Created
April 11, 2019 13:00
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RS after MCMC
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using Distributions | |
K = 10^5 | |
μ1 = 1.0 | |
μ2 = -1.0 | |
σ1 = σ2 = 0.3 | |
args = (μ1 = μ1, σ1 = σ1, μ2 = μ2, σ2 = σ2) | |
lp(x, args) = log(pdf(Normal(args.μ1, args.σ2), x) + pdf(Normal(args.μ2, args.σ2), x)) | |
function mcmc!(xs, x, (lp, args), Q, s, S, verbose = false) | |
while s < last(S) | |
xᵒ = rand(Q(x)) | |
lα = lp(xᵒ, args) - lp(x, args) + logpdf(Q(xᵒ), x) - logpdf(Q(x), xᵒ) | |
verbose && print("$lα $xᵒ") | |
if rand() < exp(lα) | |
x = xᵒ | |
verbose && print("✓") | |
end | |
verbose && println() | |
s += 1 | |
if s in S | |
push!(xs, x) | |
end | |
end | |
xs, x | |
end | |
xs, _ = mcmc!(Float64[], 0.0, (lp, args), x->Normal(x, 0.1), 0, 0:K) | |
std(xs) | |
function wmcmc!(xs, x, (lp, args), Q, s, S; weight=(x->1.0, 1.0), verbose = false) | |
f, fmin = weight | |
while s < last(S) | |
xᵒ = rand(Q(x)) | |
lα = log(f(xᵒ)) - log(f(x)) + lp(xᵒ, args) - lp(x, args) + logpdf(Q(xᵒ), x) - logpdf(Q(x), xᵒ) | |
verbose && print("$lα $xᵒ") | |
if rand() <= exp(lα) | |
x = xᵒ | |
verbose && print("✓") | |
end | |
verbose && println() | |
s += 1 | |
if s in S | |
if rand() <= fmin/f(x) | |
push!(xs, x) | |
end | |
end | |
end | |
xs, x | |
end | |
xs2, _ = wmcmc!(Float64[], 0.0, (lp, args), x->Normal(x, 0.1), 0, 0:K, weight=(x->0.1 + pdf(Normal(0.0, 0.5),x), 0.1)) |
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