摘要：Recent developments in Bayesian computing allow accurate estimation
of integrals, making advanced Bayesian analysis feasible. However, some problems
remain dicult, such as estimating posterior distributions for variance parameters.
For models with three or more variances, this paper proposes a simplex parame-
terization for the variance structure, which has appealing properties and eases the
related burden of specifying a reference prior. This parameterization can be prof-
itably used in several multiple-precision models, including crossed random-e
ect
models, many linear mixed models, smoothed ANOVA, and the conditionally au-
toregressive (CAR) model with two classes of neighbor relations, often useful for
spatial data. The simplex parameterization has at least two attractive features.
First, it typically leads to simple MCMC algorithms with good mixing proper-
ties regardless of the parameterization used to specify the model's reference prior.
Thus, a Bayesian analysis can take computational advantage of the simplex param-
eterization even if its prior was speci ed using another parameterization. Second,
the simplex parameterization suggests a natural reference prior that is proper,
invariant under multiplication of the data by a constant, and which appears to
reduce the posterior correlation of smoothing parameters with the error precision.
We use simulations to compare the simplex parameterization, with its reference
prior, to other parameterizations with their reference priors, according to bias
and mean-squared error of point estimates and coverage of posterior 95% credible
intervals. The results suggest advantages for the simplex approach, particularly
when the error precision is small. We o
er results in the context of two real data
sets from the elds of periodontics and prosthodontics.
