Lecture

2023-09-29

Today

Reflections

Revisions

Practice problems

- Average: 47.5
- Standard deviation: 15.9
- Maximum: 70
- Median: 49.5
- Easiest: maximum likelihood
- Hardest: computation, conditional probability

- Reorganized schedule – two modules not three
- Practice problems at start of class
- More links to suggested reading for each lecture

- ThinkBayes: simple and conceptual online textbook on Bayesian statistics
- Rethinking Statistics: a more serious text on Bayesian thinking and estimation
- Code examples on the website, including implementations in Turing

- An Introduction to Statistical Learning: a machine learning perspective
- Code examples in R and Python

There are many other resources available online; use them critically.

- Come to office hours
- Review lecture notes
- Don’t just read
- Work through examples
- Understand
*why* - Ask questions

I have encouraged you to use tools (Copilot, GPT, etc) to help you with *computing syntax* so you can spend more time on *understanding concepts*.

Today

Reflections

Revisions

Practice problems

- Exam I is graded
- Final grades will be curved, not each exam
- Revisions will be allowed

- Friday, October 6th at 11:00AM.
- Hand in to me in class
- Legible and clear handwritten work OR
- Type up your work
^{1} - Hand in your original exam with your revisions

- Subject to Rice Honor Code
- DO: consult class notes, textbooks, linked resources, or write your own code
- DO NOT: Consult with a classmate, search the internet, usie AI chat tools, or otherwise collaborate is not permitted
- Ask if you’re not sure

If you have questions about what is permitted, please ask.

For each problem:

- State how many points you earned on the original exam.
- Derive the correct answer. Your answer should be
**clearly written**and easy to follow. - Explain why your original answer was incorrect and what confused you (no revisions are needed if your original answer was correct!)

- On each problem, you will earn up to 60% of the points you missed
- Grading on the revision will be more strict than on the original exam

- Additional 10% for clear and insightful explanation of your original mistake (where applicable)
- T/F questions: up to 50% for a clear and correct explanation of
**why**the statement is true or false - If your revision is worse than the original, your score will not be lowered.

- Precipitation:
- CDF: \(F(x) = P(X \leq x)\)
- Can assume that \(F(0)=0.6\)

- Conditional probability: think hard about how to define \(A\) and \(B\)
- Return period: read the wording carefully (“according to the distribution shown…”, “…true return period”)
- Recording of review session

Today

Reflections

Revisions

Practice problems

A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the flu, while the other 10% are sick with measles. Assume for simplicity that there are no other illnesses and that no children have both the flu and measles.

A well-known symptom of measles is a rash. The probability of having a rash if one has measles is 0.95. However, occasionally children with flu also develop rash, and the probability of having a rash if one has flu is 0.08. Upon examining the child, the doctor finds a rash. What is the probability that the child has measles?

We collect some count data and model it using a Poisson likelihood. The Poisson likelihood is given by: \[ p(y_i | \lambda) = \frac{\lambda^{y_i} e^{-\lambda}}{y_i!} \] where \(y_i\) is the number of counts and \(\lambda\) is the rate parameter of the Poisson distribution. We want to do inference on \(\lambda\). We have a prior belief that \(\lambda\) is distributed as an Exponential distribution with the modified parameterization: \[ p(\lambda | \theta) = \frac{1}{\theta} e^{-\frac{\lambda}{\theta}} \] After collecting data \(y_1, y_2, \ldots, y_n\), what is the posterior distribution of \(\lambda\) given our prior parameter \(\theta\)?## Next week:

- Monday: Gridded climate data lab
- Wednesday: Generalized Linear Models
- Friday: Loss functions