More generally, since the distribution model as a probability mixture may be an approximate one, an interesting problem would be to know to what extent a given distribution may be approximated by our proposed model in order to perform BSS.
MCMC is an application of the Law of Large Numbers and allows approximating expectations by averages of random draws from a given distribution.
Project summary: The interacting particle method approximates a given probability distribution by allowing particles in real space to evolve according to a system of coupled (hence interacting") differential equations, so that the particles' empirical density approaches the target distribution.
This paper considers the problem of approximating a given crystallite orientation distribution function (codf) by a set of texture components.
Theorem 1 states that for any normal random variable X with positive mean and coefficient of variation δ X ≤ 1, there exists another independent normal variable Y with a positive mean and a small coefficient of variation, fulfilling some conditions, such that their ratio Z can be well approximated within a given interval to a normal distribution.
IPknot predicts a pseudoknotted secondary structure that maximizes the approximate expected gain function (3), which represents the expectation of the (weighted) number of true predictions of base pairs under a given probability distribution.
To approximate the fitness distribution on a given tree, we will solve this equation numerically.
Together, the three plots in the diagnostic tab give a view of how well the MCMC chains are likely to approximate the true posterior distribution for a given parameter.
Thus, a random number selected from this distribution approximates the time required for a given particle to travel a specified distance.
The variation of selective constraint is approximated by a discrete gamma distribution [ 38],[ 39] in which a given number of categories represent a Γ distribution with unequal probabilities virtually to increase the number of categories.
We mention how probabilities can be estimated from a given data set and how a probability distribution can be approximated using a fuzzy histogram technique.
