doctest failure in ~/.julia/packages/PSIS/fU76x/src/core.jl:212-233 ```jldoctest psis; setup = :(using Random; Random.seed!(42)) julia> using Distributions julia> proposal, target = Normal(), TDist(7); julia> x = rand(proposal, 1_000, 1, 30); # (ndraws, nchains, nparams) julia> log_ratios = @. logpdf(target, x) - logpdf(proposal, x); julia> result = psis(log_ratios) ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— ``` Subexpression: result = psis(log_ratios) Evaluated output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— Expected output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— diff = Warning: Diff output requires color. ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) ——

doctest failure in ~/.julia/packages/PSIS/fU76x/src/core.jl:238-255 ```jldoctest psis julia> using MCMCDiagnosticTools julia> reff = ess(log_ratios; kind=:basic, split_chains=1, relative=true); julia> result = psis(log_ratios, reff) ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— ``` Subexpression: result = psis(log_ratios, reff) Evaluated output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— Expected output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— diff = Warning: Diff output requires color. ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) ——

doctest failure in ~/.julia/packages/PSIS/fU76x/src/core.jl:212-233 ```jldoctest psis; setup = :(using Random; Random.seed!(42)) julia> using Distributions julia> proposal, target = Normal(), TDist(7); julia> x = rand(proposal, 1_000, 1, 30); # (ndraws, nchains, nparams) julia> log_ratios = @. logpdf(target, x) - logpdf(proposal, x); julia> result = psis(log_ratios) ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— ``` Subexpression: result = psis(log_ratios) Evaluated output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— Expected output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— diff = Warning: Diff output requires color. ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (23.3%) 959 (0.5, 0.7] okay 13 (43.3%) 938 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) ——

doctest failure in ~/.julia/packages/PSIS/fU76x/src/core.jl:238-255 ```jldoctest psis julia> using MCMCDiagnosticTools julia> reff = ess(log_ratios; kind=:basic, split_chains=1, relative=true); julia> result = psis(log_ratios, reff) ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— ``` Subexpression: result = psis(log_ratios, reff) Evaluated output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— Expected output: ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) —— diff = Warning: Diff output requires color. ┌ Warning: 9 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ┌ Warning: 1 parameters had Pareto shape values k > 1. Corresponding importance sampling estimates are likely to be unstable and are unlikely to converge with additional samples. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:376 PSISResult with 1000 draws, 1 chains, and 30 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 9 (30.0%) 806 (0.5, 0.7] okay 11 (36.7%) 842 (0.7, 1] bad 9 (30.0%) —— (1, Inf) very bad 1 (3.3%) ——

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/model_weights.jl:38-57 ```jldoctest model_weights; filter = [r"└.*"] julia> using ArviZExampleData julia> models = ( centered=load_example_data("centered_eight"), non_centered=load_example_data("non_centered_eight"), ); julia> elpd_results = map(models) do idata log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1)) return loo(log_like) end; ┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... julia> model_weights(elpd_results; method=Stacking()) |> pairs pairs(::NamedTuple) with 2 entries: :centered => 5.34175e-19 :non_centered => 1.0 ``` Subexpression: model_weights(elpd_results; method=Stacking()) |> pairs Evaluated output: pairs(::NamedTuple) with 2 entries: :centered => 3.50538e-31 :non_centered => 1.0 Expected output: pairs(::NamedTuple) with 2 entries: :centered => 5.34175e-19 :non_centered => 1.0 diff = Warning: Diff output requires color. pairs(::NamedTuple) with 2 entries: :centered => 5.34175e-19 3.50538e-31 :non_centered => 1.0

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/model_weights.jl:61-66 ```jldoctest model_weights; setup = :(using Random; Random.seed!(94)) julia> model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs pairs(::NamedTuple) with 2 entries: :centered => 0.483723 :non_centered => 0.516277 ``` Subexpression: model_weights(elpd_results; method=BootstrappedPseudoBMA()) |> pairs Evaluated output: pairs(::NamedTuple) with 2 entries: :centered => 0.492513 :non_centered => 0.507487 Expected output: pairs(::NamedTuple) with 2 entries: :centered => 0.483723 :non_centered => 0.516277 diff = Warning: Diff output requires color. pairs(::NamedTuple) with 2 entries: :centered => 0.483723 0.492513 :non_centered => 0.5162770.507487

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/compare.jl:35-60 ```jldoctest compare; filter = [r"└.*"] julia> using ArviZExampleData julia> models = ( centered=load_example_data("centered_eight"), non_centered=load_example_data("non_centered_eight"), ); julia> function myloo(idata) log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1)) return loo(log_like) end; julia> mc = compare(models; elpd_method=myloo) ┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ModelComparisonResult with Stacking weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯ 1 column omitted julia> mc.weight |> pairs pairs(::NamedTuple) with 2 entries: :non_centered => 1.0 :centered => 5.34175e-19 ``` Subexpression: mc = compare(models; elpd_method=myloo) Evaluated output: ┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ModelComparisonResult with Stacking weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.5 0 0.0 1.0 0.9 ⋯ centered 2 -31 1.4 0.03 0.061 0.0 0.9 ⋯ 1 column omitted Expected output: ┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ModelComparisonResult with Stacking weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯ 1 column omitted diff = Warning: Diff output requires color. ┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ~/.julia/packages/PSIS/fU76x/src/core.jl:373 ModelComparisonResult with Stacking weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 1.5 0 0.0 1.0 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.03 0.061 0.0 0.9 ⋯ 1 column omitted

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/compare.jl:35-60 ```jldoctest compare; filter = [r"└.*"] julia> using ArviZExampleData julia> models = ( centered=load_example_data("centered_eight"), non_centered=load_example_data("non_centered_eight"), ); julia> function myloo(idata) log_like = PermutedDimsArray(idata.log_likelihood.obs, (2, 3, 1)) return loo(log_like) end; julia> mc = compare(models; elpd_method=myloo) ┌ Warning: 1 parameters had Pareto shape values 0.7 < k ≤ 1. Resulting importance sampling estimates are likely to be unstable. └ @ PSIS ~/.julia/packages/PSIS/... ModelComparisonResult with Stacking weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 0 0.0 1.0 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.0 0.9 ⋯ 1 column omitted julia> mc.weight |> pairs pairs(::NamedTuple) with 2 entries: :non_centered => 1.0 :centered => 5.34175e-19 ``` Subexpression: mc.weight |> pairs Evaluated output: pairs(::NamedTuple) with 2 entries: :non_centered => 1.0 :centered => 3.50538e-31 Expected output: pairs(::NamedTuple) with 2 entries: :non_centered => 1.0 :centered => 5.34175e-19 diff = Warning: Diff output requires color. pairs(::NamedTuple) with 2 entries: :non_centered => 1.0 :centered => 5.34175e-193.50538e-31

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/compare.jl:65-74 ```jldoctest compare; setup = :(using Random; Random.seed!(23)) julia> elpd_results = mc.elpd_result; julia> compare(elpd_results; weights_method=BootstrappedPseudoBMA()) ModelComparisonResult with BootstrappedPseudoBMA weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯ 1 column omitted ``` Subexpression: compare(elpd_results; weights_method=BootstrappedPseudoBMA()) Evaluated output: ModelComparisonResult with BootstrappedPseudoBMA weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.5 0 0.0 0.51 0.9 ⋯ centered 2 -31 1.4 0.03 0.061 0.49 0.9 ⋯ 1 column omitted Expected output: ModelComparisonResult with BootstrappedPseudoBMA weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 0 0.0 0.52 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.48 0.9 ⋯ 1 column omitted diff = Warning: Diff output requires color. ModelComparisonResult with BootstrappedPseudoBMA weights rank elpd elpd_mcse elpd_diff elpd_diff_mcse weight p ⋯ non_centered 1 -31 1.4 1.5 0 0.0 0.52 0.51 0.9 ⋯ centered 2 -31 1.4 0.06 0.067 0.48 0.03 0.061 0.49 0.9 ⋯ 1 column omitted