Bayesmenetelmät

Bayesmenetelmät, also known as Bayesian methods, are a class of statistical inference techniques based on Bayes' theorem. This theorem provides a way to update the probability of a hypothesis as more evidence or information becomes available. In Bayesian statistics, probabilities are interpreted as degrees of belief.

The core idea involves combining prior knowledge or beliefs about a parameter with observed data to produce an updated or posterior belief. The prior probability represents what is believed before observing any data, while the posterior probability reflects the updated belief after the data has been considered. Bayes' theorem mathematically expresses this update: Posterior Probability is proportional to Likelihood of Data times Prior Probability.

This approach is widely used in various fields, including machine learning, signal processing, and econometrics. Bayesian methods offer a principled way to handle uncertainty and incorporate prior information into statistical models. They can be particularly useful when dealing with complex models or limited data. The computational implementation of Bayesian methods often relies on Markov Chain Monte Carlo (MCMC) techniques to approximate the posterior distributions.