Bayesian sequential joint detection and estimation under multiple hypotheses

We consider the problem of jointly testing multiple hypotheses and estimating a random parameter underlying distribution. This is investigated in sequential setup under mild assumptions on process. The optimal method minimizes expected number samples while ensuring that average detection/estimation errors do not exceed certain level. After converting constrained to an unconstrained one, we characterize general solution by non-linear Bellman equation, which parametrized set cost coefficients. A strong connection between derivatives function with respect coefficients procedure derived. Based this fundamental property, further show for suitably chosen solutions coincide. present two approaches finding For first approach, final optimization converted into linear program, whereas second approach solves it projected gradient ascent. To illustrate theoretical results, problems schemes are designed numerically. Using Monte Carlo simulations, validated numerical results agree theory.