The formulation of statistical models using Bayesian statistics has the identifying feature of requiring the specification of prior distributions for any unknown parameters.

2025年2月4日 · In this article, we’ll walk through your first Bayesian model, covering prior specification, Markov Chain Monte Carlo (MCMC) sampling, and essential diagnostic plots using ArviZ. We will also utilize PyMC, a probabilistic programming library allowing us to build Bayesian models and fit them using Markov Chain Monte Carlo (MCMC) techniques.

2023年2月20日 · Answering complex research questions requires the right kind of analytical tools. One of the most powerful of these tools is Bayesian modeling. But what is it exactly, and what are its advantages?

Bayesian statistics gives us a solid mathematical means of incorporating our prior beliefs, and evidence, to produce new posterior beliefs. Bayesian statistics provides us with mathematical tools to rationally update our subjective beliefs in light of new data or evidence.

2024年12月5日 · Bayesian statistics is a statistical approach that utilizes Bayes’ theorem for data analysis and parameter estimation. What sets Bayesian statistics apart is that all observed and unobserved parameters in a statistical model are assigned a joint probability distribution, known as the prior and data distributions.

• Concepts and methods of Bayesian inference. • Bayesian hypothesis testing and model comparison. • Derivation of the Bayesian information criterion (BIC). • Simulation methods and Markov chain Monte Carlo (MCMC). • Bayesian computation via variational inference. • Some subtle issues related to Bayesian inference.

Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem: = () (), where

A model describes data that one could observe from a system If we use the mathematics of probability theory to express all forms of uncertainty and noise associated with our model... ...then inverse probability (i.e. Bayes rule) allows us to infer unknown quantities, adapt our models, make predictions and learn from data.

Bayesian modelling methods provide natural ways for people in many disciplines to structure their data and knowledge, and they yield direct and intuitive answers to the practitioner’s questions. There are many varieties of Bayesian analysis.

2024年12月11日 · Bayesian statistics is a branch of statistics based on Bayes’ theorem, which provides a framework to update probabilities and predictions as new evidence or additional data becomes available. You can use Bayesian statistics across many exciting fields, including health care policy, machine learning, finance, and marketing. Explore the ...