In classical likelihood an important goal is to learn about a parameter \(\theta \) regarded as a fixed unknown quantity. This is accomplished collecting data y assumed to be a realisation from a probability model \(p(y|\theta )\) indexed by \(\theta \) . This probability model gives rise to the likelihood, a function of \(\theta \) conditional on the realised y, from which the maximum likelihood estimate \(\hat {\theta }\) is obtained. The ML estimator is a random variable (a function of y), whose distribution is characterised by conceptual replications of y. This distribution describes the (sampling) uncertainty of \(\hat {\theta }\) and is typically unknown.

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Bayesian Methods

  • Daniel Sorensen

摘要

In classical likelihood an important goal is to learn about a parameter \(\theta \) regarded as a fixed unknown quantity. This is accomplished collecting data y assumed to be a realisation from a probability model \(p(y|\theta )\) indexed by \(\theta \) . This probability model gives rise to the likelihood, a function of \(\theta \) conditional on the realised y, from which the maximum likelihood estimate \(\hat {\theta }\) is obtained. The ML estimator is a random variable (a function of y), whose distribution is characterised by conceptual replications of y. This distribution describes the (sampling) uncertainty of \(\hat {\theta }\) and is typically unknown.