Question 1

Figure from the original question paper 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 1000 users, where 150 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 suggesting that conversion rates of click typically fall within the range of 0.1 to 0.3, and you decide to use a beta distribution as your prior. You choose a beta distribution with parameters $\alpha = 5$ and $\beta = 20$ to capture your prior beliefs. Calculate the posterior mean? You are working on a text classification problem using a Naive Bayes classifier to determine whether an email is "Spam" or "Not Spam" . You have trained your model using a dataset of 1000 emails, with 600 of them labeled as "Spam" and 400 labeled as "Not Spam." You've collected statistics on the occurrence of two words, "Won" and "Money" in these emails: | Keyword | label of email | Probability | |---|---|---| | Won | Spam | $P(\text{Won} \Vert Spam) = 0.45$ | | Won | Not Spam | $P(\text{Won} \Vert NotSpam) = 0.05$ | | Money | Spam | $P(\text{Money} \Vert Spam) = 0.3$ | | Money | Not Spam | $P(\text{Money} \Vert NotSpam) = 0.02$ | You receive a new email containing both the "Won" and "Money" 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 "Spam." Hint: Assume that these are only two possible words (that is there are only two features)