IITM MLT Week 4 Questions
Maximum Likelihood and MAP Estimation
Week 4 question PDF
Practice estimating distribution parameters from observations. The questions cover likelihoods, log-likelihoods, priors and the difference between maximum likelihood and maximum a posteriori estimation.
The complete question statements, options, numerical data and any supporting graphs or tables are in the PDF. Numbered comprehension questions can include several subquestions. Answer keys are included for checking your attempt; these are not full worked solutions.
Topics covered in this collection
- Likelihood and log-likelihood
- Maximum likelihood estimation (MLE)
- Beta distributions and Bayesian priors
- Maximum a posteriori estimation (MAP)
How to approach these questions
- Write the joint likelihood for independent observations before taking logarithms.
- Differentiate with respect to the parameter and check the allowed parameter range.
- For MAP estimation, include the prior as well as the likelihood before finding the optimum.
Attempt the questions using the assumptions and notation stated in each problem. For short-answer questions, round only at the final step to the requested precision. Check the provided key after solving and revisit the relevant concept when an answer differs.