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This talk will give an introduction to some of the advantages of Bayesian statistical methods for modeling and data analysis in psychological research. Bayesian methods work especially well in a number of common and important situations. The first is when there are relatively few data, as often happens in clinical or other applied settings. The second is when data follow complicated distributions, as often happens in naturally occurring data or field experiments, where data are missing or experimental designs are complicated or non-existent. The third is when there is strong guiding theory that needs to be incorporated into understanding the data, as should be the case almost always in psychology, given existing theories about sensation, perception, cognition, and related theory from biology and neuroscience. Some tutorial examples and real-world case studies will be presented that emphasize these advantages of Bayesian methods, highlighting their ability to make inferences from data, make predictions about data, and choose between competing models for data.