(example_gallery)= # Example gallery :::{seealso} {ref}`plots_intro`: A general overview of batteries-included plotting functions, their common use cases, and the underlying logic. ::: ## Distribution visualization :::{toctree} :hidden: :caption: Distribution visualization plot_dist_ecdf plot_dist_hist plot_dist_kde plot_dist_qds plot_forest plot_forest_shade plot_prior_posterior plot_pair_focus_distribution plot_pair_distribution plot_ridge plot_dgof plot_dgof_dist ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_dist_ecdf :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Faceted ECDF plots for 1D marginals of the distribution ::: :::{image} /gallery/_images/plot_dist_ecdf.png :alt: ::: +++ Posterior ECDFs :::: ::::{grid-item-card} :link: plot_dist_hist :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Faceted histogram plots for 1D marginals of the distribution. The `point_estimate_text` option is set to False to omit that visual from the plot. ::: :::{image} /gallery/_images/plot_dist_hist.png :alt: ::: +++ Posterior Histograms :::: ::::{grid-item-card} :link: plot_dist_kde :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay KDE plot of the variable `mu` from the centered eight model. The `sample_dims` parameter is used to restrict the KDE computation along the `draw` dimension only. ::: :::{image} /gallery/_images/plot_dist_kde.png :alt: ::: +++ Posterior KDEs :::: ::::{grid-item-card} :link: plot_dist_qds :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Quantile dot plot of the variable `mu` from the centered eight model. We have removed the point estimate text and changed the number of quantiles to 200. ::: :::{image} /gallery/_images/plot_dist_qds.png :alt: ::: +++ Posterior quantile dot plots :::: ::::{grid-item-card} :link: plot_forest :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Default forest plot with marginal distribution summaries ::: :::{image} /gallery/_images/plot_forest.png :alt: ::: +++ Forest plot :::: ::::{grid-item-card} :link: plot_forest_shade :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Forest plot marginal summaries with row shading to enhance reading ::: :::{image} /gallery/_images/plot_forest_shade.png :alt: ::: +++ Forest plot with shading :::: ::::{grid-item-card} :link: plot_prior_posterior :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot prior and posterior marginal distributions. ::: :::{image} /gallery/_images/plot_prior_posterior.png :alt: ::: +++ Plot prior and posterior :::: ::::{grid-item-card} :link: plot_pair_focus_distribution :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot one variable against other variables in the dataset. ::: :::{image} /gallery/_images/plot_pair_focus_distribution.png :alt: ::: +++ Scatterplot one variable against all others :::: ::::{grid-item-card} :link: plot_pair_distribution :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot all variables against each other in the dataset. ::: :::{image} /gallery/_images/plot_pair_distribution.png :alt: ::: +++ Scatterplot all variables against each other :::: ::::{grid-item-card} :link: plot_ridge :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Visual representation of marginal distributions over the y axis for a single model ::: :::{image} /gallery/_images/plot_ridge.png :alt: ::: +++ Ridge plot :::: ::::{grid-item-card} :link: plot_dgof :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Diagnostics for assessing the goodness-of-fit of estimated distributions to the underlying data using the Probability Integral Transform (PIT) and the Δ-ECDF-PIT plots. ::: :::{image} /gallery/_images/plot_dgof.png :alt: ::: +++ Diagnostics for density estimation :::: ::::{grid-item-card} :link: plot_dgof_dist :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Diagnostics for assessing the goodness-of-fit of estimated distributions to the underlying data using the Probability Integral Transform (PIT) and the Δ-ECDF-PIT plots. ::: :::{image} /gallery/_images/plot_dgof_dist.png :alt: ::: +++ Density and diagnostics for density estimation :::: ::::: ## Posterior comparison :::{toctree} :hidden: :caption: Posterior comparison plot_dist_models plot_forest_models plot_ridge_multiple ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_dist_models :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Full marginal distribution comparison between different models ::: :::{image} /gallery/_images/plot_dist_models.png :alt: ::: +++ Posterior KDEs for two models :::: ::::{grid-item-card} :link: plot_forest_models :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Forest plot summaries for 1D marginal distributions ::: :::{image} /gallery/_images/plot_forest_models.png :alt: ::: +++ Posterior forest for two models :::: ::::{grid-item-card} :link: plot_ridge_multiple :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Visual representation of marginal