Bayesian MCMC and Parameter Estimation for Engineers

When modeling physical, chemical, or biological systems, deterministic parameter estimation often falls short of capturing real-world uncertainty. Bayesian statistics offers a robust framework to not only estimate parameters but also quantify the exact confidence we have in our data. This text-based course guides you from the foundational concepts of probability to implementing practical Markov Chain Monte Carlo (MCMC) algorithms for engineering applications. By reading through clear explanations and structured code examples, you will learn how to transition from prior beliefs to posterior distributions, enabling you to make highly reliable, data-driven predictions. What you'll learn: - Understand the fundamental principles of Bayesian inference and parameter estimation. - Formulate prior distributions and likelihood functions for scientific models. - Implement Markov Chain Monte Carlo (MCMC) algorithms, including the Metropolis-Hastings method. - Extract and analyze 1D marginal posterior distributions to quantify parameter uncertainty. - Apply modern best practices for diagnostic checks, convergence testing, and algorithm optimization. You will begin with core probability definitions and Bayesian terminology before moving step-by-step through algorithm design, code implementation, and scientific parameter estimation workflows. This course is designed for engineering students, researchers, and data analysts who want a clear, beginner-friendly introduction to Bayesian numerical methods without needing an advanced statistical background. Start reading today to unlock the power of Bayesian uncertainty quantification in your technical workflows.