Probabilistic likelihood model

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In simple terms a probabilistic likelihood model is a mathematical model which gives the probability of some observation (data) for some stated mathematical model capable of predicting said data as an outcome (observation). It is typically denoted as p(D|M) which is simply the conditional probability for the data D given some model M. In parameter estimation exercises, it is often written as p(D|a) where a is a mathematical parameter of the model class M which indicates which member out of a family of associated models differing only by the value of the parameter that one is referring to, e.g., a family of models which give the likelihood (probability) of observing a coin flip of heads, where the parameter a might indicate different possible weightings of a coin which would then lead to different probabilities of landing on heads in an unbiased flip.

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