fittedRates <- rep(0,lengthData)\n",
    "    fittedError <- rep(0,lengthData)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to apply linear regressions to the segments. The $fittedError$ is the Root Mean Square Error (RMSE) of the rates and the regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "##--------------------------------------------------------------------------------------------##                                                                                         \n",
    "    ## fitting the segments                                                                                                                                                                  \n",
    "    for (i in seq(2,segPosLength)) {\n",
    "        ##  least square                                                                                                                                                                     \n",
    "        Xsegment <- (segPos[i-1]+1):segPos[i]\n",
    "        Lsegment <- length(Xsegment)\n",
    "        ##  create X matrix                                                                                                                                                                  \n",
    "        X <- replicate(2,rep(1,Lsegment))\n",
    "        X[,2] <- ageData$depth[Xsegment]\n",
    "        ##  create error matrix                                                                                                                                                              \n",
    "        g <- solve(t(X) %*% X)\n",
    "        ##  print(g)                                                                                                                                                                         \n",
    "        beta <- g %*% t(X) %*% accRates[Xsegment]\n",
    "        ##  print(beta)                                                                                                                                                                      \n",
    "        fittedRates[Xsegment] <- X %*% beta\n",
    "        ##  res                                                                                                                                                                              \n",
    "        fittedError[Xsegment] <- sqrt(1/(Lsegment-1) * sum((fittedRates[Xsegment]-accRates[Xsegment])^2))\n",
    "        ##  print(fittedError[Xsegment])                                                                                                                                                     \n",
    "    }\n",
    "    ##--------------------------------------------------------------------------------------------##        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After fitting the rates we calculate the Bayesian Information Criterion (BIC) and write the result into a file. The BIC helps us to find the optimal number of segments. It prevents for overfitting by judging the goodness of the fit by the Mean Square Error (MSE) and using the number of segments as a penalty parameter. Thus, the smallest (which is the optimal) BIC is observed by achieving the smallest MSE while simultaneously using as few as possible segments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "##--------------------------------------------------------------------------------------------##                                                                                         \n",
    "    ##  BIC                                                                                                                                                                                  \n",
    "    ##  BIC for Gaussian approx. is BIC=N*ln(epsilon^2)+k*ln(N)                                                                                                                              \n",
    "    ##  for fitting a linear regression one need k=q+2 parameters to be estimated                                                                                                            \n",
    "    ##  one for the intercept, q for the slopes and one for the rmse                                                                                                                         \n",
    "    ##  thus in the case of fitting the mean I need k=2 (intercept, rmse)                                                                                                                    \n",
    "    ##  BIC[segments] <- N * log(rmse^2) + 2*segments * log(N)                                                                                                                               \n",
    "    mse <- 1/lengthData * sum((fittedRates-accRates)^2)\n",
