1,060 research outputs found
Variational approximation for mixtures of linear mixed models
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped
data and can be estimated by likelihood maximization through the EM algorithm.
The conventional approach to determining a suitable number of components is to
compare different mixture models using penalized log-likelihood criteria such
as BIC.We propose fitting MLMMs with variational methods which can perform
parameter estimation and model selection simultaneously. A variational
approximation is described where the variational lower bound and parameter
updates are in closed form, allowing fast evaluation. A new variational greedy
algorithm is developed for model selection and learning of the mixture
components. This approach allows an automatic initialization of the algorithm
and returns a plausible number of mixture components automatically. In cases of
weak identifiability of certain model parameters, we use hierarchical centering
to reparametrize the model and show empirically that there is a gain in
efficiency by variational algorithms similar to that in MCMC algorithms.
Related to this, we prove that the approximate rate of convergence of
variational algorithms by Gaussian approximation is equal to that of the
corresponding Gibbs sampler which suggests that reparametrizations can lead to
improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG
New Agegraphic Dark Energy in Gravity
In this paper we study cosmological application of new agegraphic dark energy
density in the gravity framework. We employ the new agegraphic model of
dark energy to obtain the equation of state for the new agegraphic energy
density in spatially flat universe. Our calculation show, taking , it is
possible to have crossing -1. This implies that one can
generate phantom-like equation of state from a new agegraphic dark energy model
in flat universe in the modified gravity cosmology framework. Also we develop a
reconstruction scheme for the modified gravity with action.Comment: 8 pages, no figur
Interacting new agegraphic Phantom model of dark energy in non-flat universe
In this paper we consider the new agegraphic model of interacting dark energy
in non-flat universe. We show that the interacting agegraphic dark energy can
be described by a phantom scalar field. Then we show this phantomic description
of the agegraphic dark energy and reconstruct the potential of the phantom
scalar field.Comment: 8 pages, no figur
Equations of State in the Brans-Dicke cosmology
We investigate the Brans-Dicke (BD) theory with the potential as cosmological
model to explain the present accelerating universe. In this work, we consider
the BD field as a perfect fluid with the energy density and pressure in the
Jordan frame. Introducing the power-law potential and the interaction with the
cold dark matter, we obtain the phantom divide which is confirmed by the native
and effective equation of state. Also we can describe the metric gravity
with an appropriate potential, which shows a future crossing of phantom divide
in viable gravity models when employing the native and effective
equations of state.Comment: 23 pages, 7 figure
A New Type of Dark Energy Model
In this paper, we propose a general form of the equation of state (EoS) which
is the function of the fractional dark energy density . At least,
five related models, the cosmological constant model, the holographic dark
energy model, the agegraphic dark energy model, the modified holographic dark
energy model and the Ricci scalar holographic dark energy model are included in
this form. Furthermore, if we consider proper interactions, the interactive
variants of those models can be included as well. The phase-space analysis
shows that the scaling solutions may exist both in the non-interacting and
interacting cases. And the stability analysis of the system could give out the
attractor solution which could alleviate the coincidence problem.Comment: Minor modifications, references adde
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