  Uniformly most powerful Bayesian tests (UMPBT's) are an objective class of
Bayesian hypothesis tests that can be considered the Bayesian counterpart of
classical uniformly most powerful tests. Because the rejection regions of
UMPBT's can be matched to the rejection regions of classical uniformly most
powerful tests (UMPTs), UMPBT's provide a mechanism for calibrating Bayesian
evidence thresholds, Bayes factors, classical significance levels and p-values.
The purpose of this article is to expand the application of UMPBT's outside the
class of exponential family models. Specifically, we introduce sufficient
conditions for the existence of UMPBT's and propose a unified approach for
their derivation. An important application of our methodology is the extension
of UMPBT's to testing whether the non-centrality parameter of a chi-squared
distribution is zero. The resulting tests have broad applicability, providing
default alternative hypotheses to compute Bayes factors in, for example,
Pearson's chi-squared test for goodness-of-fit, tests of independence in
contingency tables, and likelihood ratio, score and Wald tests.