    "    BIC <- lengthData * log(mse) + (2*(segPosLength-1)+1) * log(lengthData)\n",
    "    ## (segPosLength-1) because above I have added 0,segPos,N to segPos                                                                                                                      \n",
    "    ## thus (segPosLength-1) is exactly the number of segments                                                                                                                               \n",
    "    ## write out the BIC                                                                                                                                                                     \n",
    "    write(BIC,file=paste(path,token,\"_BIC.txt\",sep=\"\"),ncolumns=1)\n",
    "    ##--------------------------------------------------------------------------------------------##     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last step before plotting the results is to tune the regressions with a Bayesian approach and finally convert the regressions of the rates back to ages. The Bayesian tuning is inspired by Bailer-Jones, 2012 (https://doi.org/10.1051/0004-6361/201220109). The idea is to use all available information for the final conlcusions. Normally we would stop here and use the fitted rates as our result. However, the linear regressions are clearly somehow artificially and we would not say that these are the truth. The original data are also not the truth, because they are prone to error. That means, the truth lies somewhere inbetween the original data and the fitted values. Using the Bayesian approach and approximating all ingredients by Gaussians we find a very simple and intuitive solution to this problem. It turns out, that the best fit is the weighted avarage of the original rate and the fitted rate at every depth. A non-Gaussian approach would require a much more complicated estimation, however it is thinkable as an extension to implement also a non-Gaussian methodology. For now we stick to the Gaussian approximation. As said above the best estimate of the rates seems to be inbetween the original \"measured\" rates and the fit.\n",
    "\n",
    "This can be formulated using probability theory and Bayes theorem. Bayes theorem is given by\n",
    "\n",
    "$\\mbox{prob}(Y|X)=\\frac{\\mbox{prob}(X|Y) \\, \\times \\mbox{prob}(Y)}{\\mbox{prob}(X)}$\n",
    "\n",
    "The left part is called posterior probability, the first term on the right side is the likelihood, the right term the prior probability, whereas the term in the denominator is mostly named evidence.\n",
    "\n",
    "For a better understanding, the terms can also be interpreted as:\n",
    "\n",
    "$\\mbox{prob}(hypothesis|data) \\propto \\mbox{prob}(data|hypothesis) \\times \\mbox{prob}(hypothesis)$\n",
    "\n",
    "We have omitted the denominator, which represents essentially a normalisation factor and thus replaced the $=$ by a $\\propto$. In the case of normalised likelihood and prior the $=$ can be used because the evidence would be unity.\n",
    "\n",
    "In words this means that we want to estimate the probability of a hypothesis given specific data. This can be indeed calculated if we know the probability of the data given the hypothesis and the probability of the hypothesis itself.\n",
    "\n",
    "Regarding our age data we can now ask what is the probabilty of observing a best estimate of the true rates given our observation:\n",
    "\n",
    "$\\mbox{prob}(fittedRates|accRates) \\propto \\mbox{prob}(accRates|fittedRates) \\, \\times \\mbox{prob}(fittedRates)$\n",
    "\n",
    "A crucial point is now to follow a Gaussian approach, which allows us to solve the above equation analytical. In the case of a non-gaussian approach the solution can most probably only be found numerically, e.g. using a Markov Chain Monte Carlo (MCMC) algorithm.\n",
    "\n",
    "Before identifying the exact Gaussians we can simplify the equation above. The likelihood, i.e. the probability of the rates given the fit reduces to $\\mbox{prob}(accRates) = \\mbox{prob}(accRates|fittedRates)$, thus:\n",
    "\n",
    "$\\mbox{prob}(fittedRates|accRates) \\propto \\mbox{prob}(accRates) \\, \\times \\mbox{prob}(fittedRates)$\n",
    "\n",
    "To every point of the estimated rates and the fit we can associate a Gaussian distribution. The probability of the estimated rates can be defined as $\\mbox{prob}(accRates) = N(\\mu=accRates,\\sigma=sigmaRates)$. The probability of the fitted rates can be defined as $\\mbox{prob}(fittedRates) = N(\\mu=fittedRates,\\sigma=fittedError)$.\n",
    "Since we are dealing with Gaussian normal distributions, which are normalised per definition and fully described by the mean and standard deviation we can replace the $\\propto$ by a $=$. \n",
