Sentence examples for distribution is proper from inspiring English sources

When developing noninformative priors, it is crucial to study whether the resulting posterior distribution is proper.

In Bayesian statistics, however, this is not regarded as a problem, provided that the posterior distribution is proper (i.e., the integral in the denominator of Eq. 3 converges to a finite value).

We determine the distribution of random error using the approaches described in [13] and find that the normal distribution is proper.

To sample from the posterior parameter distribution, one needs to verify that the posterior distribution is proper.

By performing PL analysis, we were able to specify sufficient priors to ensure that the posterior distribution was proper and could be sampled from.

Posterior distributions are proper.

Comment 4. This proof holds for improper prior distributions provided the posterior distributions are proper.

The t-processes with μ = 1, 2, 4 do not have a finite variance, but the distributions are proper (i.e., the density integrates to 1).

After checking whether the posterior distribution of parameters is proper, a sample from this distribution can be obtained using Markov Chain Monte Carlo (MCMC) [ 22, 28].

This implies that the posterior distribution of the joint model is proper because the distribution conditions on the observed leaf sequence lengths.

Interestingly, if we choose α = 0 within our prior distribution, the p-value according to Fisher's Exact Test is equal to P{log OR > 0} [ 54], implying perfect agreement between the two methods when c = 0. We decided to set α = 0.001, which practically gives the same results as Fisher's Exact Test (again when c = 0), but guarantees that our posterior distribution will be proper.