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 ...
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 ...
The standard interpretation is correct, at least for near perfect collinearity with frequentist approaches (I am not familiar enough with Bayesian methods to comment, but I think the same would apply). The problem is how to apportion the effects. One of the major problems caused by collinearity is that very small changes in the data can have huge effects on the parameter estimates, even ...
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...
Bayesian approaches formulate the problem differently. Instead of saying the parameter simply has one (unknown) true value, a Bayesian method says the parameter's value is fixed but has been chosen from some probability distribution -- known as the prior probability distribution.
I understand what the posterior predictive distribution is, and I have been reading about posterior predictive checks, although it isn't clear to me what it does yet. What exactly is the posterior
@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.
The Bayesian interpretation of probability as a measure of belief is unfalsifiable. Only if there exists a real-life mechanism by which we can sample values of $\theta$ can a probability distribution for $\theta$ be verified. In such settings probability statements about $\theta$ would have a purely frequentist interpretation.