    "\n",
    "Thus we have to calculate:\n",
    "\n",
    "$\\mbox{prob}(fittedRates|accRates) = N(\\mu=accRates,\\sigma=sigmaRates) \\times N(\\mu=fittedRates,\\sigma=fittedError)$\n",
    "\n",
    "We see that we can find a solution by multiplying two Gaussian distributions. The multiplication of two Gaussians $f$ and $g$ with means $\\mu_f$ and $\\mu_g$ and variances $V_f$ and $V_g$ is given by the following formulas:\n",
    "\n",
    "mean $=\\frac{\\mu_f V_g + \\mu_g V_f}{V_f+V_g}$\n",
    "\n",
    "variance = $\\frac{V_f \\times V_g}{V_f+V_g}$\n",
    "\n",
    "which yield the mean and variance. However, it has to be noted that the product of two Gaussians is.\n",
    "\n",
    "Interestigly it turns out that the new estimate of the fitted rates is exactly the weighted mean of the observations and the fitted rates, whereas the errors represent the weights. This result is due to fact that we used a Gaussian assumption. Further it can be seen that this approach is a so called objective Bayesian analysis, because it involves no subjective prior information, again due to the Gaussian approach.\n",
    "\n",
    "Applying these formulas to our data, we get a new estimate for the fitted accumulation rates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "##-------------------------------------------------------------------------------------------##                                                                                         \n",
    "    ## apply the Bayesian approach, i.e. for the Gaussian assumption the weighted mean                                                                                                       \n",
    "    BayesFittedRates <- (fittedRates * sigmaRates^2 + accRates * fittedError^2)/(fittedError^2 + sigmaRates^2)\n",
    "    ## disable Bayes                                                                                                                                                                         \n",
    "    ##BayesFittedRates <- fittedRates                                                                                                                                                        \n",
    "\n",
    "    ## and the weighted std                                                                                                                                                                  \n",
    "    BayesSigmaRates <- sqrt((fittedError^2 * sigmaRates^2)/(fittedError^2 + sigmaRates^2))\n",
    "    ## disable Bayes                                                                                                                                                                         \n",
    "    ##BayesSigmaRates <- fittedError                                                                                                                                                         \n",
    "\n",
    "\n",
    "    ## calculate the ages from the rates                                                                                                                                                     \n",
    "    ageFit <- cumsum(BayesFittedRates * c(NullDiff,diffDepths))\n",
    "    ##  print(\"sum1\")                                                                                                                                                                        \n",
    "    ##  print(sum((ageFit-ageData$age)^2))                                                                                                                                                   \n",
    "\n",
    "    ##  and the errors                                                                                                                                                                       \n",
    "    ageFitError <- rep(0,lengthData)\n",
    "    ageFitError[1] <- BayesSigmaRates[1]*NullDiff\n",
    "    for (i in seq(1,(lengthData-1))) {\n",
    "        ageFitError[i+1] <- sqrt(ageFitError[i]^2+(BayesSigmaRates[i+1]*diffDepths[i])^2)\n",
    "    }\n",
    "    ##--------------------------------------------------------------------------------------------##     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen from above, we calculate the regression for the age data by simply inverting the rate estimation, i.e. we calculate the cumulative sum of the rate regression to get the age regression.\n",
