Bayesian Logistic Regression

Requirements Clarification & Assessment

1. Understanding the Basics:

   • Ensure you have a solid grasp of classical logistic regression, including its mathematical formulation and how it predicts binary outcomes.
   • Familiarize yourself with the concept of Bayesian inference, which involves updating beliefs based on prior knowledge and observed data.

2. Identifying Key Components:

   • Recognize the role of the logistic function (sigmoid function) in mapping predictions to probabilities between 0 and 1.
   • Understand the difference between maximum likelihood estimation (MLE) used in classical logistic regression and the Bayesian approach.

3. Exploring Bayesian Elements:

   • Clarify the need for prior distributions in Bayesian logistic regression and how they incorporate prior beliefs about model parameters.
   • Identify how Bayesian methods update these priors with observed data to generate posterior distributions.

4. Understanding Practical Applications:

   • Explore scenarios where Bayesian logistic regression is beneficial, such as when prior knowledge is available or when dealing with small datasets.
   • Consider the computational implications, including the use of techniques like Markov Chain Monte Carlo (MCMC) for sampling from posterior distributions.

5. Defining Goals:

   • Determine the objective of Bayesian logistic regression, which is to build a probabilistic model that provides uncertainty estimates for model parameters and predictions.