Module 1: Binary Hypothesis Testing

Hypothesis Testing

Hypothesis Testing is a statistical method that is used in making decisions using experimental data. Hypothesis Testing is basically an assumption that we make about the population parameter.

Binary and M-ary Hypothesis Testing

Detection problems can usually be casted as Binary or M-ary hypothesis testing problems.

Binary Hypothesis Testing helps in deciding between two hypotheses based on random observation. The goal of M-ary Hypothesis Testing is to decide among M possible hypotheses.

Estimation

Estimation is concerned with inference about the numerical value of unknown population values from incomplete data such as a sample.

Log-Likelihood Ratio Test

Log-Likelihood Ratio is a statistical test to assess the goodness of fit between two models based on the ratio of their likelihoods.

Neyman-Pearson Lemma

The Neyman-Pearson Lemma is a way to find out if the hypothesis test you are using is the one with the greatest statistical power.

Kullback-Leibler Divergence

Kullback–Leibler Divergence is a way to measure the difference between two probability distributions.

Properties of Kullback-Leibler Divergence


• Data processing inequality
• Pinsker’s inequality
• Additivity