    "Similarly the errors are estimated. An interesting effect is observed here, i.e. the errors are monotonically increasing with depth, because the error at one depth is fully propagated to the next depth, because of the cumulative summation. This makes a lot of sense, because deeper measurements should be more uncertain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last part of the method is the visualization of the results. First we plot the fitted rates without the Bayesian approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAACXBIWXMAABJ0AAASdAHeZh94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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plotting the intermediate result of fitted segments                                                                                                                                   \n",
    "    for (k in plot_format){    \n",
    "        if (k == \"jupyter\"){\n",
    "            Ascale <- 1 #4\n",
    "            Bscale <- 1 #6\n",
    "            Cscale <- 2 #8\n",
    "            Dscale <- 4 #12    \n",
    "        } else {\n",
    "            Ascale <- 4\n",
    "            Bscale <- 6\n",
    "            Cscale <- 8\n",
    "            Dscale <- 12    \n",
    "\n",
    "            par(mar=c(14,14,4,2),mgp=c(10,4,0),bg=rgb(248/255,250/255,252/255))    \n",
    "            if (k == \"png\"){\n",
    "                png(filename=paste(path,token,\"_intermediate.png\",sep=\"\"),width=2000,height=1400,pointsize=10)#,width=11,height=8)                                                               \n",
    "            }\n",
    "            if (k == \"pdf\"){\n",
    "                pdf(file=paste(path,token,\"_intermediate.pdf\",sep=\"\"),width=40,height=28)#,width=11,height=8)                                                                                    \n",
    "            }\n",
    "        }\n",
    "        \n",
    "\n",
    "        \n",
    "\n",
    "\n",
    "        ymin <- min(c(accRates-sigmaRates),na.rm=TRUE)\n",
    "        ymax <- max(c(accRates+sigmaRates),na.rm=TRUE)\n",
    "        xmin <- 0 ##min(ageDataOrig$depth)                                                                                                                                                   \n",
    "        xmax <- max(ageDataOrig$depth)\n",
    "        plot(ageData$depth,accRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),xlab=\"Depth [cm]\",ylab=\"Rates [ka/cm]\",cex.lab=Ascale,cex.axis=Ascale)\n",
    "        if (Lsegments > 0) {\n",
    "            for (i in seq(1,length(segPosPlot))) {\n",
    "                par(new=TRUE)\n",
    "                segPosDepth <- (ageData$depth[segPosPlot[i]]+ageData$depth[segPosPlot[i]+1])/2\n",
    "                plot(c(segPosDepth,segPosDepth),c(ymin,ymax),ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(200/255,200/255,200/255),type=\"l\",lwd=Dscale,lty=2,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "            }\n",
    "        }\n",
    "        par(new=TRUE)\n",
    "        polygon(c(ageData$depth, rev(ageData$depth)), c(fittedRates-fittedError,\n",
    "                                                        rev(fittedRates+fittedError)), col=rgb(0.8,0.8,0.8),border=NA)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,accRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(42/255,190/255,230/255),pch=19,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,fittedRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),xlab=\"\",pch=19,ylab=\"\",xaxt=\"n\",yaxt=\"n\",col=\"red\",cex=Ascale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,fittedRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),lwd=Cscale,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",type=\"l\",col=\"red\",cex=Cscale)\n",
    "\n",
    "        arrows(ageData$depth, accRates-sigmaRates, ageData$depth,\n",
    "               accRates+sigmaRates, length=0.2, angle=90, code=3,col=\"black\",lwd=Bscale,cex=Cscale)\n",
    "\n",
    "        legend(xmax, ymax, xjust=1,legend=c(\"data\",\"fit\",\"sequences\"),\n",
    "               col=c(rgb(42/255,190/255,230/255),\"red\",rgb(200/255,200/255,200/255)), lwd=c(NaN,Cscale,Dscale), lty=c(1,1,2), pch=c(19,19,NaN), cex=c(Bscale), pt.cex=c(Cscale,Ascale,Cscale))\n",
    "        if (k != \"jupyter\"){\n",
    "            dev.off()\n",
    "        }\n",
    "    }\n",
    "    ##--------------------------------------------------------------------------------------------## "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we plot the rates including the Bayesian approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAACXBIWXMAABJ0AAASdAHeZh94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\nQBEEOwAAAEX8D/jj41Je9BUCAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plotting rates                                                                                                                                                                        \n",
