This is note I wrote as I was take following lecture http://www.kocw.net/home/search/kemView.do?kemId=1189957 ================================================================================ * Code # Random variables X1, X2 # c N: number of sample N=100 # ================================================================================ # c mu_1: expectation value of random variable X1 mu_1=[380,300] # c sigma_1: covariance matrix sigma_1=[[300,30],[30,200]] # Generate random data (100,2) which follows above parameters X1=generate_data_using_parameters(mu_1,sigma_1,N) # ================================================================================ # c mu_2: expectation value of random variable X1 mu_2=[430,350] # c sigma_2: covariance matrix sigma_2=[[400,100],[100,90]] # Generate random data (100,2) which follows above parameters X2=generate_data_using_parameters(mu_2,sigma_2,N) # ================================================================================ ================================================================================ plot(X1,X2) ================================================================================ plot_gaus(X1,X2) Abvoe shows "TRUE" mean and covariance ================================================================================ * Let's inference mean and variance of population by using Maximum Likelihood (ML) inference inferenced1=ML(X1) inferenced2=ML(X2) plot(inferenced1,inferenced2) * Meaning: parameters ($$$\mu$$$ and $$$\sigma$$$) correctly inferenced ================================================================================ data=generate_one_sample_data_point() plot(data) * Posterior probability of "new data" occuring from class1 (red) = 0.0020 * Posterior probability of "new data" occuring from class1 (green) = 0.4476 * Selected class for that new data: green class ================================================================================ * Summary you should remember * You are given population data * You sample data from population * You inference parameters from sampled data by using ML, MLE * You inference "probability density function of population" from inferenced parameters * You use posterior probability by using for example LRT, Bayes risk, etc to classify given new data into best proper class ================================================================================