{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "500e329b-04b5-4b0a-bcd3-69f42aa3a5eb",
   "metadata": {},
   "source": [
    "# Eruption/deposition age estimation demonstration\n",
    "\n",
    "This Jupyter notebook demonstrates the eruption (/deposition) age estimation algorithm of [Keller, Schoene, and Samperton (2018)](https://doi.org/10.7185/geochemlet.1826) as implemented in [Chron.jl](https://github.com/brenhinkeller/Chron.jl).\n",
    "\n",
    "<a href=\"https://mybinder.org/v2/gh/brenhinkeller/Chron.jl/main?filepath=examples%2FEruptionDepositionAgeDemonstration.ipynb\" target=\"_blank\"><img src=\"https://static.mybinder.org/badge_logo.svg\" alt=\"Launch Binder notebook\" align=\"left\"></a> \n",
    "<p style=\"text-indent: 5px\">If running this notebook as an online Binder notebook and the webpage times out, click the badge at left to relaunch (refreshing will not work). Note that any changes will be lost!</p>\n",
    "\n",
    "Hint: `shift`-`enter` to run a single cell, or from the `Cell` menu select `Run All` to run the whole file. Any code from this notebook can be copied and pasted into the Julia REPL or a `.jl` script.\n",
    "***\n",
    "\n",
    "## (1) Load required Julia packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "63930c99-ddd3-466a-8837-9d5efec6582c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load (and install if necessary) the Chron.jl package\n",
    "using Chron\n",
    "using Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab5a0099-314c-45fc-80f7-6093ab2512ba",
   "metadata": {},
   "source": [
    "***\n",
    "## (2a) Test Bayesian eruption age estimation with a synthetic dataset\n",
    "#### Generate synthetic zircon dataset, drawing from `MeltsVolcanicZirconDistribution`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "64358fe2-b056-4103-9256-eaba6fa6512d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dt_sigma = 30; # Timescale relative to analytical uncertainty\n",
    "N = 42; # Number of zircons\n",
    " \n",
    "# Draw set of pseudorandom ages from MELTS volcanic zircon distribution, \n",
    "# with true minimum == 0 and analytical sigma == 1\n",
    "ages = draw_from_distribution(MeltsVolcanicZirconDistribution,N).*dt_sigma + randn(N);\n",
    "uncert = ones(N)\n",
    "\n",
    "# Calculate the weighted mean age\n",
    "(wx, wsigma, mswd) = awmean(ages, uncert)\n",
    "\n",
    "h = plot(framestyle=:box,\n",
    "    ylabel=\"Time before eruption (sigma)\", \n",
    "    xlabel=\"N\", \n",
    "    fg_color_legend=:white, \n",
    "    legend=:topleft, \n",
    ")\n",
    "plot!(h,1:length(ages),sort(ages),yerror=uncert*2,seriestype=:scatter, label=\"Synthetic zircon ages\")\n",
    "plot!(h,collect(xlims()), [0,0], label=\"Eruption age\")\n",
    "plot!(h,collect(xlims()), [wx,wx], label=\"Weighted mean, MSWD $(round(mswd,sigdigits=2))\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bd084fd-6542-47a0-a671-9077a66f09cb",
   "metadata": {},
   "source": [
    "#### Calculate bootstrapped $\\ \\mathcal{\\vec{f}}_{xtal}(t_r)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "12fbc10c-c862-4059-b23c-8d8fae18db40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Bootstrap the crystallization distribution, \n",
    "# accounting for any expected analytical \"tail\" beyond eruption/deposition\n",
    "dist = BootstrapCrystDistributionKDE(ages, uncert)\n",
    "dist ./= nanmean(dist) # Normalize\n",
    "\n",
    "# Plot bootstrapped distribution\n",
