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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.
The event ' R=0' is the event by which X and S are generated by two independent models: one for X and another for S. The parameters of all models are random variables that have been integrated out, with fixed (and common) hyperparameters.
The old Chrysler hasn't been integrated out of existence.
For population data, the likelihood function is the product across individual marginal likelihoods where the random effects η contained in equation (13), when y ^ is given by equation (6), have been integrated out.
So the context of AIC is then also the one where the ηs have been integrated out (but with the parameters at their estimated values), which is to be done when all data are acquired.
Variance component estimation by restricted maximum likelihood (REML), prediction of random effects, and Bayesian inference are all based on the likelihood after marginalization of the fixed effects, i.e., the fixed effects have been integrated out.
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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].
It will be integrated out through our stochastic sampling.
In some specific situations, these chain orientational degrees of freedom can be integrated out, and the quasi-static approximation is valid.
We show that under particular assumptions on the sampling scheme the unobserved confounders can be integrated out conditioning on the empirical distribution of covariates and policy variable within the cluster.
A key feature of our methods is that the signals being sensed are treated as random variables and are integrated out in the likelihood.
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