Turing HMC vs Gen MH & SMC

GenVsTuring.ipynb

{
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  {
   "cell_type": "code",
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   "source": [
    "using Turing\n",
    "using Gen\n",
    "using MacroTools\n",
    "using MacroTools: prettify\n",
    "using StatsPlots\n",
    "using Statistics\n",
    "using MCMCDiagnostics\n",
    "using StatsBase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "σ = 3\n",
    "μ = 9\n",
    "Y = μ .+ σ*randn(N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "histogram(Y, )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "quote\n",
       "    σ ~ exponential(1)\n",
       "    μ ~ normal(0, 100)\n",
       "    for i = 1:N\n",
       "        y[i] ~ normal(μ, σ)\n",
       "    end\n",
       "end"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prog = quote\n",
    "    σ ~ exponential(1)\n",
    "    μ ~ normal(0, 100)\n",
    "    for i in 1:N\n",
    "        y[i] ~ normal(μ, σ)\n",
    "    end\n",
    "    end |> prettify"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "stan_to_gen (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function stan_to_gen(prog; model_name=\"model\", data=[], ret=nothing)\n",
    "    prog = prog |> prettify\n",
    "    new_expr = Expr(:function)\n",
    "    append!(new_expr.args, [Expr(:call, Symbol(model_name), data...)])\n",
    "    append!(new_expr.args, [Expr(:block)])\n",
    "    for line in prog.args\n",
    "            if @capture(line, a_ = b_)\n",
    "                append!(new_expr.args[2].args, [line])\n",
    "            end\n",
    "            if @capture(line, a_ ~ b_)\n",
    "                if @capture(b, normal(mu_, sig_))\n",
    "                    symbol = QuoteNode(a)\n",
    "                    append!(new_expr.args[2].args, [:($a = @trace($b, $symbol))])\n",
    "                    continue\n",
    "                end\n",
    "                \n",
    "                if @capture(b, exponential(lambda_))\n",
    "                    symbol = QuoteNode(a)\n",
    "                    append!(new_expr.args[2].args, [:($a = @trace($b, $symbol))])\n",
    "                    continue\n",
    "                end\n",
    "            \n",
    "            elseif line.head==:for\n",
    "                inner_block = line.args[2]\n",
    "                inner_expr = Expr(line.head, line.args[1], Expr(:block))\n",
    "                if inner_block.head != :block\n",
    "                    inner_block = [inner_block]\n",
    "                else\n",
    "                    inner_block = inner_block.args\n",
    "                end\n",
    "                for inner_line in inner_block\n",
    "                    if @capture(inner_line, a_ ~ b_)\n",
    "                        if a.head == :ref\n",
    "                            symbol = QuoteNode(a.args[1])\n",
    "                        else\n",
    "                            symbol = QuoteNode(a)\n",
    "                        end\n",
    "                        if @capture(b, normal(mu_, sig_))\n",
    "                            append!(inner_expr.args[2].args, [:(@trace($b, ($symbol, i)))])\n",
    "                            continue\n",
    "                        end\n",
    "                    end\n",
    "                end\n",
    "                append!(new_expr.args[2].args, [inner_expr])\n",
    "            end\n",
    "            \n",
    "    end\n",
    "    if ret != nothing\n",
    "        append!(new_expr.args[2].args, [Expr(:return, ret)])\n",
    "    end\n",
    "    new_call = Expr(:macrocall, Symbol(\"@gen\"), nothing, new_expr)\n",
    "    println(new_call |> prettify)\n",
    "    eval(new_call |> prettify)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "@gen function model()\n",
      "        σ = @trace(exponential(1), :σ)\n",
      "        μ = @trace(normal(0, 100), :μ)\n",
      "        for i = 1:N\n",
      "            @trace normal(μ, σ) (:y, i)\n",
      "        end\n",
      "    end\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DynamicDSLFunction{Any}(Dict{Symbol,Any}(), Dict{Symbol,Any}(), Type[], ##model#368, Bool[], false)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stan_to_gen(prog; data=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "stan_to_turing (generic function with 1 method)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function stan_to_turing(prog; model_name=\"model\", data=[], ret=nothing)\n",
    "    prog = prog |> prettify\n",
    "    new_expr = Expr(:function)\n",
    "    append!(new_expr.args, [Expr(:call, Symbol(model_name), data...)])\n",
    "    append!(new_expr.args, [Expr(:block)])\n",
    "    for line in prog.args\n",
    "            if @capture(line, a_ = b_)\n",
