11 Bayesian learning

Introduction to Bayesian probabilities.

After this practice session, the student

• is able to formulate a decision task in Bayesian framework;
• understands all parts of Bayesian decision task formulation (hidden states, observations, decisions, probability distribution over states and observations, loss function, decision strategy, its risk, partial/conditional risk, finding/constructing the optimal strategy);
• finds optimal strategy for a given decision task.

• Q/A
• Discussion of the bonus quiz from the last week
• Exercise 1: Probability of illness given a positive test
• Exercise 2: Bayesian decision task (power outage)
• Introduction of the bonus quiz for this week

Although I don't have any symptoms yet, I'm worried about disease X. I'm considering getting tested for it, but haven't yet. I therefore want to study the following phenomena:

• $X$ - the person is sick (has disease X)
• $\bar X$ - the person is healthy (does not have disease X)
• $\ominus$ - the test for disease X came out negative (according to the test, the person does not have disease X)
• $\oplus$ - the test for disease X came out positive (according to the test, the person has disease X)

For the test I'm considering taking, the manufacturer says it has 90% accuracy for both healthy and sick people. The prevalence of disease X in the population is 5%. Try to answer the following questions:

1. What is the probability that a person randomly selected from the population has disease X?
2. What is the probability that I have disease X?
3. How to understand (and denote) test information from the manufacturer?
4. What is the probability that I have disease X if I test positive?
5. What is the probability that I have disease X if I test negative?

Introduction to Bayesian probabilities on estimation of gender of people if we know the weight distribution of male and female colleagues (see pdf).

• Estimation of the value of old coins based on the weights of the sub-set of a bag of coins.
• 0.5 points
• submit your solution to BRUTE lab11quiz by May 07, midnight
• format: text file, photo of your solution on paper, pdf - what is convenient for you
• solution will be discussed on the next lab
• Students with their family name starting from A to K (included) have to solve and upload subject A , while students with family name from L to Z have to solve and upload subject B

• Start working on the machine learning assignment