We discuss contemporary ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce the Metropolis and the factorized Metropolis algorithms and lifted non-reversible Markov chains. We, furthermore, illustrate the concept of thinning, where moves are accepted by simple bounding potentials rather than the harmonic and quartic contributions to the anharmonic oscillator. We point out the multiple connections of our example algorithms with real-world sampling problems. This paper is self-contained, and Python implementations are provided.
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See supplementary material online for Python programs and a Mathematica notebook.
© 2024 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2024
Author(s)
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