    "                append!(new_expr.args[2].args, [line])\n",
    "            end\n",
    "            if @capture(line, a_ ~ b_)\n",
    "                if @capture(b, normal(mu_, sig_))\n",
    "                    symbol = QuoteNode(a)\n",
    "                    append!(new_expr.args[2].args, [:($a ~ Normal($mu, $sig))])\n",
    "                    continue\n",
    "                end\n",
    "                \n",
    "                if @capture(b, exponential(lambda_))\n",
    "                    symbol = QuoteNode(a)\n",
    "                    append!(new_expr.args[2].args, [:($a ~ Exponential($lambda))])\n",
    "                    continue\n",
    "                end\n",
    "            \n",
    "            elseif line.head==:for\n",
    "                inner_block = line.args[2]\n",
    "                inner_expr = Expr(line.head, line.args[1], Expr(:block))\n",
    "                if inner_block.head != :block\n",
    "                    inner_block = [inner_block]\n",
    "                else\n",
    "                    inner_block = inner_block.args\n",
    "                end\n",
    "                for inner_line in inner_block\n",
    "                    if @capture(inner_line, a_ ~ b_)\n",
    "                        if a.head == :ref\n",
    "                            symbol = QuoteNode(a.args[1])\n",
    "                        else\n",
    "                            symbol = QuoteNode(a)\n",
    "                        end\n",
    "                        if @capture(b, normal(mu_, sig_))\n",
    "                            append!(inner_expr.args[2].args, [:($a ~ Normal($mu, $sig))])\n",
    "                            continue\n",
    "                        end\n",
    "                    end\n",
    "                end\n",
    "                append!(new_expr.args[2].args, [inner_expr])\n",
    "            end\n",
    "            \n",
    "    end\n",
    "    if ret != nothing\n",
    "        append!(new_expr.args[2].args, [Expr(:return, ret)])\n",
    "    end\n",
    "    new_call = Expr(:macrocall, Symbol(\"@model\"), nothing, new_expr)\n",
    "    println(new_call |> prettify)\n",
    "    eval(new_call |> prettify)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "@model function turing_model(y, N)\n",
      "        σ ~ Exponential(1)\n",
      "        μ ~ Normal(0, 100)\n",
      "        for i = 1:N\n",
      "            y[i] ~ Normal(μ, σ)\n",
      "        end\n",
      "        return y\n",
      "    end\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "turing_model (generic function with 3 methods)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stan_to_turing(prog; model_name=\"turing_model\", data=[:y, :N], ret=:y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "infer_turing_hmc (generic function with 2 methods)"
      ]
     },
     "execution_count": 317,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function infer_turing_hmc(my_model, y, n_samples)\n",
    "    Distribution = Turing.Distribution\n",
    "    turing_trace = sample(my_model(y, N), HMC(0.05, 10), n_samples; verbose=false, progress=false)\n",
    "    trace = Dict()\n",
    "    trace[:μ] = reshape(turing_trace[[:μ]].value.data, (n_samples))\n",
    "    trace[:σ] = reshape(turing_trace[[:σ]].value.data, (n_samples))\n",
    "    return trace\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((8.918890428560008, 3.0854815796031008), 8.92825758016632, 3.09775760694777)"
      ]
     },
     "execution_count": 318,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "turing_trace = infer_turing_hmc(turing_model, Y, 1000);\n",
    "(mean(turing_trace[:μ]), mean(turing_trace[:σ])), mean(Y), std(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "infer_gen_mh (generic function with 1 method)"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function infer_gen_mh(my_model, y::Vector{Float64}, num_iters::Int)\n",
    "    # Create a set of constraints fixing the \n",
    "    # y coordinates to the observed y values\n",
    "    constraints = choicemap()\n",
    "    out_trace = Dict()\n",
    "    out_trace[:σ] = []\n",
    "    out_trace[:μ] = []\n",
    "    \n",
    "    for (i, yi) in enumerate(y)\n",
    "        constraints[(:y, i)] = yi\n",
    "    end\n",
    "    (trace, _) = generate(my_model, (), constraints)\n",
    "    for _ in 1:num_iters\n",
    "        (trace, _) = mh(trace, select(:σ))\n",
    "        (trace, _) = mh(trace, select(:μ))\n",
    "        choices = get_choices(trace)\n",
    "        append!(out_trace[:σ], (choices[:σ]))\n",
    "        append!(out_trace[:μ], (choices[:μ]))\n",
    "    end\n",
