Data Source and Methodology
All calculations are based strictly on Bayesian statistical formulas. For more details, refer to the Social Science Statistics.
The Formula Explained
Glossary of Terms
- Prior Probability: The initial judgement before new evidence is considered.
- Likelihood: The probability of observing the evidence given the hypothesis.
- Evidence: The overall probability of the evidence under all hypotheses.
- Posterior Probability: The updated probability after considering the evidence.
How It Works: A Step-by-Step Example
Suppose you have a prior belief that a coin is biased towards heads with a 60% probability. You observe 10 flips and see 8 heads. Using Bayesian inference, you update your belief based on this new evidence.
Frequently Asked Questions (FAQ)
What is Bayesian Inference?
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.
How is Bayesian Inference different from Frequentist statistics?
Frequentist statistics relies on the frequency or proportion of data, whereas Bayesian statistics provides a probabilistic framework to incorporate prior knowledge or beliefs.
Can I use Bayesian Inference for non-binomial distributions?
Yes, Bayesian inference can be applied to various types of distributions. This calculator focuses on binomial distributions.
What is the role of prior probability in Bayesian Inference?
The prior probability represents your initial belief about a hypothesis before you have new evidence.
Why is Bayesian Inference important?
Bayesian inference allows for flexible modeling and the ability to update beliefs with new data, making it a valuable tool for decision-making under uncertainty.