Time Series and Monte Carlo Inference



 

Time Series and Monte Carlo Inference (2 units)

The course consists of two components. Time Series and Monte Carlo Inference, each having 8 lectures. Together these make up one 2 unit (16 lecture) course. You must take the two components together for the examination.

Time Series (M8) A. P. Dawid

Time series analysis refers to problems in which observations are collected at regular time intervals and there are correlations among successive observations. Applications cover virtually all areas of Statistics but some of the most important include economic and nancial time series, and many areas of environmental or ecological data.

This course will cover some of the most important methods for dealing with these problems, including basic definitions of autocorrelations etc., time-domain model fitting including autoregressive and moving average processes, and spectral methods.

Pre-requisite Mathematics
You should have attended introductory Probability and Statistics courses.

Literature:

1. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods. Springer Series in Statistics (2006).
2. C. Chatfield, The Analysis of Time Series: Theory and Practice. Chapman and Hall (2004).
3. P. J. Diggle, Time Series: A Biostatistical Introduction. Oxford University Press (1990).
4. M. Kendall, Time Series. Charles Grifin (1976).

Monte Carlo Inference (L8) A.P.Dawid

Monte Carlo methods are concerned with the use of stochastic simulation techniques for statistical inference. These have had an enormous impact on statistical practice, especially Bayesian computation, over the last 20 years, due to the advent of modern computing architectures and programming languages. This course covers the theory underlying some of these methods and illustrates how they can be implemented
and applied in practice.

The following topics will be covered: Techniques of random variable generation. Markov chain Monte Carlo (MCMC) methods for Bayesian inference. Gibbs sampling, Metropolis-Hastings algorithm, reversible jump MCMC.

Pre-requisite Mathematics
You should have attended introductory Probability and Statistics courses. A basic knowledge of Markov chains would be helpful. Prior familiarity with a statistical programming package such as R or MATLAB would also be useful.

Literature: Markov Chain inference

  1. Gentle, J. E. Random Number Generation and Monte Carlo Methods, Second Edition, Springer (2003)
  2. Ripley, B. D. Stochastic Simulation, Wiley (1987)
  3. Gamerman, D. and Lopes, H. F. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition, Chapman and Hall (2006)
  4. Robert, C. P. and Casella, G. Monte Carlo Statistical Methods, Springer (1999)


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