Maximum Likelihood Estimation

Bayesian and Non-Bayesian Statistics

One of the best ways to describe the impact of MLE is through a comparison of Bayesian and non-Bayesian approaches to statistics. In the case of assumptions about the normal density function (normal curve), the MLE formulas for the mean and variance operate in the same manner. The impact of the choice is dictated by the underlying statistical model and in a sense, many of them would operate consistently with the assumptions of the underlying model.

A Bayesian model considers a statistical model and then determines the conformity of observed values to that model. For example, the normal non-Bayesian model selects a sample of persons and estimates the statistical parameters and then provides a comparison between the model of observed data and some defined outcome or group. A Bayesian model would test one case at a time to determine an answer and collect cases until a statistical answer is reached.

Consider a poll that wants to compare two candidates for an office to determine whether or not a single candidate is ahead. A typical polling service would generate a sample frame and then go on to survey a group of people. The results would be a set of accumulated responses that provide a percentage of respondents favoring each of the candidates. Using the statistics for determining a confidence interval and a normal alpha error of .05 (5%), the determination is reached that one candidate is leading or that neither candidate is leading. One application would be the collection of data that continues until it is clear that one candidate is leading or that some estimation level is reached; this would be accompanied by the conclusion that no differences in opinion exist. The technique shares a lot in common with inferential techniques but may permit smaller sample sizes under conditions where the distribution of opinion is very clearly favoring one candidate.

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