A Bayesian model is a statistical model made of the pair prior x likelihood = posterior x marginal. Bayes' theorem is somewhat secondary to the concept of a prior.
Confessions of a moderate Bayesian, part 4 Bayesian statistics by and for non-statisticians Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian Probability Read part 3: How Bayesian Inference Works in the Context of Science Predictive distributions A predictive distribution is a distribution that we expect for future observations. In other ...
19 In plain english, update a prior in bayesian inference means that you start with some guesses about the probability of an event occuring (prior probability), then you observe what happens (likelihood), and depending on what happened you update your initial guess. Once updated, your prior probability is called posterior probability.
The Bayesian Choice for details.) In an interesting twist, some researchers outside the Bayesian perspective have been developing procedures called confidence distributions that are probability distributions on the parameter space, constructed by inversion from frequency-based procedures without an explicit prior structure or even a dominating ...
I am currently reading about Bayesian Methods in Computation Molecular Evolution by Yang. In section 5.2 it talks about priors, and specifically Non-informative/flat/vague/diffuse, conjugate, and hyper- priors.
@Xi'an's answer (below) helped me - clarifying that the Dirichlet distribution is A prior for the multinomial, not THE prior. It's chosen because it is a conjugate prior that works well to describe certain systems such as documents in NLP.
In a Bayesian framework, we consider parameters to be random variables. The posterior distribution of the parameter is a probability distribution of the parameter given the data. So, it is our belief about how that parameter is distributed, incorporating information from the prior distribution and from the likelihood (calculated from the data).
When evaluating an estimator, the two probably most common used criteria are the maximum risk and the Bayes risk. My question refers to the latter one: The bayes risk under the prior $\\pi$ is defi...
