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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].
A key feature of our methods is that the signals being sensed are treated as random variables and are integrated out in the likelihood.
Unlike in maximum-likelihood estimation, the model parameters have been integrated out in variational inference schemes and optimizing the KL divergence in fastSTRUCTURE does not run the risk of overfitting.
As model parameters are integrated out in this procedure, the model evidence includes a complexity term that penalizes models with more parameters, e.g., more columns in the design matrix in a general linear model.
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Alternatively, the pathway effects can be considered as nuisance parameters and integrated out of the model given in Equation (3).
In the H-step, the random effects are integrated out.
In their Bayesian approaches, all branch lengths are integrated out analytically, thereby greatly reducing the computational burden.
If the unknown parameters θ are integrated out as in equation 4, the posterior model probability incorporates a balance between complexity and fit.
Although we primary focused on answering the question of whether the entire promoter has a binding site for a TF, we also developed a method for computing binding probabilities at each nucleotide position by essentially integrating out other locations in a promoter.
One solution is to integrate out the prediction error in the wage equations, at the cost of increasing the dimensionality of the estimation problem.
Leventhal et al. (2014) fitted a stochastic model using numerical approximation to the solution of the underlying master equation, in order to integrate out the (unknown) number of transmission events in the population that occur between coalescent intervals in the sample.
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