GammaStateSpace NUTS.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: could not import DistributionsAD._mv_categorical_logpdf into ReverseDiffX\n"
     ]
    }
   ],
   "source": [
    "using Turing, AdvancedVI, Bijectors, Distributions, Random, Plots, LinearAlgebra\n",
    "using ReverseDiff, Memoization\n",
    "\n",
    "Random.seed!(1234);\n",
    "Turing.setadbackend(:reversediff);\n",
    "Turing.setrdcache(true);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "text = readlines(\"SN_y_tot_V2.0.txt\")\n",
    "dataset = []\n",
    "for i=246:length(text)-1\n",
    "    line = text[i]\n",
    "    spot = Int(round(parse(Float64,split(line)[2])))\n",
    "    push!(dataset, spot)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = length(dataset);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "model (generic function with 2 methods)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@model model(y) = begin\n",
    "    n = length(y)\n",
    "    b ~ Gamma(1000,1)\n",
    "    z = Vector{Float64}(undef, N)\n",
    "    z[1] ~ Gamma(1, 1/b) # Shape Scale parameterization in Distributions.jl\n",
    "    y[1] ~ Poisson(z[1])\n",
    "    for i = 2:n\n",
    "        z[i] ~ Gamma(z[i-1], 1/b)\n",
    "        y[i] ~ Poisson(z[i])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Instantiate model\n",
    "sc_model = model(dataset);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Found initial step size\n",
      "│   ϵ = 0.05\n",
      "└ @ Turing.Inference /Users/sakbayrak/.julia/packages/Turing/oas6M/src/inference/hmc.jl:188\n",
      "\u001b[32mSampling: 100%|█████████████████████████████████████████| Time: 0:00:02\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "runtime = @elapsed chain = sample(sc_model, NUTS(200, 0.65), 1000);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.306615576"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "runtime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ids = findall(map(name -> occursin(\"z\", string(name)), names(chain)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_list = []\n",
    "var_list = []\n",
    "for n=2:N+1\n",
    "    push!(mean_list, mean(chain[:,n,:]))\n",
    "    push!(var_list, var(chain[:,n,:]))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(collect(1:N),dataset,color=:black,size=(900,200),legend=:topright, \n",
    "        xtick=([1, 12, 23, 34, 45, 56, 67, 76], [1945, 1956, 1967, 1978, 1989, 2000, 2011, 2020]), \n",
    "        xlabel=\"Years\", ylabel=\"Sunspots\", label=\"Observations\", left_margin = 10Plots.mm, bottom_margin = 5Plots.mm)\n",
    "plot!(mean_list,ribbon=var_list,label=\"Estimations\", lw=2, size=(1000,400),color=:green,fillalpha=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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