    "    for (k in plot_format){\n",
    "        if (k == \"jupyter\"){\n",
    "            Ascale <- 1 #4                                                                                                                                                                   \n",
    "            Bscale <- 1 #6                                                                                                                                                                   \n",
    "            Cscale <- 2 #8                                                                                                                                                                   \n",
    "            Dscale <- 4 #12                                                                                                                                                                  \n",
    "        } else {\n",
    "            Ascale <- 4\n",
    "            Bscale <- 6\n",
    "            Cscale <- 8\n",
    "            Dscale <- 12\n",
    "\n",
    "            par(mar=c(14,14,4,2),mgp=c(10,4,0),bg=rgb(248/255,250/255,252/255))\n",
    "            if (k == \"png\"){\n",
    "                png(filename=paste(path,token,\"_rates.png\",sep=\"\"),width=2000,height=1400,pointsize=10)#,width=11,height=8)                                                                  \n",
    "            }\n",
    "            if (k == \"pdf\"){\n",
    "                pdf(file=paste(path,token,\"_rates.pdf\",sep=\"\"),width=40,height=28)#,width=11,height=8)                                                                                       \n",
    "            }\n",
    "        }\n",
    "\n",
    "        ymin <- min(c(accRates-sigmaRates),na.rm=TRUE)\n",
    "        ymax <- max(c(accRates+sigmaRates),na.rm=TRUE)\n",
    "\n",
    "        xmin <- 0 ##min(ageDataOrig$depth)                                                                                                                                                   \n",
    "        xmax <- max(ageDataOrig$depth)\n",
    "        plot(ageData$depth,accRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),xlab=\"Depth [cm]\",ylab=\"Rates [ka/cm]\",cex.lab=Ascale,cex.axis=Ascale)\n",
    "        if (Lsegments > 0) {\n",
    "            for (i in seq(1,length(segPosPlot))) {\n",
    "                par(new=TRUE)\n",
    "                segPosDepth <- (ageData$depth[segPosPlot[i]]+ageData$depth[segPosPlot[i]+1])/2\n",
    "                plot(c(segPosDepth,segPosDepth),c(ymin,ymax),ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(200/255,200/255,200/255),type=\"l\",lwd=Dscale,lty=2,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "            }\n",
    "        }\n",
    "        par(new=TRUE)\n",
    "        polygon(c(ageData$depth, rev(ageData$depth)), c(BayesFittedRates-BayesSigmaRates,\n",
    "                                                        rev(BayesFittedRates+BayesSigmaRates)), col=rgb(0.8,0.8,0.8),border=NA)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,accRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(42/255,190/255,230/255),pch=19,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,BayesFittedRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),xlab=\"\",pch=19,ylab=\"\",xaxt=\"n\",yaxt=\"n\",col=\"red\",cex=Ascale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,BayesFittedRates,ylim=c(ymin,ymax),xlim=c(xmin,xmax),lwd=Cscale,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",type=\"l\",col=\"red\",cex=Cscale)\n",
    "        arrows(ageData$depth, accRates-sigmaRates, ageData$depth,\n",
    "               accRates+sigmaRates, length=0.2, angle=90, code=3,col=\"black\",lwd=Bscale,cex=Cscale)\n",
    "\n",
    "        legend(xmax, ymax, xjust=1,legend=c(\"data\",\"fit\",\"sequences\"),\n",
    "               col=c(rgb(42/255,190/255,230/255),\"red\",rgb(200/255,200/255,200/255)), lwd=c(NaN,Cscale,Dscale), lty=c(1,1,2), pch=c(19,19,NaN), cex=c(Bscale), pt.cex=c(Cscale,Ascale,Cscale))\n",
    "\n",
    "        if (k != \"jupyter\"){\n",
    "            dev.off()\n",
    "        }\n",
    "    }\n",
    "    ##--------------------------------------------------------------------------------------------##      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we plot the ages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAACXBIWXMAABJ0AAASdAHeZh94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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plotting ages                                                                                                                                                                         \n",
