Lecture
2023-09-29
Today
Reflections
Revisions
Practice problems
There are many other resources available online; use them critically.
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
If you have questions about what is permitted, please ask.
For each problem:
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: