Statistical Rethinking: A Bayesian Course with Examples in R and STAN, Second Edition (Solutions, Instructor Solution Manual) [2 ed.] 036713991X, 9780367139919

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STATISTICAL RETHINKING SECOND EDITION PRACTICE PROBLEM SOLUTIONS Contents 2. 3. 4. 5. 6. 7. 8. 9. 11. 12. 13. 14. 15. 16.

Chapter 2 Solutions Chapter 3 Solutions Chapter 4 Solutions Chapter 5 Solutions Chapter 6 Solutions Chapter 7 Solutions Chapter 8 Solutions Chapter 9 Solutions Chapter 11 Solutions Chapter 12 Solutions Chapter 13 Solutions Chapter 14 Solutions Chapter 15 Solutions Chapter 16 Solutions

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Date: April 6, 2020.

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STATISTICAL RETHINKING 2ND EDITION SOLUTIONS

2. Chapter 2 Solutions

2E1. Both (2) and (4) are correct. (2) is a direct interpretation, and (4) is equivalent.

2E2. Only (3) is correct.

2E3. Both (1) and (4) are correct. For (4), the product Pr(rain|Monday) Pr(Monday) is just the joint probability of rain and Monday, Pr(rain, Monday). Then dividing by the probability of rain provides the conditional probability.

2E4. This problem is merely a prompt for readers to explore intuitions about probability. The goal is to help understand statements like “the probability of water is 0.7” as statements about partial knowledge, not as statements about physical processes. The physics of the globe toss are deterministic, not “random.” But we are substantially ignorant of those physics when we toss the globe. So when someone states that a process is “random,” this can mean nothing more than ignorance of the details that would permit predicting the outcome. As a consequence, probabilities change when our information (or a model’s information) changes. Frequencies, in contrast, are facts about particular empirical contexts. They do not depend upon our information (although our beliefs about frequencies do). This gives a new meaning to words like “randomization,” because it makes clear that when we shuffle a deck of playing cards, what we have done is merely remove our knowledge of the card order. A card is “random” because we cannot guess it.

2M1. Since the prior is uniform, it can be omitted from the calculations. But I’ll show it here, for conceptual completeness. To compute the grid approximate posterior distribution for (1): R code

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p_grid