In conventional statistical analysis, sample statistics are used to estimate unknown, constant population parameters. In Bayesian inference, on the other hand, the parameter is treated as a random value from another distribution. Such a distribution is called the prior and is used to model a priori knowledge about the parameter. By combining the information from the data and the prior, we then obtain a new distribution for the parameter. This new distribution is called the posterior, which describes how the parameter varies conditionally upon what we have observed from the data.
Compared to conventional statistical methods, Bayesian methods are very flexible in building complex hierarchical models, and often have more intuitive interpretations for data analysis. One of my research projects applies Bayesian methods to the study of human memory. Modern psychological theories suggest that human memory has both the conscious component (Recollection: one knows one remembers) and the unconscious component (Automatic Activation: one does not know one remembers). Together with my collaborators, I proposed a Bayesian model that describes and accurately evaluates these different components. The Bayesian model was used to analyze data from a psychology experiment of word completion tasks under three study durations: no study time, 1 second/word study time, and 10 second/word study time. The posterior distributions of the parameters that measure the main effects (in Probit transformation) of Recollection and Automatic Activation under different study durations are demonstrated below. From the plots, we see that that the conscious memory (Recollection) improved as the subject had more time to study the words, while the unconscious memory (Automatic Activation) would be in place once the subject studied the words but was not affected by the length of exposure.