    "    return out_trace\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "infer_gen_smc (generic function with 1 method)"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function infer_gen_smc(my_model, y::Vector{Float64}, num_samples::Int)\n",
    "    # Create a set of constraints fixing the \n",
    "    # y coordinates to the observed y values\n",
    "    out_trace = Dict()\n",
    "    out_trace[:σ] = []\n",
    "    out_trace[:μ] = []\n",
    "    init_constraints = choicemap()\n",
    "    \n",
    "    for (i, yi) in enumerate(y)\n",
    "        init_constraints[(:y, i)] = yi\n",
    "    end\n",
    "    state = Gen.initialize_particle_filter(my_model, (), init_constraints, 5000)\n",
    "    traces =  Gen.sample_unweighted_traces(state, num_samples)\n",
    "    trace = Dict()\n",
    "    trace[:μ] = [traces[i][:μ] for i=1:length(traces)]\n",
    "    trace[:σ] = [traces[i][:σ] for i=1:length(traces)]\n",
    "    trace\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((9.284254745292289, 2.9782889955337515), 8.92825758016632, 3.09775760694777)"
      ]
     },
     "execution_count": 298,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace = infer_gen_smc(model, Y, 1000)\n",
    "(mean(trace[:μ]), mean(trace[:σ])), mean(Y), std(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((8.77389110818249, 3.1994190197437042), 8.92825758016632, 3.09775760694777)"
      ]
     },
     "execution_count": 299,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace = infer_gen_mh(model, Y, 1000)\n",
    "(mean(trace[:μ]), mean(trace[:σ])), mean(Y), std(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation Based Calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "generate_samples_from_prior (generic function with 1 method)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function generate_samples_from_prior(n_samples)\n",
    "    σ =  rand(Exponential(1), n_samples)\n",
    "    μ = rand(Normal(0, 1), n_samples)\n",
    "    return Dict(:σ => σ, :μ => μ)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "conditioned_generator_turing (generic function with 2 methods)"
      ]
     },
     "execution_count": 308,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function conditioned_generator_turing(Θ, my_model, N)\n",
    "#     Couldn't find any easy way to do this\n",
    "    ys = []\n",
    "    for i=1:length(Θ[collect(keys(Θ))[1]])\n",
    "        append!(ys, [rand(Normal(Θ[:μ][i], Θ[:σ][i]), N)])\n",
    "    end\n",
    "    ys\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "conditioned_generator_gen (generic function with 2 methods)"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function conditioned_generator_gen(Θ, my_model, N)\n",
    "    constraints = choicemap()\n",
    "    ys = []\n",
    "    for i=1:length(Θ[collect(keys(Θ))[1]])\n",
    "        for var in keys(Θ)\n",
    "            constraints[var] = Θ[var][i]\n",
    "        end\n",
    "        (trace, _) = generate(my_model, (), constraints)\n",
    "        y_ = [trace[(:y, i)] for i in 1:N]\n",
    "        append!(ys, [y_])\n",
    "    end\n",
    "    return ys\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {},
   "outputs": [],
   "source": [
    "# conditioned_generator(Dict(:μ=>[9, 90], :σ=>[3, 3]), model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "find_rank (generic function with 1 method)"
      ]
     },
     "execution_count": 314,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function find_rank(elem, array, ≺)\n",
    "    sort!(array, lt=≺)\n",
    "    rank = 0\n",
    "    for a in array\n",
    "        if elem ≺ a\n",
    "            break\n",
    "        end\n",
    "        rank+=1\n",
    "    end        \n",
    "    return rank\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SBC (generic function with 3 methods)"
      ]
     },
     "execution_count": 335,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function SBC(L::Int, N, conditioned_generator, my_inference_program, my_model)\n",
    "    ranks = []\n",
    "    L_dash = L\n",
    "    for n in 1:N\n",
    "        print(n, \" \")\n",
    "        Θ = generate_samples_from_prior(1)\n",
    "        ỹ = conditioned_generator(Θ, my_model, N)[1]\n",
    "        trace = my_inference_program(my_model, ỹ, L_dash)\n",
    "        ESS = effective_sample_size(trace[:μ])\n",
    "        if ESS<L\n",
    "            trace = my_inference_program(my_model, ỹ, Int(floor(L_dash*L/ESS)))\n",
    "            trace[:μ] = sample(trace[:μ], L)\n",
    "            trace[:σ] = sample(trace[:σ], L)\n",
    "            append!(ranks, find_rank(Θ[:μ][1], trace[:μ], <))\n",
    "            continue\n",
    "        end\n",
    "        append!(ranks, find_rank(Θ[:μ][1], trace[:μ], <))\n",
    "    end\n",
