Bayesiläiset

Bayesiläiset, also known as Bayesians, are a group of statisticians and philosophers who interpret probability within the context of the Bayesian interpretation of probability. This interpretation contrasts with the frequentist interpretation, which is based on the frequency of outcomes in repeated trials. Bayesians view probability as a measure of belief or confidence in the truth of a proposition, rather than as a frequency of occurrence.

The Bayesian approach is named after the Reverend Thomas Bayes, an 18th-century statistician and minister. Bayes' theorem, a fundamental concept in Bayesian statistics, describes the probability of an event based on prior knowledge of conditions that might be related to the event. The theorem is expressed as:

P(A|B) = [P(B|A) * P(A)] / P(B)

where P(A|B) is the probability of event A occurring given that B is true, P(B|A) is the probability of event B occurring given that A is true, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.

Bayesians use Bayes' theorem to update the probability for a hypothesis as more evidence or information becomes available. This process is known as Bayesian inference. Bayesian methods are widely used in various fields, including machine learning, artificial intelligence, and data analysis, where they provide a framework for making predictions and decisions under uncertainty.

Despite their name, Bayesians are not a monolithic group. There are different schools of thought within Bayesianism, including subjective Bayesianism, which allows for a wide range of interpretations of probability, and objective Bayesianism, which seeks to provide a more rigorous and mathematically grounded approach to Bayesian inference.