Using Prior Expansions for Prior-Data Conflict Checking

Abstract

Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict in Bayesian models by expanding the prior used for the analysis into a larger family of priors, and considering a marginal likelihood score statistic for the expansion parameter. Consideration of different expansions can be informative about the nature of any conflict, and extensions to hierarchically specified priors and connections with other approaches to prior-data conflict checking are discussed. Implementation in complex situations is illustrated with two applications. The first concerns testing for the appropriateness of a LASSO penalty in shrinkage estimation of coefficients in linear regression. Our method is compared with a recent suggestion in the literature designed to be powerful against alternatives in the exponential power family, and we use this family as the

The Measurement of Statistical Evidence as the Basis for Statistical Reasoning

“…For the computations associated with bias and prior-data conflict, however, this is mitigated by requiring only a very low level of accuracy for the relevant probabilities in question. See, for example, Nott et al (2016), Nott et al (2019) and Wang et al (2018) where approximate calculation approaches have been successfully employed. In any case, we subscribe to the view that is better to approximately compute what is believed to be correct rather than exactly compute what isn't.…”

“…) as the amount of data increases and so the tail probability is a consistent check on the prior. Further refinements can be proposed to deal with invariance and Nott et al (2018) generalizes (1) to provide a fully invariant check that connects nicely with the measure of evidence used for inference. It is shown in Al Labadi and Evans (2017) that, when prior-data conflict exists, then inferences can be very sensitive to perturbations of the prior.…”

Quantifying Observed Prior Impact

“…Prior-likelihood conflict, e.g., Evans et al (2006); Bousquet (2008); Walter and Augustin ( 2009); Nott et al (2020Nott et al ( , 2021. The topic of prior likelihood-data conflict is very much related to EPSS measures in the sense that such conflict can indicate that the prior distribution has a large influence on the final analysis.…”

Spatial Statistical Models: An Overview under the Bayesian Approach

“…Checking for prior data conflict in Bayesian spatial statistics is an important technique to measure the adequacy of the adopted prior information and the data likelihood. The check designs some statistic and compares its observed values to the reference distribution derived from the prior predictive density of the data [92]. Prior conflict occurs whenever the prior assigns most of its mass to regions of the parameter space that lie in the tail of the likelihood.…”

“…In this case, the source of prior knowledge conflicts with the observed information. Nott et al [92] proposed a technique that deals with prior expansion for prior data conflict checking. Egidi et al [93] proposed an automatic elicited prior with a mixture of informative and uninformative components, which favors uninformative components whenever prior conflict occurs.…”