This course provides a comprehensive introduction to the principles and practice of advanced data analysis, with particular focus on their application in physics and astronomy and on the growing use of Bayesian Inference methods in these fields.

To be determined

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1) Continuous assessement via practical exercises and homework assignments (50%)

2) Final report on mock data challenge (50%)

1) To acquire a working knowledge of advanced data analysis methods - i.e. to a level sufficient to permit their successful application to real data analysis problems, as would be encountered in students' own research projects.

2) To develop awareness of the current literature on advanced data analysis for the physical sciences, and the software available to support its application to real problems.

At the end of the course students should be able to:

1) Describe qualitatively the theoretical foundations of the nature of probability, in the context of both a frequentist and Bayesian framework.

2) Define what is meant by a probability density function (pdf), and cumulative distribution function (cdf), as well as various descriptive statistics (e.g. mean, median, mode, moments, variance, covariance) used to characterize pdfs and cdfs.

3) Apply the principles of least squares and maximum likelihood to formulate and solve line and curve model fitting problems - using a matrix formulation where appropriate, and adapting the formulation to various cases and approximations (e.g. weighted least squares, correlated errors, non-linear problems).

4) Describe and apply the basic concepts of frequentist hypothesis testing, using the chi-squared goodness-of-fit test as an archetypal example.

5) Define in a Bayesian context the likelihood, prior and posterior distributions and their role in Bayesian inference and hypothesis testing, contrasting Bayesian and frequentist treatments of hypothesis testing.

6) Define the evidence and explain its role in Bayesian model selection, describing several numerical approximations to the evidence and their applicability.

7) Describe and apply data compression techniques for analysis of very large data sets, including singular value decomposition and principal component analysis.

8) Describe and apply efficient numerical techniques for generating random numbers and performing Monte Carlo simulations, including Markov Chain Monte Carlo methods for parameter estimation and model selection in problems of high dimensionality.

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