Bayesian statistics is a statistical paradigm that updates the probability for a hypothesis as more evidence or information becomes available, using Bayes' theorem as its foundation. It contrasts with frequentist statistics by incorporating prior knowledge or beliefs, expressed as a prior distribution, into the analysis to produce a posterior distribution that reflects both the prior information and the new data.

Bayesian Statistics

Bayesian statistics

statistical paradigm

probability for a hypothesis

more evidence or information

Bayes' Theorem provides a mathematical framework for updating the probability of a hypothesis based on new evidence, balancing prior beliefs with the likelihood of observed data. It is foundational in fields like statistics, machine learning, and data science for making informed inferences and decisions under uncertainty.

Bayes' theorem

Frequentist statistics is an approach to statistical inference that interprets probability as the long-run frequency of events and emphasizes the use of data from repeated sampling. It relies heavily on hypothesis testing, confidence intervals, and p-values to draw conclusions about population parameters based on sample data.

frequentist statistics

prior knowledge or beliefs

A prior distribution in Bayesian statistics represents the initial beliefs about a parameter before observing any data, influencing the posterior distribution after data is taken into account. It allows for the incorporation of existing knowledge or subjective judgment into statistical analysis, making Bayesian methods flexible and adaptive to new information.

prior distribution

Posterior distribution represents the updated probability of a hypothesis after considering new evidence and is a fundamental concept in Bayesian statistics. It combines prior beliefs with likelihood from observed data to provide a comprehensive probability model for inference and decision-making.

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