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The variance reduction technique Rao-Blackwellization has been used to accurately approximate p(x t, a t, o t | z1 t) This technique assumes that the random variables have a special structure that allows to analytically marginalize out some of the variables conditioned to the rest ones, improving the estimation in high dimensional problems.
It turns out that even EM is too slow for our application, because of the need to marginalize out Z t g, and because of EM's relatively slow convergence.
To marginalize out the underlying allele frequencies, we need to sum over all possible values of p 0, p 1, …, p t, and the number of summations equals the number of nuisance parameters.
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A joint problem formulation, where quantities that are not of particular interest are marginalized out from a joint posterior distribution, or an intrinsically marginal formulation, which is based on an integrated likelihood function, can be chosen according to the inferential objective and computational convenience.
These unobserved or latent variables are marginalized out instead of being explicitly calculated.
First, the approach breaks up the interdependence of the hidden states and the static parameters by marginalizing out the states using a particle filter.
Evaluation of the full posterior turns out to be not only computationally prohibitive but useless if states cannot be marginalized out analytically.
Similarly, the a posteriori pdf of the channel vector is obtained as a Gaussian mixture by marginalizing out all possible ISI state transitions (41).
Under the minimum mean square error (MMSE) criterion, the forward filtered channel vector estimated at instant is obtained by marginalizing out the ISI state variable (42).
Similarly, the MMSE smoothed estimate of the channel vector at instant is obtained by marginalizing out all possible ISI state transitions (43).
In state-based marginalization, each state output PDF is a function of the reliable components only, while the unreliable components are marginalized out, i.e., each unreliable component is integrated over the range of values it can assume.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com