Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems

Chapter 3Computer-Assisted Bayesian Computation

3.1 Getting Started

In Chapter 2, we were able to obtain all of our results using an analytic approach to Bayesian inference. The analytic approach is attractive in smaller problems. This is because we can use formulas and formula manipulations to find exact values for the parameters of interest.

The analytic approach can be contrasted with the numeric approach, where we use a computer to provide approximate answers. Why would anyone be interested in an approximate answer when exact answers are available? There are at least three reasons. First, as the number of parameters increases, the complexity of the math required to produce an exact result also tends to increase. Hence, for more advanced models that we might find useful in business, the analytic approach can become very burdensome. Second, we can improve the accuracy of our approximations by instructing the computer to run for a longer period. With ever-increasing computing power, we may be able to get a result that is exact to many significant digits in a few minutes. Hence, the result could be considered exact for practical business purposes if the approximation error is below the threshold of having a substantial impact on business undertakings. Third and finally, there is freely available software that is very useful for performing the kinds of analyses we will be considering. These software packages contain a variety of capabilities that further speeds up the process ...