Probabilistic data analysis: an introductory guide

Quantitative science requires the assessment of uncertainty, and this means that measurements and inferences should be described as probability distributions. This is done by building data into a probabilistic likelihood function which produces a posterior ‘answer’ by modulating a prior ‘question’. Probability calculus is the only way of doing this consistently, so that data can be included gradually or all at once while the answer remains the same. However, probability calculus is only a language; it does not restrict the questions one can ask by setting one's prior. We discuss how to set sensible priors, in particular for a large problem like image reconstruction. We also introduce practical modern algorithms (Gibbs sampling, Metropolis algorithm, genetic algorithms, and simulated annealing) for computing probabilistic inference.