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TitleBayesian Statistics
File Size3.2 MB
Total Pages97
Document Text Contents
Page 1

Introduction to Bayesian Statistics
(And some computational methods)

Theo Kypraios
http://www.maths.nott.ac.uk/∼tk

MSc in Applied Bioinformatics @ Cranfield University.

Statistics and Probability Research Group
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Page 2

My Background

Bayesian Statistics;

Computational methods, such as Markov Chain and
Sequential Monte Carlo (MCMC & SMC);

Large and complex (real) data analysis, mainly Infectious
Disease Modelling, Neuroimaging, Time series . . ..

Recent interest in Bioinformatics (Gene Expression Data).

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Page 48

Some Examples on the Effect of the Prior

83/100 successes: interested in probability of success θ

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Page 49

Some Examples on the Effect of the Prior

83/100 successes: interested in probability of success θ

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Page 96

Conclusions

Quantification of the uncertainty both in parameter estimation
and model choice is essential in any modelling exercise.

A Bayesian approach offers a natural framework to deal with
parameter and model uncertainty.

It offers much more than a single “best fit” or any sort
“sensitivity analysis”.

Markov Chain Monte Carlo methods are only one of the
available tools that enables us to draw samples posterior
distribution.

There exist others such as Approximate Bayesian Computation
(ABC), Sequential Monte Carlo, (Particle) Filtering etc.

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Page 97

Conclusions (2)

Although we have focused on some very simple models, the
same techniques apply for more complicated situations.

Nevertheless, it is often the case (depending on the model,
the data etc) that alternative methods should be
used/developed to improve the efficiency of standard
methods.

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