def cumulative_mean(title,
samples,
time,
μ,
stepsize,
post,
plot,
legend_pos=None):
nplot = len(samples)
nsample = len(time)
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("Time")
axis.set_ylabel(r"$μ$")
axis.set_title(title)
axis.set_xlim([10.0, nsample])
axis.semilogx(time,
numpy.full((len(time)), μ),
label="Target μ",
color="#000000")
for i in range(nplot):
axis.semilogx(time,
stats.cummean(samples[i]),
label=f"stepsize={format(stepsize[i], '2.2f')}")
if legend_pos is None:
axis.legend()
else:
axis.legend(bbox_to_anchor=legend_pos)
config.save_post_asset(figure, post, plot)
def cumulative_mean(title, samples, time, μ, ylim, file):
nsample = len(time)
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("Time")
axis.set_ylabel(r"$μ$")
axis.set_title(title)
axis.set_ylim(ylim)
axis.set_xlim([10.0, nsample])
axis.semilogx(time,
numpy.full((len(time)), μ),
label="Target μ",
color="#000000")
axis.semilogx(time, stats.cummean(samples))
config.save_post_asset(figure, "hamiltonian_monte_carlo", file)
def mean_convergence(title, samples, μ, plot_name):
nsamples = len(samples)
time = range(nsamples)
figure, axis = pyplot.subplots(figsize=(10, 6))
axis.set_xlabel("Sample Number")
axis.set_ylabel("μ")
axis.set_title(title)
axis.set_xlim([1.0, nsamples])
axis.set_ylim( [0.5, 1.5])
cmean = stats.cummean(samples)
μs = numpy.full(len(samples), μ)
axis.semilogx(time, μs, label="Target μ")
axis.semilogx(time, cmean, label="Sampled μ")
axis.legend(bbox_to_anchor=([0.9, 0.9]))
config.save_post_asset(figure, "rejection_sampling", plot_name)
# %%
μ = 0.5
sample_idx = [0]
title = f"Arcsine Distribution, Uniform Proposal, sample μ"
time = range(nsample)
mean_samples = all_samples[0][time]
figure, axis = pyplot.subplots(figsize=(12, 6))
axis.set_xlabel("Time")
axis.set_ylabel(r"$μ$")
axis.set_title(title)
axis.set_xlim([10.0, nsample])
axis.semilogx(time, numpy.full((len(time)), μ), label="Target μ", color="#000000")
axis.semilogx(time, stats.cummean(samples), label=f"Samples")
axis.legend()
# %%
σ = numpy.sqrt(0.125)
title = f"Arcsine Distribution, Uniform Proposal, sample σ convergence"
time = range(nsample)
sigma_samples = all_samples[0]
figure, axis = pyplot.subplots(figsize=(12, 6))
axis.set_xlabel("Time")
axis.set_ylabel(r"$σ$")
axis.set_title(title)
axis.set_xlim([1.0, nsample])
axis.semilogx(time, numpy.full((len(time)), σ), label="Target σ", color="#000000")
μ = stats.weibull_mean(k, λ)
title = r"Weibull Target, Normal Proposal, $μ_E$ Convergence: " + f"stepsize={format(stepsize, '2.2f')}"
time = range(nsample)
nplot = len(all_samples)
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("Time")
axis.set_ylabel(r"$μ$")
axis.set_title(title)
axis.set_xlim([1.0, nsample])
axis.set_ylim([-0.2, 3.7])
axis.yaxis.set_ticks([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5])
axis.semilogx(time, numpy.full(nsample, μ), label="Target μ", color="#000000")
for i in range(nplot):
axis.semilogx(time, stats.cummean(all_samples[i]), label=r"$X_0$="+f"{format(x0[i], '2.1f')}")
axis.legend(bbox_to_anchor=(0.9, 0.95))
config.save_post_asset(figure, "metropolis_hastings_sampling", "normal_proposal_burnin-mean-convergence")
# %%
σ = stats.weibull_sigma(k, λ)
title = r"Weibull Target, Normal Proposal, $σ_E$ Convergence: " + f"stepsize={format(stepsize, '2.2f')}"
time = range(nsample)
nplot = len(all_samples)
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("Time")
axis.set_ylabel(r"$σ$")
axis.set_title(title)
axis.set_xlim([1.0, nsample])
μ = stats.weibull_mean(k, λ)
title = r"Thinned Weibull Target, Normal Proposal, $μ_E$ Convergence: " + f"stepsize={format(stepsize, '2.2f')}, " + r"$X_0$="+f"{format(x0, '2.1f')}"
nplot = len(all_samples)
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("Time")
axis.set_ylabel(r"$μ$")
axis.set_title(title)
axis.set_xlim([1.0, nsample])
axis.set_ylim([0.4, 1.2])
axis.yaxis.set_ticks([0.5, 0.75, 1.0])
axis.semilogx(range(0, nsample - burn_in), numpy.full(nsample - burn_in, μ), label="Target μ", color="#000000")
for i in range(nplot):
thinned_range = range(burn_in, nsample, i+1)
mean = stats.cummean(all_samples[0][thinned_range])
axis.semilogx(range(len(mean)), mean, label=f"η={format(i+1, '2.0f')}")
axis.legend(bbox_to_anchor=(0.95, 0.5))
config.save_post_asset(figure, "metropolis_hastings_sampling", "normal_proposal_thinning-mean-convergence")
# %%
σ = stats.weibull_sigma(k, λ)
title = r"Thinned Weibull Target, Normal Proposal, $σ_E$ Convergence: " + f"stepsize={format(stepsize, '2.2f')}, " + r"$X_0$="+f"{format(x0, '2.1f')}"
nplot = len(all_samples)
figure, axis = pyplot.subplots(figsize=(10, 7))
axis.set_xlabel("Time")
axis.set_ylabel(r"$μ$")
axis.set_title(title)
axis.set_xlim([1.0, nsample])
# %%
μ = discrete_mean(df)
title = f"Sampled Discrete Distribution μ Convergence"
x = range(nsamples)
figure, axis = pyplot.subplots(figsize=(10, 6))
axis.set_xlabel("Sample Number")
axis.set_ylabel("μ")
axis.set_title(title)
axis.set_xlim([1.0, nsamples])
axis.set_ylim([0.0, 6.0])
axis.set_yticks([1.0, 2.0, 3.0, 4.0, 5.0])
axis.semilogx(x, numpy.full(nsamples, μ), label="Target μ")
axis.semilogx(x, stats.cummean(df_samples), label="Sampled μ")
axis.legend(bbox_to_anchor=(1.0, 0.85))
config.save_post_asset(figure, "inverse_cdf_sampling", "discrete_sampled_mean_convergence")
# %%
σ = discrete_sigma(df)
title = f"Sampled Discrete Distribution σ Convergence"
x = range(nsamples)
figure, axis = pyplot.subplots(figsize=(10, 6))
axis.set_xlabel("Sample Number")
axis.set_ylabel("σ")
axis.set_title(title)
axis.set_xlim([1.0, nsamples])
axis.set_ylim([0.0, 3.0])