Bayesian Statistics: Foundations and Applied Inference

Traditional statistics can often feel rigid when you want to update your models with new evidence or incorporate prior knowledge. Bayesian statistics offers an intuitive, probabilistic framework to model uncertainty and make decisions based on real-world data. In this text-based course, you will transition from a frequentist mindset to a Bayesian perspective. You will learn to construct prior distributions, calculate posterior probabilities, and apply modern computational tools to solve real-world statistical problems. What you'll learn: 1. Understand the core concepts of Bayes' theorem, prior distributions, likelihood, and posteriors. 2. Apply conjugate priors to analytically solve foundational probability problems. 3. Formulate and interpret Bayesian linear regression models for predictive tasks. 4. Explore modern computational methods like Markov Chain Monte Carlo (MCMC) and variational inference. 5. Analyze data using probabilistic programming concepts to implement models in code. 6. Evaluate model fit and perform posterior predictive checks to validate your results. The course begins with essential terminology and the mathematical foundations of probability before guiding you through practical modeling scenarios, comparing analytical approaches with modern computational simulation techniques. This course is designed for beginners in statistics, data analysis, or data science who want to build a solid conceptual foundation in Bayesian methods without needing advanced mathematical prerequisites. Begin reading today to master the power of probabilistic reasoning and upgrade your data analysis toolkit.