Reading 9: Bayesian Analysis I

Reading 9: Bayesian Analysis I#

For the class on Wednesday, February 12th

Reading assignments#

Read the following sections of [ICVG20]:

  • Sec. 5.1 “Introduction to the Bayesian Method”, including all the subsections (5.1.1–-5.1.3)

  • Sec. 5.3 “Bayesian Parameter Uncertainty Quantification”, including all the subsections (5.3.1–-5.3.2)

(Note that Sec. 5.2 is skipped for now. We will read that section in a later reading assignment.)

Questions#

Submit your answer on Canvas. Due at noon, Wednesday, February 12th.

  1. List anything from your reading that confuses you. Explain why they confuse you. If nothing confuses you, briefly summarize what you have learned from this reading assignment.

  2. You have a coin. A flip of that coin results in heads with an unknown probability \(\theta\). You flipped the said coin 3 times, and you got no heads. Answer the following questions. Show your steps.

    • (a) Write down the likelihood function (in terms of \(\theta\)) given your flips (you’ve done this in Reading 4).

    • (b) What is the maximum likelihood estimate of \(\theta\)?

    • (c) Now, assume a prior distribution for \(\theta\), \(p(\theta) = 6 \theta (1-\theta)\). Write down the posterior distribution of \(\theta\) given your flips. (Hint: posterior = likelihood times prior).

    • (d) What is the maximum a posteriori estimate of \(\theta\)?

    • (e) What is the expected value of \(\theta\) given the posterior distribution?