Which of the following scenarios best illustrates the application of Bayesian inference for parameter estimation?
Question 2
Given Bayes' rule, $P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)}$, what does the term $P(D)$ represent and why is it often computationally challenging to calculate?
Question 3
In Bayesian inference, when is a prior distribution considered 'informative'?
Question 4
You are trying to estimate the average height of students in a university. You have a prior belief that the average height is around 170 cm with a standard deviation of 5 cm. After collecting data from 100 students, you find the sample mean height is 172 cm. If you use a Normal prior and a Normal likelihood (with known variance), what type of distribution will the posterior distribution for the mean height be?
Question 5
In the context of Bayesian decision making under uncertainty, what is the 'loss function' and why is it crucial?
