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/waic.jl:48-59 ```jldoctest julia> using ArviZExampleData julia> idata = load_example_data("centered_eight"); julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school)); julia> waic(log_like) WAICResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.33 ``` Subexpression: waic(log_like) Evaluated output: WAICResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.32 Expected output: WAICResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.33 diff = Warning: Diff output requires color. WAICResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.330.32

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/loo_pit.jl:47-74 ```jldoctest loo_pit1 julia> using ArviZExampleData julia> idata = load_example_data("centered_eight"); julia> y = idata.observed_data.obs; julia> y_pred = PermutedDimsArray(idata.posterior_predictive.obs, (:draw, :chain, :school)); julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school)); julia> log_weights = loo(log_like).psis_result.log_weights; julia> loo_pit(y, y_pred, log_weights) ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.943511 "Deerfield" 0.63797 "Phillips Andover" 0.316697 "Phillips Exeter" 0.582252 "Hotchkiss" 0.295321 "Lawrenceville" 0.403318 "St. Paul's" 0.902508 "Mt. Hermon" 0.655275 ``` Subexpression: loo_pit(y, y_pred, log_weights) Evaluated output: ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.942759 "Deerfield" 0.641057 "Phillips Andover" 0.32729 "Phillips Exeter" 0.581451 "Hotchkiss" 0.288523 "Lawrenceville" 0.393741 "St. Paul's" 0.886175 "Mt. Hermon" 0.638821 Expected output: ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.943511 "Deerfield" 0.63797 "Phillips Andover" 0.316697 "Phillips Exeter" 0.582252 "Hotchkiss" 0.295321 "Lawrenceville" 0.403318 "St. Paul's" 0.902508 "Mt. Hermon" 0.655275 diff = Warning: Diff output requires color. ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.943511 0.942759 "Deerfield" 0.63797 0.641057 "Phillips Andover" 0.316697 0.32729 "Phillips Exeter" 0.582252 0.581451 "Hotchkiss" 0.295321 0.288523 "Lawrenceville" 0.403318 0.393741 "St. Paul's" 0.902508 0.886175 "Mt. Hermon" 0.6552750.638821

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/loo_pit.jl:79-102 ```jldoctest loo_pit1 julia> using Statistics julia> mu = idata.posterior.mu; julia> T = y .- median(mu); julia> T_pred = y_pred .- mu; julia> loo_pit(T .^ 2, T_pred .^ 2, log_weights) ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.873577 "Deerfield" 0.243686 "Phillips Andover" 0.357563 "Phillips Exeter" 0.149908 "Hotchkiss" 0.435094 "Lawrenceville" 0.220627 "St. Paul's" 0.775086 "Mt. Hermon" 0.296706 ``` Subexpression: loo_pit(T .^ 2, T_pred .^ 2, log_weights) Evaluated output: ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.868148 "Deerfield" 0.27421 "Phillips Andover" 0.321719 "Phillips Exeter" 0.193169 "Hotchkiss" 0.370422 "Lawrenceville" 0.195601 "St. Paul's" 0.817408 "Mt. Hermon" 0.326795 Expected output: ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.873577 "Deerfield" 0.243686 "Phillips Andover" 0.357563 "Phillips Exeter" 0.149908 "Hotchkiss" 0.435094 "Lawrenceville" 0.220627 "St. Paul's" 0.775086 "Mt. Hermon" 0.296706 diff = Warning: Diff output requires color. ╭───────────────────────────────╮ │ 8-element DimArray{Float64,1} │ ├───────────────────────────────┴──────────────────────────────────────── dims ┐ ↓ school Categorical{String} [Choate, Deerfield, …, St. Paul's, Mt. Hermon] Unordered └──────────────────────────────────────────────────────────────────────────────┘ "Choate" 0.873577 0.868148 "Deerfield" 0.243686 0.27421 "Phillips Andover" 0.357563 0.321719 "Phillips Exeter" 0.149908 0.193169 "Hotchkiss" 0.435094 0.370422 "Lawrenceville" 0.220627 0.195601 "St. Paul's" 0.775086 0.817408 "Mt. Hermon" 0.2967060.326795

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/loo.jl:62-81 ```jldoctest julia> using ArviZExampleData, MCMCDiagnosticTools julia> idata = load_example_data("centered_eight"); julia> log_like = PermutedDimsArray(idata.log_likelihood.obs, (:draw, :chain, :school)); julia> reff = ess(log_like; kind=:basic, split_chains=1, relative=true); julia> loo(log_like; reff) PSISLOOResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.34 and PSISResult with 500 draws, 4 chains, and 8 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (87.5%) 151 (0.5, 0.7] okay 1 (12.5%) 446 ``` Subexpression: loo(log_like; reff) Evaluated output: PSISLOOResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.33 and PSISResult with 500 draws, 4 chains, and 8 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 5 (62.5%) 290 (0.5, 0.7] okay 3 (37.5%) 399 Expected output: PSISLOOResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.34 and PSISResult with 500 draws, 4 chains, and 8 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (87.5%) 151 (0.5, 0.7] okay 1 (12.5%) 446 diff = Warning: Diff output requires color. PSISLOOResult with estimates elpd elpd_mcse p p_mcse -31 1.4 0.9 0.34 0.33 and PSISResult with 500 draws, 4 chains, and 8 parameters Pareto shape (k) diagnostic values: Count Min. ESS (-Inf, 0.5] good 7 (87.5%) 151 5 (62.5%) 290 (0.5, 0.7] okay 1 (12.5%) 4463 (37.5%) 399

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/summarize.jl:189-200 ```jldoctest summarize; setup = (using Random; Random.seed!(84)) julia> using Statistics, StatsBase julia> x = randn(1000, 4, 3) .+ reshape(0:10:20, 1, 1, :); julia> summarize(x, mean, std, :mcse_mean => sem; name="Mean/Std") Mean/Std mean std mcse_mean 1 0.0003 0.990 0.016 2 10.02 0.988 0.016 3 19.98 0.988 0.016 ``` Subexpression: summarize(x, mean, std, :mcse_mean => sem; name="Mean/Std") Evaluated output: Mean/Std mean std mcse_mean 1 0.0003 0.989 0.016 2 10.02 0.988 0.016 3 19.98 0.988 0.016 Expected output: Mean/Std mean std mcse_mean 1 0.0003 0.990 0.016 2 10.02 0.988 0.016 3 19.98 0.988 0.016 diff = Warning: Diff output requires color. Mean/Std mean std mcse_mean 1 0.0003 0.990 0.989 0.016 2 10.02 0.988 0.016 3 19.98 0.988 0.016