Methods of Data Analysis Probabilistic models and inference

One of the basic tasks in data analysis is in confronting parametric models with data: this consists of inferring the parameters of the model from data, and subsequently checking how well the model (with the inferred parameters) predicts new phenomena, or at least how well it performs on a repeat of the same experiment. How inference is done depends in practice very much in the tradition of the field, and on the kind of data (e.g. how many measurements are available compared to the number of parameters to be learned) and prior knowledge that is available about the problem (e.g., do laws of physics / theory put constraints on the parameters or the properties of the measurement process). Even within a discipline, some subfields might use frequentist approaches and statistics (e.g., particle physics), while Bayesian inference is accepted in other fields (e.g., cosmology).