more likely to produce inadequate estimates at termination.

Since the true mean for this target density is known, we compare coverage probabilities of the resulting confidence regions using ABM and RBM over 1000 replications in Table \[table:rosenbrock\_coverage\_m\_5\]. The results for $m = 5$ and $m = 10$ are similar; the ABM estimator yields abysmally low coverage, especially at the beginning of the process. The RBM estimator, on the other hand, yields a high coverage probability despite the slow mixing nature of the Markov chain.

Bayesian multinomial regression
-------------------------------

Consider the 1989 Dutch parliamentary election study [@anker:1993] which contains 1754 self-reported voting choices of survey respondents among four contesting parties and 11 explanatory variables. The dataset is available in `Nethvote` in the `R` package `MCMCpack` [@mcmcpack]. We consider a Bayesian multinomial regression with four levels for the response variable, each for a contesting political party. Let $y_{i}$ and $x_{ij}$ denote the response variable and the $j$th covariate for the $i$th observation, respectively. Let $\beta$ denote the $22$-dimensional vector of regression coefficients and $\pi_i$ denote the 4-dimensional vector of probabilities for respondent $i$. Let $$y_{i} \sim \text{Multinomial} (\pi_{i})\,,$$ where $\pi_i = (\pi_{i1}, \pi_{i2}, \pi_{i3}, \pi_{i4})$ with $$\pi_{ij} = \dfrac{\exp(x'_{ij}\beta)}{\sum_{k=1}^{p}\exp(x'_{ik}\beta)} \,.$$ As considered 