POSTERIOR PROBABILITY Meaning and
Definition
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The term "posterior probability" refers to the updated probability of a hypothesis or event after observing new evidence or data. It is a concept commonly used in Bayesian statistics, which aims to estimate probabilities by combining prior knowledge with observed data.
In simple terms, the posterior probability is the probability of a hypothesis being true given the data or information at hand. It is calculated using Bayes' theorem, which mathematically combines a prior probability (the belief in the hypothesis before observing any data) with the likelihood of the observed data under the hypothesis. By incorporating new evidence, the posterior probability provides a revised and more accurate estimate of the likelihood of the hypothesis.
The posterior probability takes into account both the prior knowledge and the observed data, allowing for a more informed and updated assessment. It is often used to make decisions or draw conclusions based on the available evidence. Higher posterior probabilities indicate stronger belief in the hypothesis, while lower probabilities suggest less confidence.
The calculation of posterior probabilities is essential in various fields, including medical diagnoses, predictive modeling, and machine learning. It enables researchers, analysts, and decision-makers to better understand the uncertainty associated with their hypotheses and make more informed judgments based on the available evidence.
Etymology of POSTERIOR PROBABILITY
The word "posterior probability" has its origins in Bayesian statistics and Bayesian inference.
"Posterior" refers to the probability distribution that is obtained after incorporating new evidence or information into prior beliefs. In Bayesian analysis, it represents the updated probability of a hypothesis or parameter value based on the observed data.
"Probability" comes from the Latin word "probabilitas", which means "likelihood" or "likelihood of being proved".
Therefore, "posterior probability" can be understood as the updated probability estimation that comes after considering new evidence or information in Bayesian statistics.
