MLT End Term: 3 September 2023, Set QPD1-S2 (May 2023 term)

Suppose you have been given a task of estimating the conversion rate of google click of new online advertisement campaign. You have collected data from a limited sample of $50$ users, where $12$ of them have converted. You want to use Bayesian estimation with a prior distribution to provide a more robust estimate of the conversion rate.

Assume you have prior information and you decide to use a beta distribution as your prior. You choose a beta distribution with parameters $\alpha = 3$ and $\beta = 4$ to capture your prior beliefs.

Calculate the posterior mean?

You have been asked to build a classifier to categorize news articles into two categories: "Technology" and "Sports." You've collected a dataset of $1000$ articles, with $600$ articles labeled as "Technology" and $400$ labeled as "Sports." You've analyzed the articles and collected statistics on the occurrence of two words "software" and "football" in the articles:

You receive a new email containing both the "Software" and "Football" keywords and want to classify it using Naive Bayes.

Use the Naive Bayes formula to calculate the probability that the new email is classified as "Technology."

Hint: Assume that these are only two possible words (that is there are only two features)