Sampling from Probability Distributions
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This chapter develops the relevant concepts and probabilistic results that are needed in order to study the problem of sampling from probability models. It probes the behaviour of a random sample, how this relates to the original model, and what aspects of a sample are important for the purposes of statistical inference (sufficiency). Key results are provided for the sampling distribution of sufficient statistics for Gaussian and exponential family models. The second part of the chapter focusses on the description the sampling behaviour of statistics by means of asymptotic approximations, introducing key notions from stochastic convergence.