    "    return ranks\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chi_Squared_Test (generic function with 1 method)"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Chi_Squared_Test(ranks, m)\n",
    "    Obs = fit(Histogram, ranks, 0:m).weights\n",
    "    Exp = (length(ranks)/m)*ones(length(Obs))\n",
    "    sum(((Obs-Exp).^2 ./ Exp))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 50\n",
    "N_ = 100\n",
    "\n",
    "SBC(Int(L), N_, conditioned_generator_turing, infer_turing_hmc, turing_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 50\n",
    "N_ = 100\n",
    "\n",
    "chis = []\n",
    "for L in 100:100:1000\n",
    "    ranks  = SBC(Int(L), N_, :hmc)\n",
    "    Exp = collect(Iterators.flatten([i*ones(Int(round(N_/(L+1)))) for i in 0:L]));\n",
    "    chi = Chi_Squared_Test(ranks, L)\n",
    "    println(L, \" \", chi)\n",
    "    append!(chis, [chi])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Exp = collect(Iterators.flatten([i*ones(Int(round(N_/(L+1)))) for i in 0:L]))\n",
    "histogram(ranks, bins=L+1)\n",
    "histogram!(Exp, bins=L+1, color=\"grey\", alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SRS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((9.007806798592817, 0.9823079315739186), 8.92825758016632, 3.09775760694777)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace = my_inference_program(model, Y, 200)\n",
    "(mean(trace[:μ]), mean(trace[:σ])), mean(Y), std(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "≺ (generic function with 1 method)"
      ]
     },
     "execution_count": 300,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Total Ordering\n",
    "≺(a, b) = a<b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SRS (generic function with 2 methods)"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function SRS(ground_truth_samples, model, theta, ≺, conditioned_generator)\n",
    "    r = []\n",
    "    for sample in ground_truth_samples\n",
    "        X = conditioned_generator(theta, model)[1]\n",
    "        append!(r, sum(X.≺sample))\n",
    "    end\n",
    "    r\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "σ = 3\n",
    "μ = 9\n",
    "Y = μ .+ σ*randn(N);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampling...\n",
      "Done Sampling\n"
     ]
    }
   ],
   "source": [
    "mh_chis = []\n",
    "println(\"Sampling...\")\n",
    "trace = infer_gen_mh(model, Y, 2000)\n",
    "println(\"Done Sampling\")\n",
    "mh_mcmc_steps_list = 10:10:2000\n",
    "for mcmc_steps = mh_mcmc_steps_list\n",
    "    rank = SRS(Y, model, Dict(:μ=>mean(trace[:μ][1:mcmc_steps]), :σ=>mean(trace[:σ][1:mcmc_steps])), ≺, conditioned_generator_gen);\n",
    "    chi = Chi_Squared_Test(rank, N)\n",
    "    append!(mh_chis, chi)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampling...\n",
      "Done Sampling\n"
     ]
    }
   ],
   "source": [
    "smc_chis = []\n",
    "println(\"Sampling...\")\n",
    "trace = infer_gen_smc(model, Y, 2000)\n",
    "println(\"Done Sampling\")\n",
    "smc_mcmc_steps_list = 10:10:2000\n",
    "for mcmc_steps = smc_mcmc_steps_list\n",
    "    rank = SRS(Y, model, Dict(:μ=>mean(trace[:μ][1:mcmc_steps]), :σ=>mean(trace[:σ][1:mcmc_steps])), ≺, conditioned_generator_gen);\n",
    "    chi = Chi_Squared_Test(rank, N)\n",
    "    append!(smc_chis, chi)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampling...\n",
      "Done Sampling\n"
     ]
    }
   ],
   "source": [
    "hmc_chis = []\n",
    "println(\"Sampling...\")\n",
    "trace = infer_turing_hmc(turing_model, Y, 2000)\n",
    "println(\"Done Sampling\")\n",
    "hmc_mcmc_steps_list = 10:10:2000\n",
    "for mcmc_steps = hmc_mcmc_steps_list\n",
    "    rank = SRS(Y, model, Dict(:μ=>mean(trace[:μ][1:mcmc_steps]), :σ=>mean(trace[:σ][1:mcmc_steps])), ≺, conditioned_generator_turing);\n",
    "    chi = Chi_Squared_Test(rank, N)\n",
    "    append!(hmc_chis, chi)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [
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       "<g clip-path=\"url(#clip3000)\">\n",
       "<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1863.71, 208.744)\" x=\"1863.71\" y=\"208.744\">MH from Gen</text>\n",
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       "</svg>\n"
      ]
     },
     "execution_count": 349,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(mh_mcmc_steps_list, mh_chis, xaxis=\"Number of Samples\", yaxis=\"Non-Uniformity of SRS\", label=\"MH from Gen\")\n",
    "plot!(smc_mcmc_steps_list, smc_chis, xaxis=\"Number of Samples\", yaxis=\"Non-Uniformity of SRS\", label=\"SMC from Gen\")\n",
    "plot!(hmc_mcmc_steps_list, hmc_chis, xaxis=\"Number of Samples\", yaxis=\"Non-Uniformity of SRS\", label=\"HMC from Turing\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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