Bayesian Parameter Estimation and MCMC for Engineers

In engineering and the physical sciences, matching mathematical models to real-world data requires more than just finding a single best-fit line. To make reliable predictions, you need to understand the uncertainty behind your parameters. This text-only course guides you from the foundational concepts of probability to implementing robust Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) algorithms, enabling you to transition from simple point estimates to full probability distributions. What you'll learn: - Understand the core principles of Bayesian statistics, prior distributions, and likelihood functions. - Implement the Metropolis-Hastings algorithm from scratch to sample complex probability spaces. - Analyze MCMC convergence diagnostics, including autocorrelation and modern metrics like R-hat. - Apply parameter estimation techniques to engineering and physical science models. - Predict system behavior with quantified uncertainty intervals instead of single-point forecasts. - Structure your numerical code using modern programming best practices for clean, reproducible scientific computing. This course begins with key terminology, basic probability concepts, and foundational definitions before guiding you through MCMC algorithm design, diagnostic checks, and practical application scenarios. It is designed for engineers, scientists, and data analysts seeking a solid, code-first introduction to Bayesian estimation without needing an advanced degree in statistics. Start reading today to master the fundamentals of Bayesian parameter estimation.