An Overview of the Bayesian Approach to Estimation
In the subsections below, I will go into considerable detail on the philosophy, methodology and characteristics of the Bayesian approach to statistical estimation. It seems appropriate to begin the discussion by presenting the famous theorem by Thomas Bayes which underpins the entire enterprise. Its most common form involves a two-stage experiment. Consider an event A of interest as a possible outcome of the first stage of the experiment and an event B, a possible outcome of the second stage. If, for example, one is drawing marbles at random from an urn containing red and white marbles, A might be the event of drawing a red marble on the first draw and B might be the event of drawing a white marble on the second draw. Such experiments are often represented by a “tree” such as that in Figure 3.1.
KeywordsPosterior Distribution Prior Distribution Posterior Density Markov Chain Monte Carlo Method Prior Density
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