The formula to calculate the Posterior Probability (P(H|E)) is:
\[ P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)} \]
Where:
A posterior probability, in the context of Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information. It is calculated using Bayes’ theorem, which is a mathematical formula for determining conditional probability. The posterior probability helps to measure how the probability of a hypothesis changes when evidence is introduced. It is a fundamental concept in Bayesian inference, a statistical paradigm that answers research questions about unknown parameters using probability statements.
Let's assume the following values:
Using the formula:
\[ P(H|E) = \frac{0.8 \cdot 0.5}{0.6} \approx 0.6667 \]
The Posterior Probability (P(H|E)) is approximately 0.6667.