This course will provide an overview of Monte Carlo methods when used for problems in Statistics. After an introduction to simulation, its purpose and challenges, we will cover in more detail Importance Sampling, Markov Chain Monte Carlo and Sequential Monte Carlo. Whilst the main focus will be on the methodology and its relevance to applications, we will often mention relevant theoretical results and their importance for problems in practice.
Keywords: Simulation, Variance reduction, Monte Carlo methods, Importance Sampling, Markov Chain Monte Carlo, Sequential Monte Carlo, Particle filters, Stochastic filtering, Hidden Markov models.
Part of the material below is delivered every year as part of the London Taught Course Centre (LTCC) for PhD students in mathematical sciences. Here is the official link of the course: http://www.ltcc.ac.uk/courses/advanced-computational-methods-in-statistics/
The lecture notes can be found here and the Matlab code used in the examples is provided above.
Immediately below you can find the course outline together the with links to slides and video-lectures (~20hrs). I have listed all the video lectures in this playlist. At the bottom of this page you can find more details on assessment, reading list, prerequisites, delivery format for the LTCC course.
We will split the introduction into two parts:
We will mainly discuss various topics and provide some some basics on theory and practice.
- Introduction to Markov Chain Monte Carlo
- Some more methodology
- Theoretical topics
Hidden Markov models and the filtering problem
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Some extensions to the basic Particle filter
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Parameter estimation methods for static parameters of Hidden Markov models
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SMC sampling for fixed dimensional state spaces: slides and video
The course will be delivered in person at Hardy room in De Morgan House every Monday 10:50-12:50 from 7 November to 5 December 2022.
The rescheduled lecture from 21/11 will take place on Monday the 12th December at Imperial College, room 144 Huxley Building, at 12-2pm.
Huxley Building has an entrance from 180 Queensgate. See here for more details on how to get to the building and here for a floorplan. Once you reach the straircase or lift head towards floor 1 at the basement.
Registration is compulsory, please vist http://www.ltcc.ac.uk/registration/
You may find the 2022 coursework instructions here
Deadline: around 18 January (about a month)
Page limit: 10 pages, recommended length around 6-8 pages
Submit by email to n.kantas at imperial.ac.uk using subject: LTCC coursework submission
Relevant introductory graduate textbooks and edited volumes:
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Chopin and Papaspiliopoulos (2020). An introduction to sequential Monte Carlo, Springer Series in Statistics.
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R. Douc, E. Moulines, & D. S. Stoffer (2014). Nonlinear Time Series Theory, Methods and Applications with R Examples, CRC Press.
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S. Sarkka (2013) Bayesian filtering and smoothing, CUP Cambridge.
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Cappé, O., Moulines, E. and Rydén, T. (2005). Inference in Hidden Markov Models. New York: Springer-Verlag.
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Doucet, de Freitas, Gordon (2001) Sequential Monte Carlo Methods in Practice, Springer.
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Liu (2001) Monte Carlo strategies in scientific computing, Springer.
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Robert and Casella (1999) Monte Carlo Statistical Methods, Springer.
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Gillks, Richardson, Spiegelhalter (1996) Markov Chain Monte Carlo in Practice, Chapman Hall.
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Basic knowledge of Statistics and Probability.
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Basic knowledge of programming in any language appropriate for scientific computing.
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Familiarity and exposure to Markov Chains or stochastic processes will be useful.
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There will be optional exercises or small courseworks posed as quizes or homeworks. There will be no separate problem sheets. Some problems will require the use of some programming.
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Lecture/computer session/tutorial/discussion hours split: 10/ 0 /0 /0
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Nikolas Kantas, Imperial College
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Email: n.kantas at imperial.ac.uk
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website: http://wwwf.imperial.ac.uk/~nkantas/