The phrase "integrate out" is correct and can be used in written English.
It is commonly used in mathematical and scientific contexts to describe the process of removing a variable or unknown value from an equation or model. For example: "The researchers were able to integrate out the noise factor from their data analysis, allowing them to produce more accurate results."
This approach is based on an efficient combination of Laplace approximations for the full conditional distributions π(θ | y ) and π(ξ i | θ, y ), i=1,…, n, and numerical integration routines to integrate out the hyperparameters θ.
It is therefore advantageous to integrate out any redundant random variable present in the estimation.
An attractive property of the current model is that we can integrate out analytically the volume variables, v τ.
In these cases, it is no more possible to integrate out f analytically as it was the case with Gaussians.
This Full Bayesian approach is illustrated as follows: One may also first integrate out one of them, for example f to obtain p ( θ g, θ 0 ) = ∫ p ( f, θ g, θ 0 ) d f, (6).
A more interesting approach suggested by van Soest (1995) is to estimate the wage equations simultaneously with the utility function and integrate out the unobserved wages of those who do not work.
The frailty (random effect) can be integrated out (in closed form or by numerical or stochastically integration, depending on the frailty distribution) to get a likelihood function not depending on unobserved quantities [ 19].
There is only one type of input, so the PDF Q is a delta function that can be integrated out. 2.
In some specific situations, these chain orientational degrees of freedom can be integrated out, and the quasi-static approximation is valid.
More specifically, it is possible to show, as an instance of the Rao-Blackwell theorem [13, 14], that integrating out some of the state variables in (9) analytically improves the accuracy of the approximation (11).
From (11), it is not difficult to see that ({E{tau (U,V |V}}), in which the random variable V is integrated out, has the same mean with ({tau (U,V }), yet a reduced variance.
