Question related to Bayesian analysis

Weakly informative priors are often used in Bayesian analysis. Give an example, outline the advantages of this approach, and contrast with other possible choices of prior.

Outline three different approaches to computing posterior distributions. What advantages and disadvantages do they have?

After fitting a model, we have to communicate the results. A common approach is to summarise the posterior probability distribution. Outline at least one approach for doing this and provide examples. How do these approaches differ from the typical methods used in frequentist statistics?

Give an example of how dummy variables are used to fit a (Bayesian) linear model when we have a (two level) categorical predictor. How would we interpret the results?

The influence of Bayesian statistics in psychology extends beyond data analysis. Give an example that illustrates how Bayesian principles may underlie cognitive or perceptual processes.

A university student is investigating whether following a vegan caffeine-free diet leads to better exam performance. She recruits 30 participants and divides them equally between the two conditions. She decides to use Bayesian analysis to analyse her data and asks for your help! Specify a suitable model and justify your choices. (R code is not necessary in your answer.)