Metropolis Algorithm for Continuous Sampling in C#

Generating random samples from complex, non-normalized probability density functions is a foundational challenge in scientific computing, statistics, and machine learning. This text-only course provides a clear, step-by-step pathway to understanding how the Metropolis algorithm solves this problem using Markov processes. You will transition from theoretical concepts to writing clean, structured simulation code. Learn to define your target distributions, set up proposal distributions, and handle the acceptance-rejection mechanics of continuous sampling. We also cover modern C# development practices, including using strongly typed records for state representation, writing unit tests with pytest-style frameworks adapted for C#, and managing random number generation efficiently. What you'll learn: Understand the core mathematical concepts of Markov chain Monte Carlo (MCMC) sampling; Implement the Metropolis algorithm from scratch using modern C# structures; Configure proposal distributions and tune step sizes for optimal acceptance rates; Analyze sample paths and diagnose burn-in periods and autocorrelation; Structure simulation code with proper encapsulation and type safety. The course begins with foundational definitions of probability distributions and Markov chains before guiding you through the step-by-step implementation of the sampling loop. This course is designed for software developers, data engineers, and students who are new to scientific sampling and want a practical, code-first introduction to the Metropolis algorithm without complex mathematical prerequisites. Start reading today to build a solid foundation in computational sampling techniques.