Literature suggests observers can extract an average of facial expressions or attractiveness of multiple faces presented simultaneously. This phenomenon is called “ensemble perception.” However, it is unclear whether observers identify the averaged appearance of faces in ensemble perception. To address this, we conducted two experiments where participants studied a set of two different faces as targets and were then asked to judge whether the test face was an average of the two targets. We prepared three types of test faces: an averaged face using the two targets (T2),an averaged face using the target and non-target faces (TN),and an averaged face using two non-target faces (N2). In both experiments, participants correctly judged T2 as targets as opposed to N2. However, participants could discriminate T2 from TN only in Experiment 2, where correct or incorrect feedback at each trial was provided. These results suggest that observers can identify an averaged face from two targets but discriminate the averaged one from others only when facilitated by feedback.
Three types of point estimates of parameters, means, medians, and maximum a posteriori (MAP) estimates, were compared with respect to bias and root mean square error (RMSE). The overall results showed that the MAP estimates were the best among the three estimators for asymmetric posterior distributions of proportion parameters of binomial models, standard deviation parameters of univariate normal models, and correlation coefficient parameters of bivariate normal models. Although the comparisons were made for simple models, the results suggested that, in general, MAP estimates are appropriate for true values because MAP estimates are included in any highest-density intervals and because MAP estimates with flat prior distributions coincide with maximum likelihood estimates, which asymptotically converge to true values when sample sizes become large. A simple Python script to calculate a MAP estimate from Markov chain Monte Carlo (MCMC) sampling was presented.