Bayes’ Theorem
Bayes’ Theorem is a fundamental principle in probability theory that describes how to update the probability of a hypothesis based on new evidence. It is used to determine the conditional probability of event A when event B has already happened.
The theorem mathematically provides a formula to calculate the probability of a hypothesis given observed evidence, taking into account the prior probability of the hypothesis and the probability of observing the evidence under different hypotheses. The formula encapsulates the essence of Bayesian inference allowing for seamless integration of prior beliefs (prior distribution) and new data (likelihood function) to compute an updated belief (posterior distribution). The formula:
where,
- P(A∣B) : Posterior distribution, updated belief about the parameter.
- P(B∣A) : Likelihood function, probability of observing the data given the parameter.
- P(A) : Prior distribution, prior belief about the parameter.
- P(B) : Marginal likelihood, probability of observing the data.
Bayes’ Theorem allows us to update our prior beliefs based on new evidence to obtain an updated or posterior distribution . The marginal likelihood ensures that the updated distribution is a proper probability distribution. This framework is fundamental to Bayesian statistics and provides a coherent way to incorporate prior knowledge and update beliefs in light of new data.
Power of Bayesian Statistics & Probability
In the data-driven world we inhabit, statistics reign supreme. They guide our decisions, reveal hidden patterns, and empower us to predict the future. But amongst the diverse statistical arsenal, Bayesian statistics and probability stand out as a unique and powerful duo, capable of transforming how we approach uncertainty and unlock deeper insights from data.
This article delves into the fundamentals of Bayesian statistics and explores its applications ,shedding light on its significance and potential impact.
Table of Content
- Bayesian Statistics
- What Is Frequentist Statistics?
- Conditional Probability
- Bayes’ Theorem
- Probability in a Bayesian Statistics
- Example of Bayesian Statistics and Probability
- Bayesian Statistics & Probability- FAQs
Contact Us