    "plot(range(0,1.3,length=length(dist)),dist, label=\"bootstrapped\", ylabel=\"Probability Density\", xlabel=\"Time before eruption (scaled)\", legend=:bottomleft, fg_color_legend=:white, framestyle=:box)\n",
    "plot!(range(0,1,length=100),MeltsVolcanicZirconDistribution,label=\"original\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67b52a2f-85e9-4c76-9bdc-5d87942bd7b1",
   "metadata": {},
   "source": [
    "#### Run MCMC to estimate eruption/deposition age distribution of synthetic dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "806b46f8-e66b-47d7-95b2-b54d825d2002",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated eruption age of synthetic dataset:\n",
      " 0.9130201471002158 +/- 2.28596695543814 Ma (2σ)\n",
      " (True synthetic age 0 Ma)"
     ]
    },
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Configure model\n",
    "nsteps = 200000; # Length of Markov chain\n",
    "burnin = 100000; # Number of steps to discard at beginning of Markov chain\n",
    "\n",
    "# Run MCMC\n",
    "tminDist = metropolis_min(nsteps,dist,ages,uncert);\n",
    "\n",
    "# Print results\n",
    "AgeEst = nanmean(tminDist[burnin:end]);\n",
    "AgeEst_sigma = nanstd(tminDist[burnin:end]);\n",
    "print(\"\\nEstimated eruption age of synthetic dataset:\\n $AgeEst +/- $(2*AgeEst_sigma) Ma (2σ)\\n (True synthetic age 0 Ma)\")\n",
    "\n",
    "# Plot results\n",
    "h = histogram(tminDist[burnin:end],\n",
    "    nbins=50,\n",
    "    label=\"Posterior distribution\",\n",
    "    xlabel=\"Eruption Age (Ma)\",\n",
    "    ylabel=\"N\", \n",
    "    framestyle=:box\n",
    ")\n",
    "plot!(h,[0,0],collect(ylims()),line=(3),label=\"True (synthetic) age\",fg_color_legend=:white)\n",
    "plot!(h,[wx,wx],collect(ylims()),line=(3),label=\"Weighted mean age\",legend=:topright)\n",
    "display(h)\n",
    "\n",
    "sleep(0.5) # (just to make sure this section is finished running)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a19c85db-1e66-404b-9c37-9aff78a4d49c",
   "metadata": {},
   "source": [
    "***\n",
    "## (2b) Estimate eruption age for real zircon data\n",
    "The example dataset here is from [Wotzlaw et al., 2013](https://doi.org/10.1130/G34366.1) FCT+MLX\n",
    "#### Input dataset (Try pasting in your own data here!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b9290a96-44fc-428e-a46b-f9eb20db260c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Age and one-sigma uncertainty.\n",
    "ages = [28.196, 28.206, 28.215, 28.224, 28.232, 28.241, 28.246, 28.289, 28.308, 28.332, 28.341, 28.359, 28.379, 28.383, 28.395, 28.4, 28.405, 28.413, 28.415, 28.418, 28.42, 28.422, 28.428, 28.452, 28.454, 28.454, 28.458, 28.468, 28.471, 28.475, 28.482, 28.485, 28.502, 28.52, 28.551, 28.561, 28.565, 28.582, 28.584, 28.586, 28.611, 28.638, 28.655]\n",
    "uncert = [0.019, 0.0155, 0.019, 0.0215, 0.018, 0.023, 0.013, 0.029, 0.0175, 0.0315, 0.0095, 0.0245, 0.0255, 0.0175, 0.0235, 0.014, 0.021, 0.022, 0.0125, 0.0135, 0.016, 0.0195, 0.0175, 0.0125, 0.01, 0.014, 0.015, 0.0205, 0.0155, 0.011, 0.0115, 0.0185, 0.0255, 0.014, 0.0125, 0.013, 0.015, 0.014, 0.012, 0.016, 0.0215, 0.0125, 0.0215]\n",
    "\n",
    "# Sort by age (just to make rank-order plots prettier)\n",
    "t = sortperm(ages)\n",
    "ages = ages[t];\n",
    "uncert = uncert[t];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcc7062c-c487-4fca-a3ee-03ef5e7dda3e",
   "metadata": {},
   "source": [
