Statistics and the Bayesian mind

When people mention statistics and human cognition in the same sentence, it is usually to complain about the limitations of the latter when applied to the former. For example, during World War II the city of London was struck by German V-1 and V-2 rockets. The locations at which the rockets landed seemed to cluster in poorer parts of the city, and it was a widespread belief that these areas were being specifically targeted. After the war, the locations of rocket landings in a portion of the city were subjected to statistical analysis, which showed that there was not sufficient evidence to reject the null hypothesis that the rockets had fallen uniformly at random. The apparent clustering that people had perceived was just a coincidence.