Bayesian procedure for regression based on latent variable approach. In this project, I am going to implement Gibbs sampling to estimate parameters of a regression problem with specific priors. Let's look at the problem itself:
We have Dose-Response Data from an Insecticide Study in which insects were exposed to various dose levels of an insecticide and the following is the result of this:
Dose:1.69 N:60 A:6
Dose:1.72 N:62 A:13
Dose:1.76 N:63 A:20
Dose:1.78 N:60 A:30
Dose:1.81 N:64 A:53
Dose:1.84 N:60 A:55
Dose:1.86 N:62 A:61
Dose:1.88 N:64 A:62
where N = number exposed; A = number adversely affected. Let P(d) = P( Exposed insect to dose d is adversely affected). and let P(d) = Φ(β0 + β1 x d + β2 x d^2; 1), the goal is finding the Bayesian estimates of β0, β1, β2 under certain assumptions explained in Project.pdf file.
- Implementation is in R
- For a detailed explanation of the project definition please look at the Project.pdf file
- the file Report.pdf contains results and mathematical derivations of the solutions
- This is part of a project for Bayesian Inference class under Dr. E. Olúṣẹ́gun George.
- The implementations are designed based on tutorials by Andreas C. Kapourani (https://rstudio-pubs-static.s3.amazonaws.com/208180_b659633007eb45aa9c48e4c50b8afc07.html)