  We consider Bayesian multiple hypothesis problem with independent and
identically distributed observations. The classical, Sanov's theorem-based,
analysis of the error probability allows one to characterize the best
achievable error exponent. However, this analysis does not generalize to the
case where the true distributions of the hypothesis are not exact or partially
known via some nominal distributions. This problem has practical significance,
because the nominal distributions may be quantized versions of the true
distributions in a hardware implementation, or they may be estimates of the
true distributions obtained from labeled training sequences as in statistical
classification. In this paper, we develop a type-based analysis to investigate
Bayesian multiple hypothesis testing problem. Our analysis allows one to
explicitly calculate the error exponent of a given type and extends the
classical analysis. As a generalization of the proposed method, we derive a
robust test and obtain its error exponent for the case where the hypothesis
distributions are not known but there exist nominal distribution that are close
to true distributions in variational distance.
