# Bayesian Method Essay

Abstract:

This document describes an example of basic pattern classification using the Bayesian method. Based on given two dimensional (2-D) training data for two classes, we created a classifier using discriminant function (which is the logarithmic version of Bayes formula) and used it to classify provided test data. We estimated the necessary statistical parameters, such as mean covariance and prior probabilities, from the training data set. We modeled two discriminant functions, which were further used on test data to discriminate between the two classes. We assumed that all the data are normally distributed.

Introduction:

Sample Size Selection:

Sample is the representative

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Different approaches are used to design a classifier. If only prior probabilities are given , we decide based on which one is bigger. For example ,if ------------ ,we decide for w1 ,otherwise we go with w2. If feature vector is given, we make a decision about the class based on the likelihood of that class with respect to the feature, so if------- we choose wi. This is called the likelihood ratio approach. We can also include a loss function (ʎ), which can manipulate our decision with respect to the consequence of the error as presented in equation 2. The maximum likelihood is an easy approach to compute but will only work for 2 category case i.e. Dichotomizer.

For more than two categories, we have to use a different method, for example discriminant functions, which can be expanded for any numbers of categories. The function can be manipulated in different manners (such as shifting, multiplying), so it is easier to calculate for the given data. The decision region that will come out as a result will be the same in any case. We decide for category wi If an equation 3 holds.

In other words, a classifier using discriminant functions is a system that computes discriminant functions for all possible categories and selects the category corresponding to the largest