    "#### Calculate bootstrapped $\\ \\mathcal{\\vec{f}}_{xtal}(t_r)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4623e05a-7454-4039-ab8d-f9ae0611d9ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Bootstrap the crystallization distribution, \n",
    "# accounting for any expected analytical \"tail\" beyond eruption/deposition\n",
    "BootstrappedDistribution = BootstrapCrystDistributionKDE(ages, uncert)\n",
    "BootstrappedDistribution ./= nanmean(BootstrappedDistribution) # Normalize\n",
    "\n",
    "# Plot bootstrapped distribution\n",
    "plot(range(0,1,length=length(BootstrappedDistribution)),BootstrappedDistribution, \n",
    "    label=\"bootstrapped f_xtal\", \n",
    "    ylabel=\"Probability Density\", \n",
    "    xlabel=\"Time before eruption (unitless)\", \n",
    "    fg_color_legend=:white, \n",
    "    framestyle=:box\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f0b9d51-f819-47b4-867f-5f4be63ad1f1",
   "metadata": {},
   "source": [
    "#### Run MCMC to estimate eruption age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "758fb9b8-8b20-4c22-8d44-d7c2b9998314",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated eruption age:\n",
      " 28.184890045741966 +/- 0.03518848913616867 Ma (2σ)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Configure model\n",
    "nsteps = 400000; # Length of Markov chain\n",
    "burnin = 150000; # Number of steps to discard at beginning of Markov chain\n",
    "\n",
    "# Choose the form of the prior closure/crystallization distribution to use\n",
    "dist = BootstrappedDistribution\n",
    "## You might alternatively consider:\n",
    "# dist = UniformDistribution              # A reasonable default\n",
    "# dist = MeltsVolcanicZirconDistribution  # A single magmatic pulse, truncated by eruption\n",
    "# dist = ExponentialDistribution          # Applicable for survivorship processes, potentially including inheritance/dispersion in Ar-Ar dates\n",
    "\n",
    "# Run MCMC\n",
    "tminDist = metropolis_min(nsteps,dist,ages,uncert);\n",
    "\n",
    "# Print results\n",
    "AgeEst = nanmean(tminDist[burnin:end]);\n",
    "AgeEst_sigma = nanstd(tminDist[burnin:end]);\n",
    "print(\"\\nEstimated eruption age:\\n $AgeEst +/- $(2*AgeEst_sigma) Ma (2σ)\\n\")\n",
    "\n",
    "# Plot results\n",
    "h = histogram(tminDist[burnin:end],nbins=100,label=\"Posterior distribution\",xlabel=\"Eruption Age (Ma)\",ylabel=\"N\",legend=:topleft,fg_color_legend=:white, framestyle=:box)\n",
    "# plot!(h,[wx,wx],collect(ylims()),line=(3),label=\"Weighted mean age\",legend=:topleft)\n",
    "display(h)\n",
    "sleep(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c72e9831-bc8c-4c72-8071-5d1256cf8d18",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot eruption age estimate relative to rank-order plot of raw zircon ages\n",
    "h = plot(framestyle=:box,\n",
    "    ylabel=\"Age (Ma)\", \n",
    "    xlabel=\"N\", \n",
    "    legend=:topleft, \n",
    "    fg_color_legend=:white,\n",
    ")\n",
    "plot!(h,1:length(ages),ages,yerror=uncert*2,seriestype=:scatter, markerstrokecolor=:auto, label=\"Observed ages\")\n",
    "plot!(h,[length(ages)],[AgeEst],yerror=2*AgeEst_sigma, markerstrokecolor=:auto, label=\"Bayesian eruption age estimate\",color=:red)\n",
    "plot!(h,collect(xlims()),[AgeEst,AgeEst],color=:red, label=\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a915e17-0590-46af-8ac5-7f433d7b8f60",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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