Accurate modeling of management and economic processes often requires that researchers accurately approximate the expectations of functions of random variables.
In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations.
To achieve this, we combine a formula obtained by Zhang and Williams [11] to compute Stieltjes constants (see also Coffey [9]) and a probabilistic perspective based on a differentiation formula for expectations of functions of the gamma process (see formula (20) in Section 3).
High expectations of functioning have been found to enhance patients' engagement in treatment services and subsequently treatment outcomes [ 43].
Thus, life context (e.g., expectations of functioning in important roles) is crucial for explaining the link between disease and significant emotional distress.
The expectation of function with respect to is denoted by.
The expectation of function f(x) with respect to x is denoted by E { f ( x ) }.
Indeed, the following is true for any two distributions π and q: (9) If we have a set of samples y1, y2, …, y m following the distribution q, then the unbiased estimation for 1, according to equation (9), is (10) (note that we sample from distribution q and would like to estimate expectation of function π/ q).
Contrary to expectations, loss-of-function of the methylcytosine dioxygenase TET2 is predominantly associated with loss of DNA methylation [ 49].
Presently, a simple form of a variance reduction strategy is proposed such that the ensemble size may be significantly reduced without affecting the accuracy of the predicted expectations of any function of the response vector process provided that the function can be adequately represented through a power-series approximation.
