Universality of Bayesian mixture predictors

The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to a given set C, but the latter is completely arbitrary (uncountably infinite, without any structure given). The performance is measured with asymptotic average log loss. In this work it is shown that the minimax asymptotic performance is always attainable, and it is attained by a convex combination of a countably many measures from the set C (a Bayesian mixture). This was previously only known for the case when the best achievable asymptotic error is 0. This also contrasts previous results that show that in the non-realizable case all Bayesian mixtures may be suboptimal, while there is a predictor that achieves the optimal performance

Event-sequence analysis of appraisals and coping during trapshooting performance

This study describes appraisal and coping patterns of trapshooters during competition, via post-performance retrospective verbal reports. Probabilities that an event (e.g., missed target) is followed by another event (e.g., negative appraisal) were calculated and state transitional diagrams were drawn. Event-sequences during critical and non-critical performance periods were compared. Negative appraisals were most likely before and after missed targets and hits with the second shot. Positive appraisals were most likely before problem-focused coping and after emotion-focused coping. These findings support the process view of coping by illustrating that athletes cope with a variety of situations via a complex set of appraisals