given observed variables in the model we can calculate a posterior probability distribution
that can be further interpreted as a quantitative risk value.
To infer the posterior probability distribution
of these, the conditional probability topic word [x.sup.t.sub.di] and [x.sup.t.sub.db] (i.e.
From a probabilistic point of view, SLAM problem is to solve the posterior probability distribution
of system state vectors composed of vehicle pose vector [x.sub.R] and map feature vector [x.sub.F], which can be expressed as follows :
The Kullback-Leibler divergence is the information gained when one revises one's beliefs from the prior probability distribution to the posterior probability distribution
; that is, the KLD measures the amount of information lost when the prior probability distribution is used to approximate the posterior probability distribution
From the priori probability and likelihood distribution theory, the weight's posterior probability distribution
calculated by Bayes formula is:
We should note that the conditional distribution of d given data y (p([theta]|y)) is what we are interested in estimating and represents the posterior probability distribution
(simply called posterior) in the Bayesian framework.
The basis for the Bayesian analysis of reporting period savings is the joint posterior probability distribution
for the baseline regression parameter vector E and the variance [[sigma.sub.pre].sup.2]] as defined in Equation (7), with y equal to the baseline gas use and X equal to [X.sub.pre] as defined in Equation (9).
Estimates are presented as the 0.025, 0.50, and 0.975 probability intervals of the posterior probability distribution
(i.e., median surrounded by 95% prob ability intervals) for the average ([mu]) value across May-September periods, plus the probability of between-year differences in parameters over the 27 time periods, given by the posterior probability p(g=1) of each respective time-varying indicator variable g.
The probability of ([[Delta].sub.1], [[Delta].sub.2]) can be measured by estimating the Bayesian posterior probability distribution
of the parameters in the reparameterized model, where the posterior probability distribution
is the probability distribution of the parameters given the data.
142], that this new probability distribution is the posterior probability distribution
derived from the prior probability P by General Logical Imaging on y.
Using the Klepper model - but without the three irrelevant variables - and assigning to all of the parameters a normal prior probability with mean zero and a substantial variance, Scheines used Gibbs sampling to compute a posterior probability distribution
for the lead-to-IQ parameter.
It seems almost truistic to say that the posterior probability distribution
will be denser at c=2.99792458 x [10.sup.8] m/s than at c=2m/s.