It is an ongoing debate, what properties of visualizations increase people's performance when solving Bayesian reasoning tasks. In the discussion of the properties of two visualizations, i.e., the tree diagram and the unit square, we emphasize how both visualizations make relevant subset relations transparent. Actually, the unit square with natural frequencies reveals the subset relation that i...

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes' rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in te...

4 String Design 5 4.1 Maximum Distance Code . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.2 Equidistant code and Bayes rule . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Equidistant code and unbiased distance . . . . . . . . . . . . . . . . . . 7 4.4 Summary of Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.5 Code Sensitivity . . . . . . . . . . . . . . . . . ...

Bayesian statistics has become a popular framework in various fields of experimental psychology such as signal detection theory, speech recognition, cue integration and decision making. However, it is still an open question how the human brain actually incorporates this functionality. One assumption is that the activities of populations of neurons encode probability distributions. Indeed, it ha...

The problem considered is sequential estimation of the mean 0 of a one-parameter exponential family of distributions with squared error loss for estimation error and a cost c > 0 for each of an i.i.d, sequence of potential observations X 1, X 2 . . . . . A Bayesian approach is adopted, and natural conjugate prior distributions are assumed. For this problem, the asymptotically pointwise optimal ...