# Posterior Exploration and Publication Graphics

`gp3bayes` separates numerical posterior summaries from graphics. The same posterior draw matrix can therefore be inspected, tabulated, and plotted without changing the fitted model or its contract.

## Backend-independent posterior tables

    library(gp3bayes)

    draws <- cbind(
      intercept = seq(-1, 1, length.out = 500),
      condition = seq(-0.5, 0.7, length.out = 500)
    )

    posterior_interval_table(draws)
    #>    variable          mean        sd lower        median upper
    #> 1 intercept -8.104628e-17 0.5790855 -0.95 -1.110223e-16  0.95
    #> 2 condition  1.000000e-01 0.3474513 -0.47  1.000000e-01  0.67
    posterior_probability_table(draws, rope = c(-0.1, 0.1))
    #>            variable probability_gt_zero probability_lt_zero probability_in_rope
    #> intercept intercept               0.500               0.500               0.100
    #> condition condition               0.584               0.416               0.166
    #>           rope_lower rope_upper
    #> intercept       -0.1        0.1
    #> condition       -0.1        0.1
    posterior_correlation_table(draws)
    #>   variable_1 variable_2 correlation  method
    #> 1  condition  intercept           1 pearson

## Publication graphics

    plot_posterior_intervals(draws)

    plot_posterior_areas(draws)

The plotting functions return ordinary plotting objects. They do not alter posterior draws, set decision thresholds, or turn interval exclusion into an automatic substantive conclusion.

## Fitted-model extraction

For an approved fitted model, the post-fit API standardises extraction through the `posterior` package:

    draw_array <- extract_posterior_draws(fit, regex = "^b_", format = "array")
    draw_df <- extract_posterior_draws(fit, regex = "^b_", format = "df")

    mcmc_diagnostic_table(fit)
    sampler_diagnostic_table(fit)
    quality <- summarise_mcmc_quality(fit)

    plot_rank_diagnostics(fit)
    plot_autocorrelation(fit)
    plot_mcmc_quality(quality)
    plot_sampler_diagnostics(fit)

Diagnostic flags request inspection. Their absence is not encoded as proof of model adequacy.