Posterior Probability

What Is a Posterior Probability?

A posterior likelihood, in Bayesian statistics, is the reconsidered or refreshed likelihood of an event happening subsequent to thinking about new data. The posterior likelihood is calculated by refreshing the prior probability utilizing Bayes' theorem. In statistical terms, the posterior likelihood is the likelihood of event A happening given that event B has happened.

Bayes' Theorem Formula

The formula to compute a posterior likelihood of A happening given that B happened:
$\begin&P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A) \times P(B \mid A)}{P(B)}\&\textbf\&A, B=\text\&P(B \mid A)=\text\&\text\&P(A) \textP(B)=\text\&\text\end$
The posterior likelihood is subsequently the subsequent distribution, P(A|B).

What Does a Posterior Probability Tell You?

Bayes' theorem can be utilized in numerous applications, like medication, finance, and economics. In finance, Bayes' theorem can be utilized to refresh a previous conviction once new data is gotten. Prior likelihood addresses what is initially accepted before new evidence is presented, and posterior likelihood considers this new data.

Posterior likelihood distributions ought to be a better impression of the underlying truth of a data generating process than the prior likelihood since the posterior included more data. A posterior likelihood can in this way turned into a prior for another refreshed posterior likelihood as new data emerges and is incorporated into the analysis.

Features

• A posterior likelihood, in Bayesian statistics, is the overhauled or refreshed likelihood of an event happening in the wake of thinking about new data.
• The posterior likelihood is calculated by refreshing the prior likelihood utilizing Bayes' theorem.
• In statistical terms, the posterior likelihood is the likelihood of event A happening given that event B has happened.