Author: Kjell Nygren

# Chapter 12: Visualizing posteriors with bayesplot

#### Kjell Nygren

    library(glmbayes)

## 1. Purpose

bayesplot provides ggplot2-based plotting for Markov chains and Bayesian workflow diagnostics. glmbayes does not depend on bayesplot (install it from CRAN if you want to run the code below). A former S3 `pp_check()` method for `glmb` lives in `legacy_code/pp_check.glmb.R`.

After fitting models in earlier chapters (Chapters 07–08 overview; Chapter 09 binomial illustration), visual summaries help assess mixing, posterior shape, and how well replicated data match the observed responses.

## 2. Minimal binomial fit (Menarche)

We reuse the Menarche grouped binomial illustration with default `Prior_Setup()` machinery.

    data(menarche, package = "MASS")

    Age2 <- menarche$Age - 13
    Menarche_Model_Data <- data.frame(
      Menarche  = menarche$Menarche,
      Total     = menarche$Total,
      Age2      = Age2
    )

    ps <- Prior_Setup(
      cbind(Menarche, Total - Menarche) ~ Age2,
      family = binomial(link = "logit"),
      data   = Menarche_Model_Data
    )

    fit_logit <- glmb(
      cbind(Menarche, Total - Menarche) ~ Age2,
      family  = binomial(link = "logit"),
      pfamily = dNormal(mu = ps$mu, Sigma = ps$Sigma),
      data    = Menarche_Model_Data,
      n             = 800,
      use_parallel  = FALSE
    )
    coef_draws <- as.matrix(fit_logit$coefficients)

## 3. Coefficient trace and density overlays

Because `glmb()` returns i.i.d. draws, you can think of the coefficient matrix as one posterior sample stream. With `bayesplot` installed separately from CRAN, `mcmc_trace()` and `mcmc_dens()` give univariate views (functions that need multiple MCMC chains, such as `mcmc_dens_overlay()`, are not appropriate here).

## 4. Posterior predictive checks

For binomial models `glmbayes` works on proportions so `y` and `yrep` line up. The chunk below builds `y_obs` and `y_rep` for optional `bayesplot::ppc_*` plots (or the `pp_check.glmb` wrapper in `legacy_code/`).

    ## Observed success proportions (aligned with simulate.glmb for binomial)
    y_obs <- Menarche_Model_Data$Menarche / Menarche_Model_Data$Total

    pred_resp <- predict(fit_logit, type = "response")
    nd <- max(1L, min(50L, nrow(pred_resp)))
    pred_sub <- pred_resp[seq_len(nd), , drop = FALSE]

    y_rep <- stats::simulate(
      fit_logit,
      pred = pred_sub,
      prior.weights = fit_logit$prior.weights
    )

    stopifnot(nrow(y_rep) == nd, ncol(y_rep) == length(y_obs))

Try other `ppc_*` helpers via the `fun` argument when bayesplot is installed (see `?bayesplot-helpers`).

## See also

- Chapter 08 — full `glmb()` walk-through and interpretation of printed summaries.
- `?simulate.glmb`, `?predict.glmb` — mechanics behind replicated responses; optional `pp_check` wrapper in `legacy_code/pp_check.glmb.R`.