# Probabilistic likelihood model

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.