Bayes Theorem

What does Bayes Theorem infer?

• Likelihood

• Prior Probability

• Marginal Probability

• Posterior Probability

What is the assumption of Naive Bayes Model for churn prediction (C) from spending (S) and package (P)?

• S and P are conditionally independence over C

• S and C are conditionally independence over P

• C and P are conditionally independence over S

• C is conditionally independence over S and P

Imagine you are a financial analyst at an investment bank. you are working to estimate the probability that the shares of a company that fires its CEO will increase by more than 5%. According to your research of publicly-traded companies, 60% of the companies that increased their share price by more than 5% in the last three years replaced their CEOs during the period.

At the same time, only 35% of the companies that did not increase their share price by more than 5% in the same period replaced their CEOs. Knowing that the probability that the stock prices grow by more than 5% is 4%. From these information, what is the likelihood?

• the probability that the CEO is replaced

• the probability of the CEO replacement given the stock price has increased by 5%

• the probability that the stock price increases by 5%

• the probability of the stock price increases by 5% given that the CEO has been replaced

Why do we need to measure the log-likelihood instead the likelihood directly?

• It is more precise measure

• It improves the calculation speed

• It helps to avoid overflow problem

• It helps to avoid the negative values

What does the marginal probability do in Bayes Theorem

• To maximize the prior probability

• To minimize the posterior probability

• To optimize the prior probability

• To normalize the posterior probability