distributions over the y axis showing for multiple models ::: :::{image} /gallery/_images/plot_ridge_multiple.png :alt: ::: +++ Ridge plot for multiple models :::: ::::: ## Inference diagnostics :::{toctree} :hidden: :caption: Inference diagnostics plot_rank plot_trace plot_ess_evolution plot_ess_local plot_ess_quantile plot_ess_models plot_mcse plot_convergence_dist plot_autocorr plot_energy plot_pair_focus plot_pair plot_parallel plot_lm ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_rank :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted plot with fractional ranks for each variable ::: :::{image} /gallery/_images/plot_rank.png :alt: ::: +++ Rank plot :::: ::::{grid-item-card} :link: plot_trace :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted plot with MCMC traces for each variable ::: :::{image} /gallery/_images/plot_trace.png :alt: ::: +++ Trace plot :::: ::::{grid-item-card} :link: plot_ess_evolution :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted plot with ESS 'bulk' and 'tail' for each variable ::: :::{image} /gallery/_images/plot_ess_evolution.png :alt: ::: +++ ESS evolution :::: ::::{grid-item-card} :link: plot_ess_local :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted local ESS plot ::: :::{image} /gallery/_images/plot_ess_local.png :alt: ::: +++ ESS local :::: ::::{grid-item-card} :link: plot_ess_quantile :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted quantile ESS plot ::: :::{image} /gallery/_images/plot_ess_quantile.png :alt: ::: +++ ESS quantile :::: ::::{grid-item-card} :link: plot_ess_models :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Full ESS (Either local or quantile) comparison between different models ::: :::{image} /gallery/_images/plot_ess_models.png :alt: ::: +++ ESS comparison :::: ::::{grid-item-card} :link: plot_mcse :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted quantile MCSE plot ::: :::{image} /gallery/_images/plot_mcse.png :alt: ::: +++ Monte Carlo standard error :::: ::::{grid-item-card} :link: plot_convergence_dist :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot the distribution of ESS and R-hat. ::: :::{image} /gallery/_images/plot_convergence_dist.png :alt: ::: +++ Convergence diagnostics distribution :::: ::::{grid-item-card} :link: plot_autocorr :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay faceted plot with autocorrelation for each variable ::: :::{image} /gallery/_images/plot_autocorr.png :alt: ::: +++ Autocorrelation Plot :::: ::::{grid-item-card} :link: plot_energy :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot transition and marginal energy distributions ::: :::{image} /gallery/_images/plot_energy.png :alt: ::: +++ Energy :::: ::::{grid-item-card} :link: plot_pair_focus :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot one variable against other variables in the dataset. ::: :::{image} /gallery/_images/plot_pair_focus.png :alt: ::: +++ Scatter plot of one variable against all other variables with divergences :::: ::::{grid-item-card} :link: plot_pair :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot all variables against each other in the dataset. ::: :::{image} /gallery/_images/plot_pair.png :alt: ::: +++ Scatter plot of all variables against each other with divergences :::: ::::{grid-item-card} :link: plot_parallel :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot parallel coordinates plot showing posterior points with divergences.. ::: :::{image} /gallery/_images/plot_parallel.png :alt: ::: +++ Parallel coordinates plot :::: ::::{grid-item-card} :link: plot_lm :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Posterior predictive and mean plots for regression-like data. The `plot_lm` function visualizes credible intervals around predictions alongside observed data points. ::: :::{image} /gallery/_images/plot_lm.png :alt: ::: +++ Linear model plot :::: ::::: ## Predictive checks :::{toctree} :hidden: :caption: Predictive checks plot_ppc_dist plot_ppc_rootogram plot_pava_calibration plot_ppc_pit plot_ppc_coverage plot_loo_pit plot_ppc_tstat plot_ppc_interval plot_ppc_censored plot_ppc_pava_residuals plot_forest_pp_obs ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_ppc_dist :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot of samples from the posterior predictive and observed data. ::: :::{image} /gallery/_images/plot_ppc_dist.png :alt: ::: +++ Predictive check with KDEs :::: ::::{grid-item-card} :link: plot_ppc_rootogram :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Rootogram for the posterior predictive and observed data. ::: :::{image} /gallery/_images/plot_ppc_rootogram.png :alt: ::: +++ Rootogram :::: ::::{grid-item-card} :link: plot_pava_calibration :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay PAV-adjusted calibration plot for binary predictions. ::: :::{image} /gallery/_images/plot_pava_calibration.png :alt: ::: +++ PAV-adjusted calibration :::: ::::{grid-item-card} :link: plot_ppc_pit :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot of the probability integral transform of the posterior predictive distribution with respect to the observed data. ::: :::{image} /gallery/_images/plot_ppc_pit.png :alt: ::: +++ PIT ECDF :::: ::::{grid-item-card} :link: plot_ppc_coverage :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Proportion of true values that fall within a given prediction interval. ::: :::{image} /gallery/_images/plot_ppc_coverage.png :alt: ::: +++ Coverage ECDF :::: ::::{grid-item-card} :link: plot_loo_pit :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot of the probability integral transform of the posterior predictive distribution with respect to the observed data using the leave-one-out (LOO) method. ::: :::{image} /gallery/_images/plot_loo_pit.png :alt: ::: +++ LOO-PIT ECDF :::: ::::{grid-item-card} :link: plot_ppc_tstat :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay T-statistic for the observed data and posterior predictive data. ::: :::{image} /gallery/_images/plot_ppc_tstat.png :alt: ::: +++ Test statistics :::: ::::{grid-item-card} :link: plot_ppc_interval :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot posterior predictive point estimate and intervals at each observation. ::: :::{image} /gallery/_images/plot_ppc_interval.png :alt: ::: +++ Interval plot :::: ::::{grid-item-card} :link: plot_ppc_censored :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Plot Kaplan-Meier survival curve vs posterior predictive draws. ::: :::{image} /gallery/_images/plot_ppc_censored.png :alt: ::: +++ Survival analysis (censored data) :::: ::::{grid-item-card} :link: plot_ppc_pava_residuals :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Residual plot using PAV-adjusted calibration for binary predictions. ::: :::{image} /gallery/_images/plot_ppc_pava_residuals.png :alt: ::: +++ PAV-adjusted residual plot :::: ::::{grid-item-card} :link: plot_forest_pp_obs :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Overlay of forest plot for the posterior predictive samples and the actual observations ::: :::{image} /gallery/_images/plot_forest_pp_obs.png :alt: ::: +++ Posterior predictive forest and observations :::: ::::: ## Prior and likelihood sensitivity checks :::{toctree} :hidden: :caption: Prior and likelihood sensitivity checks plot_psense plot_psense_quantities ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_psense :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay The posterior sensitivity is assessed by power-scaling the prior or likelihood and visualizing the resulting changes. Sensitivity can then be quantified by considering how much the perturbed posteriors differ from the base posterior. ::: :::{image} /gallery/_images/plot_psense.png :alt: ::: +++ Sensitivity posterior marginals :::: ::::{grid-item-card} :link: plot_psense_quantities :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay The posterior quantities are computed by power-scaling the prior or likelihood and visualizing the resulting changes. Sensitivity can then be quantified by considering how much the perturbed quantities differ from the base quantities. ::: :::{image} /gallery/_images/plot_psense_quantities.png :alt: ::: +++ Sensitivity posterior quantities :::: ::::: ## Model Comparison :::{toctree} :hidden: :caption: Model Comparison plot_compare plot_khat plot_khat_aesthetics plot_khat_facet_cols plot_khat_facet_grid plot_bf ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_compare :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Compare multiple models using predictive accuracy estimated using PSIS-LOO-CV. Usually the DataFrame ``cmp_df`` is generated using ArviZ's ``compare`` function. ::: :::{image} /gallery/_images/plot_compare.png :alt: ::: +++ Predictive model comparison :::: ::::{grid-item-card} :link: plot_khat :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Default Pareto k diagnostic plot from PSIS-LOO-CV to assess importance sampling reliability ::: :::{image} /gallery/_images/plot_khat.png :alt: ::: +++ Pareto k parameter diagnostics :::: ::::{grid-item-card} :link: plot_khat_aesthetics :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Faceted Pareto k plot with row layout and color aesthetic mapping by team ::: :::{image} /gallery/_images/plot_khat_aesthetics.png :alt: ::: +++ Pareto k diagnostics with aesthetic mapping :::: ::::{grid-item-card} :link: plot_khat_facet_cols :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Faceted Pareto k plot using column layout to compare diagnostics across field dimensions ::: :::{image} /gallery/_images/plot_khat_facet_cols.png :alt: ::: +++ Pareto k diagnostics with column faceting :::: ::::{grid-item-card} :link: plot_khat_facet_grid :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Faceted