    "    for (k in plot_format){\n",
    "        if (k == \"jupyter\"){\n",
    "            Ascale <- 1 #4                                                                                                                                                                   \n",
    "            Bscale <- 1 #6                                                                                                                                                                   \n",
    "            Cscale <- 2 #8                                                                                                                                                                   \n",
    "            Dscale <- 4 #12                                                                                                                                                                  \n",
    "        } else {\n",
    "            Ascale <- 4\n",
    "            Bscale <- 6\n",
    "            Cscale <- 8\n",
    "            Dscale <- 12\n",
    "\n",
    "            par(mar=c(14,14,4,2),mgp=c(10,4,0),bg=rgb(248/255,250/255,252/255))\n",
    "            if (k == \"png\"){\n",
    "                png(filename=paste(path,token,\"_ages.png\",sep=\"\"),width=2000,height=1400,pointsize=10)#,width=11,height=8)                                                                   \n",
    "            }\n",
    "            if (k == \"pdf\"){\n",
    "                pdf(file=paste(path,token,\"_ages.pdf\",sep=\"\"),width=40,height=28)#,width=11,height=8)                                                                                        \n",
    "            }\n",
    "        }\n",
    "\n",
    "\n",
    "        ymin <- min(c(ageData$age-ageData$error,ageDataOrig$age),na.rm=TRUE)\n",
    "        ymax <- max(c(ageData$age+ageData$error,ageDataOrig$age,ageFit+ageFitError),na.rm=TRUE)\n",
    "        xmin <- 0 ##min(ageDataOrig$depth)                                                                                                                                                   \n",
    "        xmax <- max(ageDataOrig$depth)\n",
    "        plot(ageData$depth,ageData$age,ylim=c(ymin,ymax),xlim=c(xmin,xmax),xlab=\"Depth [cm]\",ylab=\"Age [ka]\",cex.lab=Ascale,cex.axis=Ascale)\n",
    "        if (Lsegments > 0) {\n",
    "            for (i in seq(1,length(segPosPlot))) {\n",
    "                par(new=TRUE)\n",
    "                segPosDepth <- (ageData$depth[segPosPlot[i]]+ageData$depth[segPosPlot[i]+1])/2\n",
    "                plot(c(segPosDepth,segPosDepth),c(ymin,ymax),ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(200/255,200/255,200/255),type=\"l\",lwd=Dscale,lty=2,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "            }\n",
    "        }\n",
    "        par(new=TRUE)\n",
    "        polygon(c(ageData$depth, rev(ageData$depth)), c(ageFit-ageFitError,\n",
    "                                                        rev(ageFit+ageFitError)), col=rgb(0.8,0.8,0.8),border=NA,xlim=c(xmin,xmax),)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,ageData$age,ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(42/255,190/255,230/255),pch=19,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageDataOrig$depth[negRatesIndex],ageDataOrig$age[negRatesIndex],ylim=c(ymin,ymax),xlim=c(xmin,xmax),col=rgb(230/255,190/255,42/255),pch=19,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",cex=Cscale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,ageFit,ylim=c(ymin,ymax),xlim=c(xmin,xmax),xlab=\"\",pch=19,ylab=\"\",xaxt=\"n\",yaxt=\"n\",col=\"red\",cex=Ascale)\n",
    "        par(new=TRUE)\n",
    "        plot(ageData$depth,ageFit,ylim=c(ymin,ymax),xlim=c(xmin,xmax),lwd=Cscale,xlab=\"\",ylab=\"\",xaxt=\"n\",yaxt=\"n\",type=\"l\",col=\"red\",cex=Cscale)\n",
    "\n",
    "        arrows(ageDataOrig$depth, ageDataOrig$age-ageDataOrig$error, ageDataOrig$depth,\n",
    "               ageDataOrig$age+ageDataOrig$error, length=0.2, angle=90, code=3,col=\"black\",lwd=Bscale,cex=Cscale)\n",
    "\n",
    "        legend(xmax, ymin, xjust=1,yjust=0,legend=c(\"data\",\"outliers\",\"fit\",\"sequences\"),\n",
    "               col=c(rgb(42/255,190/255,230/255),rgb(230/255,190/255,42/255),\"red\",rgb(200/255,200/255,200/255)), lwd=c(NaN,NaN,Cscale,Dscale), lty=c(1,1,1,2), pch=c(19,19,19,NaN), cex=c(Bscale), pt.cex=c(Cscale,Cscale,Ascale,NaN))\n",
    "\n",
    "        if (k != \"jupyter\"){\n",
    "            dev.off()\n",
    "        }\n",
    "    }\n",
    "    ##--------------------------------------------------------------------------------------------##  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}