Sentence examples for the prior function from inspiring English sources

Based on established results of the probability distribution of earthquake vulnerability, it is assumed that the prior function has the form of a beta-distribution (Spence et al. 2008), and the likelihood function, which is fitted using field surveys as observational data, also follows a beta-distribution, and therefore the posterior distribution also has a beta-distribution.

The first step of the normalisation is a global 12-parameter affine transformation based on the maximalization of the product of the likelihood function (derived from the residual squared difference) and the prior function (which is based on the probability of obtaining a particular set of zooms and shears) [49].

A first run of 10 million generations was first performed to optimize the scale factors of the prior function.

Initial MCMC test runs consisted of 10 million generations to optimize the scale factors of the prior function.

The normalization algorithm determined the optimum 12 parameter affine transformation using a Bayesian framework to maximize the product of the likelihood function and the prior function and then estimated nonlinear deformations, defined by a linear combination of 3D discrete cosine transform basis functions.

After an optimization step during which parameters of the prior function were changed at each run to reach optimum performance and achieve a reasonable effective sampling size (ESS, number of independent samples of the posterior distribution that the trace is equivalent to) of parameters of interest, we carried out two independent runs of 20 million generations each.

The last functions only explained 2.1%% of the remaining variance in the variable sets after the extraction of the prior functions.

Since α1 constitutes assessment of the likelihood and the prior functions that can be calculated as shown above, we subsequently consider only α2.

So we introduced the Cauchy prior function ({user2{p}}_{text{Cauchy}} ({mathbf{m}})) to our Laplace mixed-domain inversion in this paper.

It is important that the likelihood function and the prior distribution function of parameters are determined.

von Davier et al. ([2009]) refer to these two parts as the likelihood function and the prior distribution function.