Pareto k plot using grid layout to separate data by field and year dimensions ::: :::{image} /gallery/_images/plot_khat_facet_grid.png :alt: ::: +++ Pareto k diagnostics with grid faceting :::: ::::{grid-item-card} :link: plot_bf :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Compute Bayes factor using Savage–Dickey ratio. We can apply this function when the null model is nested within the alternative. In other words when the null (``ref_val``) is a particular value of the model we are building (see [here](https://statproofbook.github.io/P/bf-sddr.html)). For others cases computing Bayes factor is not straightforward and requires more complex methods. Instead, of Bayes factors, we usually recommend Pareto smoothed importance sampling leave one out cross validation (PSIS-LOO-CV). In ArviZ, you will find them as functions with ``loo`` in their names. ::: :::{image} /gallery/_images/plot_bf.png :alt: ::: +++ Bayes_factor :::: ::::: ## Simulation Based Calibration :::{toctree} :hidden: :caption: Simulation Based Calibration plot_ecdf_pit plot_ecdf_coverage ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_ecdf_pit :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Faceted plot with PIT Δ-ECDF values for each variable The ``plot_ecdf_pit`` function assumes the values passed to it has already been transformed to PIT values, as in the case of SBC analysis or values from ``arviz_base.loo_pit``. The distribution should be uniform if the model is well-calibrated. To make the plot easier to interpret, we plot the Δ-ECDF, that is, the difference between the expected CDF from the observed ECDF. As small deviations from uniformity are expected, the plot also shows the credible envelope. ::: :::{image} /gallery/_images/plot_ecdf_pit.png :alt: ::: +++ PIT-ECDF :::: ::::{grid-item-card} :link: plot_ecdf_coverage :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Coverage refers to the proportion of true values that fall within a given prediction interval. For a well-calibrated model, the coverage should match the intended interval width. For example, a 95% credible interval should contain the true value 95% of the time. The distribution should be uniform if the model is well-calibrated. To make the plot easier to interpret, we plot the Δ-ECDF, that is, the difference between the expected CDF from the observed ECDF. As small deviations from uniformity are expected, the plot also shows the credible envelope. We can compute the coverage for equal-tailed intervals (ETI) by passing `coverage=True` to the `plot_ecdf_pit` function. This works because ETI coverage can be obtained by transforming the PIT values. However, for other interval types, such as HDI, coverage must be computed explicitly and is not supported by this function. ::: :::{image} /gallery/_images/plot_ecdf_coverage.png :alt: ::: +++ Coverage ECDF :::: ::::: ## Mixed plots :::{toctree} :hidden: :caption: Mixed plots plot_rank_dist plot_trace_dist plot_forest_ess combine_plots ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: plot_rank_dist :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Two column layout with marginal distributions on the left and fractional ranks on the right ::: :::{image} /gallery/_images/plot_rank_dist.png :alt: ::: +++ Rank and distribution plot :::: ::::{grid-item-card} :link: plot_trace_dist :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Two column layout with marginal distributions on the left and MCMC traces on the right ::: :::{image} /gallery/_images/plot_trace_dist.png :alt: ::: +++ Trace and distribution plot :::: ::::{grid-item-card} :link: plot_forest_ess :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Multiple panel visualization with a forest plot and ESS information ::: :::{image} /gallery/_images/plot_forest_ess.png :alt: ::: +++ Forest plot with ESS :::: ::::{grid-item-card} :link: combine_plots :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Arrange three diagnostic plots (ESS evolution plot, rank plot and autocorrelation plot) in a custom column layout. ::: :::{image} /gallery/_images/combine_plots.png :alt: ::: +++ Custom diagnostic plots combination :::: ::::: ## Helper Functions :::{toctree} :hidden: :caption: Helper Functions add_reference_lines add_reference_bands ::: :::::{grid} 1 2 3 3 :gutter: 2 2 3 3 ::::{grid-item-card} :link: add_reference_lines :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Draw lines on plots to highlight specific thresholds, targets, or important values. ::: :::{image} /gallery/_images/add_reference_lines.png :alt: ::: +++ Add Lines :::: ::::{grid-item-card} :link: add_reference_bands :link-type: doc :text-align: center :shadow: none :class-card: example-gallery :::{div} example-img-plot-overlay Draw reference bands to highlight specific regions. ::: :::{image} /gallery/_images/add_reference_bands.png :alt: ::: +++ Add Reference Bands :::: :::::