English

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The aim of the course is for the doctoral student to acquire knowledge of advanced and modern simulation-based statistical methods; to understand the connection between these methods and stochastic processes; and to apply the methods to estimate complex models that arise in various application domains (e.g., machine learning, economics, signal processing, biology, and climate statistics).

The purpose of the course is to provide the doctoral student with both an overview of available simulation-based tools and an understanding of their theoretical foundations. Furthermore, the student should be able to assess the advantages and limitations of different methods for simulation-based inference, select and implement appropriate methods to solve complex statistical problems, and evaluate the results.

The course begins with a brief review of basic simulation-based methods, with a focus on Markov Chain Monte Carlo (MCMC) and the Metropolis-Hastings algorithm. The following topics are then covered:

Methods for one-dimensional sampling (e.g., slice sampling and adaptive rejection sampling)

Stochastic differential equations and kernel-based methods

Optimal scaling and acceptance probabilities in random-walk Metropolis-Hastings

Adaptive proposal mechanisms in random-walk Metropolis-Hastings

Variance reduction using control functionals

Advanced proposal distributions such as the Metropolis-adjusted Langevin algorithm (MALA) and Hamiltonian Monte Carlo (HMC)

Use of stochastic gradients in MCMC

Non-reversible and continuous-time MCMC algorithms

Evaluation of MCMC algorithms with a focus on convergence diagnostics

be able to explain the relationship between stochastic differential equations (SDEs), Langevin diffusions, and the resulting sampling algorithms.
be able to describe principles and techniques for variance reduction.
be able to describe diagnostic methods for the simulation-based methods in the course.
be able to explain the difference between exact and approximate Markov Chain Monte Carlo (MCMC) methods.

be able to implement simulation-based statistical methods in computer code.
be able to select and design appropriate kernels for variance reduction.
be able to construct suitable kernels and proposal distributions for Metropolis-Hastings-based algorithms.
be able to orally and in writing account for the theory and implementation of simulation-based statistical methods.

Discuss the advantages and disadvantages of different MCMC algorithms and select appropriate algorithms for a practical problem.
Evaluate the results of an MCMC algorithm and suggest adjustments to resolve potential convergence issues.

Föreläsningar

Seminarier

Projekt

Teaching consists of lectures and student lead seminars.

Inlämningsuppgifter

Seminarieföredrag av deltagarna

Underkänd, godkänd

Basic knowledge of simulation based inference, E.g. the course: Monte Carlo and Empirical Methods for Stochastic Inference (FMS092F/FMSN50/MASM11).

Fearnhead, P., Nemeth, C., Oates, Chris J. & Sherlock, C.: Scalable Monte Carlo for Bayesian Learning. Cambridge University Press, 2025. ISBN 9781009288446.

In addition to the book journal articles will be selected by the lecturers.

FMS100F

2025-10-08

Jonas Johansson