Bayesian Analysis & Inference

Project Overview

This project involves reading material and comprehensive assignments designed to develop proficiency in probability and Bayesian statistics, utilizing probabilistic programming tools for Bayesian inference. The assignments incorporate theoretical understanding and practical application using Jupyter notebooks\Google Colab.

Assignment 1:

Description: This assignment explores the probabilities associated with drawing jelly beans from a jar with specific flavors and Betabinomial and Gaussian Distribution. The tasks include:

• Defining the sample space for the experiment.
• Calculating the probabilities of drawing strawberry-flavored and non-cinnamon-flavored jelly beans.
• Analyzing whether the events are mutually exclusive.
• Used the Preliz explored the different parameters of Gaussian Distribution, Betabinomial Distribution and Skewnormal Distribution.

Assignment 2:

Description: This assignment focuses on defining and analyzing a Bayesian probabilistic model with a normal distribution. The tasks include:

• Identifying the prior and the likelihood of the model.
• Determining the number of parameters in the posterior distribution.
• Comparing the model with a coin-flipping problem.
• Writing Bayes' theorem for the given model.
• Used the PyMC library changed the parameters of the prior Beta Distribution

Learning Outcomes

To become well-versed in probability and Bayesian statistics and use probabilistic programming tools, the following approaches and techniques were applied:

• Probability and Bayesian Statistics: Studied fundamental concepts and applied them through probabilistic programming using MCMC for Bayesian inference.
• Model Visualization and Diagnosis: Utilized ArviZ for visualizing and diagnosing models, and examined hierarchical models in probabilistic programming.
• Advanced Regression Analysis: Expanded linear regression models and evaluated them using posterior predictive checks and LOO cross-validation.
• Modeling Techniques: Explored model averaging, modeling using Bambi, and interpretability with variable selection techniques and splines.

Results

• Proficiency Gained: Developed proficiency in probability and Bayesian statistics, employing PyMC for probabilistic programming.
• Application on Real-World Data: Utilized Bayesian techniques on real-world datasets to enhance model comparison, selection, and generalization.