Quantifying Observed Prior Impact

When summarizing a Bayesian analysis, it is important to quantify the contribution of prior distribution final posterior inference because this informs other researchers whether information needs be carefully scrutinized, and alternative priors are likely substantially alter conclusions drawn. One appealing interpretable way do report an effective sample size (EPSS), which captures how many observations in corresponds to. However, typically most aspect its location relative data, therefore traditional measures somewhat deficit for purpose quantifying EPSS, they concentrate on variance or spread (in isolation from data). To partially address difficulty, Reimherr et al. (2014) introduced class EPSS based prior-likelihood discordance. In paper, we take idea further by proposing new measure that not only incorporates general mathematical form likelihood (as proposed al., 2014) but also specific data at hand. Thus, our considers current observed rather than average multiple datasets working model, latter being approach taken (2014). Consequently, can highly variable, demonstrate impact analysis intrinsically variable. Our called (posterior) mean Observed Prior Effective Sample Size (mOPESS), Bayes estimate meaningful quantity. The mOPESS well communicates extent determined prior, framed differently, amount sampling effort saved due having relevant information. We illustrate ideas through number examples including Gaussian conjugate non-conjugate models (continuous observations), Beta-Binomial model (discrete linear regression (two unknown parameters).