The Bootstrap likelihood function for Bayesian inference

See also: The Bootstrap, Analyzing and using data introduction, The parametric Bootstrap, The non-parametric Bootstrap, VoseNBoot, Bayesian inference

The Bayesian Bootstrap is considered to be a robust Bayesian approach for estimating a parameter of a distribution where one has a random sample X from that distribution. It proceeds in the usual Bootstrap way, determining a distribution of , the distribution density of which is then interpreted as the likelihood function l(X|q). This is then used in the standard Bayesian inference formula along with a prior distribution p(q) for q to determine the posterior distribution. In many cases, the Bootstrap distribution for  closely approximates a Normal distribution, so by calculating the mean and standard deviation of the B Bootstrap estimates  one can quickly define a likelihood function.