Bayesian Statistics
If you’ve been following my Twitter stream, you have probably seen that I’m doing some reading and study on Bayesian statistics lately. For a variety of reasons, I find the Bayesian model of statistics quite compelling and am hoping to be able to use it in some of my research.
Traditional statistics, encapsulating well-known methods such as t-tests, ANOVA, etc. are from the frequentist school of statistical thought. The basic idea of frequentist statistics is that the world is described by parameters that are fixed and unknown. These parameters can be all manner of things — the rotation rate of the earth, the average life span of a naked mole rat, or the average number of kittens in a litter of cats. It is rare that we can have access to the entire population of interest (e.g. all mature female cats) to be able to directly measure the parameter, so we estimate parameters by taking random samples from the population, computing some statistic over the sample, and using that as our estimate of the population parameter. Since these parameters are unknown, we do not know their exact values. Since they are fixed, however, we cannot discuss them in probabilistic terms. Probabilistic reasoning only applies to random variables, and parameters are not random — we just don’t know what their values are. Probabilities, expected values, etc. are only meaningful in the context of the outcome of multiple repeated random experiments drawn from the population.