Probability is the measure of the likelihood that an event will occur that is, what is the certainty that a specific event will occur? Where-as a likelihood function is a function of parameters within the parameter space that describes the probability of obtaining the observed data.
In the context of statistics and machine learning, the terms “probability” and “likelihood” are closely related but have distinct meanings:
- Probability: Probability refers to the likelihood of a particular event occurring, given some underlying model or assumption. It quantifies the uncertainty associated with different outcomes of a random experiment. In simpler terms, probability tells us how likely it is for an event to occur, based on our prior knowledge or assumptions.
- Likelihood: Likelihood, on the other hand, is a measure of the support provided by the observed data for different values of a parameter in a statistical model. It indicates the degree to which a particular set of data supports one parameter value over another. In essence, likelihood tells us how well a given set of parameters explains the observed data.
To summarize:
- Probability is concerned with the likelihood of events happening given a known set of parameters or conditions.
- Likelihood is concerned with how well specific parameter values explain the observed data.
In practical terms, probability is used to make predictions about future events, while likelihood is used in statistical inference to estimate parameters of a model based on observed data.