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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.

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.

[[Category:Mathematics]]

[[category:Probability and Statistics]]