Using Prior Expansions for Prior-Data Conflict Checking

Any Bayesian analysis involves combining information represented through different model components, and when sources of are in conflict it is important to detect this. Here we consider checking for prior-data models by expanding the prior used into a larger family priors, considering marginal likelihood score statistic expansion parameter. Consideration expansions can be informative about nature any conflict, an appropriate choice provide more sensitive checks conflicts certain types. Extensions hierarchically specified priors connections with other approaches considered, implementation complex situations illustrated two applications. The first concerns testing appropriateness LASSO penalty shrinkage estimation coefficients linear regression. Our method compared recent suggestion literature designed powerful against alternatives exponential power family, use this as constructing our check. A second application problem quantum state estimation, where multinomial considered physical constraints on parameters. In example, usefulness demonstrated obtaining which aspects prior.