bayesianas

Bayesianas, in common statistical usage, refer to Bayesian methods, a family of techniques based on Bayes' theorem, which updates the probability of a hypothesis as new data become available. Central to the approach is the posterior distribution, obtained by combining a prior distribution with the likelihood of observed data. In formula form, the posterior is proportional to the prior times the likelihood: P(theta|data) ∝ P(data|theta)P(theta). The prior expresses beliefs before observing data, while the likelihood expresses how probable the data are under different parameter values.

These methods provide a coherent probabilistic framework for inference and decision making, offering natural uncertainty quantification. They are used for parameter estimation, model comparison, and predictive inference. Common models include Bayesian linear and logistic regression, hierarchical models, Gaussian processes, and Bayesian networks. Bayesian networks are graphical models that encode probabilistic relationships and conditional independencies among variables, enabling structured inference in complex systems.

Computation often relies on numerical techniques such as Markov chain Monte Carlo and variational inference, especially when analytic solutions are not available. Conjugate priors can yield closed-form posteriors in some cases, but many modern applications rely on approximate methods.

Bayesian methods have broad applications across science and industry, including medicine, finance, environmental science, and machine learning. They require careful prior specification and model checking, as results can be sensitive to prior choices and to model misspecification. The approach originated with Thomas Bayes and was significantly developed in the 18th century, with substantial advances in the late 20th century that expanded its practical use.