Bayesian Parameter Estimation and MCMC for Engineers

Engineers and scientists often need to extract reliable model parameters from noisy experimental data. Traditional fitting methods often fall short when capturing true physical uncertainty. This text-based course guides you through the foundations of Bayesian statistics, parameter estimation, and Markov Chain Monte Carlo (MCMC) algorithms. You will transition from understanding basic probability concepts to predicting system behaviors with quantified confidence intervals, applying these methods to real-world engineering and scientific problems. What you'll learn: - Understand the core principles of Bayesian probability, priors, likelihoods, and posteriors. - Configure and run Markov Chain Monte Carlo (MCMC) simulations to sample complex probability distributions. - Estimate physical parameters from noisy experimental data with robust uncertainty quantification. - Apply modern scientific computing workflows to evaluate model convergence and diagnostics. - Predict system behaviors by generating Bayesian predictive distributions from posterior samples. You will start by mastering the fundamental terminology and mathematical foundations of Bayesian inference. From there, you will progress to constructing likelihood functions, implementing MCMC sampling algorithms, and analyzing the resulting parameter distributions through step-by-step written explanations and code-based scenarios. This course is designed for engineering students, researchers, and data professionals who want to move beyond simple least-squares fitting. No prior background in Bayesian statistics is required, though a basic familiarity with algebra and programming concepts is helpful. Start reading today to unlock the power of Bayesian estimation in your engineering and scientific workflows.