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sharanry/GenVsTuring.ipynb

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Turing HMC vs Gen MH & SMC
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GenVsTuring.ipynb
{
"cells": [
{
"cell_type": "code",
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"metadata": {},
"outputs": [],
"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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"metadata": {},
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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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" 1195.31,1307.98 1205.37,1359.39 1215.44,1344.27 1225.51,1301.93 1235.57,1301.93 1245.64,1301.93 1255.71,1304.96 1265.78,1247.5 1275.84,1277.74 1285.91,1208.19 \n",
" 1295.98,1292.86 1306.05,1223.31 1316.11,1286.81 1326.18,1223.31 1336.25,1311.01 1346.32,1271.69 1356.38,1304.96 1366.45,1268.67 1376.52,1283.79 1386.59,1250.52 \n",
" 1396.65,1286.81 1406.72,1214.24 1416.79,1304.96 1426.86,1271.69 1436.92,1307.98 1446.99,1338.22 1457.06,1232.38 1467.13,1244.48 1477.19,1262.62 1487.26,1274.72 \n",
" 1497.33,1307.98 1507.4,1259.6 1517.46,1304.96 1527.53,1283.79 1537.6,1298.91 1547.66,1247.5 1557.73,1241.45 1567.8,1235.4 1577.87,1214.24 1587.93,1347.3 \n",
" 1598,1320.08 1608.07,1268.67 1618.14,1223.31 1628.2,1307.98 1638.27,1289.84 1648.34,1280.77 1658.41,1317.05 1668.47,1241.45 1678.54,1344.27 1688.61,1247.5 \n",
" 1698.68,1311.01 1708.74,1238.43 1718.81,1280.77 1728.88,1289.84 1738.95,1298.91 1749.01,1338.22 1759.08,1250.52 1769.15,1277.74 1779.22,1268.67 1789.28,1226.33 \n",
" 1799.35,1265.64 1809.42,1311.01 1819.48,1274.72 1829.55,1280.77 1839.62,1311.01 1849.69,1277.74 1859.75,1217.26 1869.82,1298.91 1879.89,1311.01 1889.96,1262.62 \n",
" 1900.02,1347.3 1910.09,1247.5 1920.16,1301.93 1930.23,1223.31 1940.29,1317.05 1950.36,1329.15 1960.43,1277.74 1970.5,1298.91 1980.56,1220.28 1990.63,1323.1 \n",
" 2000.7,1174.92 2010.77,1280.77 2020.83,1277.74 2030.9,1174.92 2040.97,1232.38 2051.04,1250.52 2061.1,1314.03 2071.17,1353.34 2081.24,1289.84 2091.31,1268.67 \n",
" 2101.37,1332.17 2111.44,1256.57 2121.51,1323.1 2131.57,1292.86 2141.64,1256.57 2151.71,1338.22 2161.78,1274.72 2171.84,1295.89 2181.91,1286.81 2191.98,1283.79 \n",
" 2202.05,1317.05 2212.11,1326.13 2222.18,1301.93 2232.25,1271.69 2242.32,1156.78 2252.38,1292.86 2262.45,1347.3 2272.52,1314.03 2282.59,1259.6 2292.65,1238.43 \n",
" \n",
" \"/>\n",
"<path clip-path=\"url(#clip3000)\" d=\"\n",
"M1671.71 372.684 L2280.76 372.684 L2280.76 130.764 L1671.71 130.764 Z\n",
" \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<polyline clip-path=\"url(#clip3000)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1671.71,372.684 2280.76,372.684 2280.76,130.764 1671.71,130.764 1671.71,372.684 \n",
" \"/>\n",
"<polyline clip-path=\"url(#clip3000)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1695.71,191.244 1839.71,191.244 \n",
" \"/>\n",
"<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",
"</g>\n",
"<polyline clip-path=\"url(#clip3000)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1695.71,251.724 1839.71,251.724 \n",
" \"/>\n",
"<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, 269.224)\" x=\"1863.71\" y=\"269.224\">SMC from Gen</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3000)\" style=\"stroke:#3da44d; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1695.71,312.204 1839.71,312.204 \n",
" \"/>\n",
"<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, 329.704)\" x=\"1863.71\" y=\"329.704\">HMC from Turing</text>\n",
"</g>\n",
"</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": []
}
],
"metadata": {
"@webio": {
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},
"kernelspec": {
"display_name": "Julia 1.1.0",
"language": "julia",
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