Bayesiani

Bayesiani is a term used in some languages, notably Italian, to refer to proponents or adherents of Bayesian statistics or Bayesian epistemology. The word combines the surname Bayes with a plural or adjectival suffix, and in English-language sources the corresponding term is Bayesians.

Bayesiani advocate Bayesian inference, a statistical paradigm that treats probability as a degree of belief and updates prior information with data through Bayes' theorem. The central idea is to combine a prior distribution with a likelihood to obtain a posterior distribution, which is then used for inference, prediction, and decision making. Priors may be subjective or formalized as noninformative or objective priors, depending on the problem and the analyst's philosophy.

Historically, Bayesian reasoning appears in the work of Thomas Bayes and was developed further by Pierre-Simon Laplace. Since the 20th century Bayesian methods have gained prominence across statistics, data science, medicine, finance, and artificial intelligence. Bayesiani commonly emphasize coherent probabilistic reasoning, model comparison with Bayes factors, and explicit accounting of uncertainty in parameters and predictions. Computational tools such as Markov chain Monte Carlo and variational inference enable practical application to complex models.

Debates about Bayesian methods include the choice and influence of priors, computational demands, and the interpretation of probability. While Bayesian and frequentist approaches differ philosophically, Bayesian methods are widely used and supported by extensive software, tutorials, and methodological literature.

See also Bayes' theorem, Bayesian statistics, probabilistic programming.