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/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

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/summarize.jl:203-210 ```jldoctest summarize julia> summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c]) SummaryStats mean std mad a 0.000305 0.990 0.978 b 10.0 0.988 0.995 c 20.0 0.988 0.979 ``` Subexpression: summarize(x, (:mean, :std) => mean_and_std, mad; var_names=[:a, :b, :c]) Evaluated output: SummaryStats mean std mad a 0.000275 0.989 0.978 b 10.0 0.988 0.995 c 20.0 0.988 0.979 Expected output: SummaryStats mean std mad a 0.000305 0.990 0.978 b 10.0 0.988 0.995 c 20.0 0.988 0.979 diff = Warning: Diff output requires color. SummaryStats mean std mad a 0.000305 0.990 0.000275 0.989 0.978 b 10.0 0.988 0.995 c 20.0 0.988 0.979

doctest failure in ~/.julia/packages/PosteriorStats/cl4WO/src/summarize.jl:228-235 ```jldoctest summarize julia> summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c]) SummaryStats mean std hdi_5.5% hdi_94.5% a 0.000305 0.990 -1.63 1.52 b 10.0 0.988 8.53 11.6 c 20.0 0.988 18.5 21.6 ``` Subexpression: summarize(x, default_stats(; prob_interval=0.89)...; var_names=[:a, :b, :c]) Evaluated output: SummaryStats mean std hdi_5.5% hdi_94.5% a 0.000275 0.989 -1.63 1.52 b 10.0 0.988 8.53 11.6 c 20.0 0.988 18.5 21.6 Expected output: SummaryStats mean std hdi_5.5% hdi_94.5% a 0.000305 0.990 -1.63 1.52 b 10.0 0.988 8.53 11.6 c 20.0 0.988 18.5 21.6 diff = Warning: Diff output requires color. SummaryStats mean std hdi_5.5% hdi_94.5% a 0.000305 0.990 0.000275 0.989 -1.63 1.52 b 10.0 0.988 8.53 11.6 c 20.0 0.988 18.5 21.6

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 => 0.483727 :non_centered => 0.516273 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 0.483727 :non_centered => 0.5162770.516273

doctest failure in ~/.julia/packages/InferenceObjects/AdCId/ext/InferenceObjectsPosteriorStatsExt/loo_pit.jl:21-42 ```jldoctest julia> using ArviZExampleData, PosteriorStats julia> idata = load_example_data("centered_eight"); julia> loo_result = loo(idata; var_name=:obs); julia> loo_pit(idata, loo_result.psis_result.log_weights; y_name=:obs) ╭────────────────────────────────────────────╮ │ 8-element DimArray{Float64, 1} loo_pit_obs │ ├────────────────────────────────────────────┴─────────────────────────── 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(idata, loo_result.psis_result.log_weights; y_name=:obs) Evaluated output: ╭───────────────────────────────────────────╮ │ 8-element DimArray{Float64,1} loo_pit_obs │ ├───────────────────────────────────────────┴──────────────────────────── 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 Expected output: ╭────────────────────────────────────────────╮ │ 8-element DimArray{Float64, 1} loo_pit_obs │ ├────────────────────────────────────────────┴─────────────────────────── 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} DimArray{Float64,1} loo_pit_obs │ ├────────────────────────────────────────────┴─────────────────────────── ├───────────────────────────────────────────┴──────────────────────────── 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