3,428 research outputs found
Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
Typical Bayesian methods for models with latent variables (or random effects)
involve directly sampling the latent variables along with the model parameters.
In high-level software code for model definitions (using, e.g., BUGS, JAGS,
Stan), the likelihood is therefore specified as conditional on the latent
variables. This can lead researchers to perform model comparisons via
conditional likelihoods, where the latent variables are considered model
parameters. In other settings, however, typical model comparisons involve
marginal likelihoods where the latent variables are integrated out. This
distinction is often overlooked despite the fact that it can have a large
impact on the comparisons of interest. In this paper, we clarify and illustrate
these issues, focusing on the comparison of conditional and marginal Deviance
Information Criteria (DICs) and Watanabe-Akaike Information Criteria (WAICs) in
psychometric modeling. The conditional/marginal distinction corresponds to
whether the model should be predictive for the clusters that are in the data or
for new clusters (where "clusters" typically correspond to higher-level units
like people or schools). Correspondingly, we show that marginal WAIC
corresponds to leave-one-cluster out (LOcO) cross-validation, whereas
conditional WAIC corresponds to leave-one-unit out (LOuO). These results lead
to recommendations on the general application of the criteria to models with
latent variables.Comment: Manuscript in press at Psychometrika; 31 pages, 8 figure
Lattice dynamics of BaTiO3, PbTiO3 and PbZrO3: a comparative first-principles study
The full phonon dispersion relations of lead titanate and lead zirconate in
the cubic perovskite structure are computed using first-principles variational
density-functional perturbation theory, with ab initio pseudopotentials and a
plane-wave basis set. Comparison with the results previously obtained for
barium titanate shows that the change of a single constituent (Ba to Pb, Ti to
Zr) has profound effects on the character and dispersion of unstable modes,
with significant implications for the nature of the phase transitions and the
dielectric and piezoelectric responses of the compounds. Examination of the
interatomic force constants in real space, obtained by a transformation which
correctly treats the long-range dipolar contribution, shows that most are
strikingly similar, while it is the differences in a few key interactions which
produce the observed changes in the phonon dispersions. These trends suggest
the possibility of the transferability of force constants to predict the
lattice dynamics of perovskite solid solutions.Comment: 9 pages, 2 figures (one in colors), revised version (small changes
essentially in Sec. III
Hexagonal as semiconducting ferroelectrics
We use a first-principles rational-design approach to identify a
previously-unrecognized class of ferroelectric materials in the LiGaGe
structure type. We calculate structural parameters, polarization and
ferroelectric well depths both for reported and as-yet hypothetical
representatives of this class. Our results provide guidance for the
experimental realization and further investigation of high-performance
materials suitable for practical applications.Comment: 5 pages, 2 figures, 3 table
Enhancement of piezoelectricity in a mixed ferroelectric
We use first-principles density-functional total energy and polarization
calculations to calculate the piezoelectric tensor at zero temperature for both
cubic and simple tetragonal ordered supercells of Pb_3GeTe_4. The largest
piezoelectric coefficient for the tetragonal configuration is enhanced by a
factor of about three with respect to that of the cubic configuration. This can
be attributed to both the larger strain-induced motion of cations relative to
anions and higher Born effective charges in the tetragonal case. A normal mode
decomposition shows that both cation ordering and local relaxation weaken the
ferroelectric instability, enhancing piezoelectricity.Comment: 5 pages, revtex, 2 eps figure
First-principles study of epitaxial strain in perovskites
Using an extension of a first-principles method developed by King-Smith and
Vanderbilt [Phys. Rev. B {\bf 49}, 5828 (1994)], we investigate the effects of
in-plane epitaxial strain on the ground-state structure and polarization of
eight perovskite oxides: BaTiO, SrTiO, CaTiO, KNbO, NaNbO,
PbTiO, PbZrO, and BaZrO. In addition, we investigate the effects of
a nonzero normal stress. The results are shown to be useful in predicting the
structure and polarization of perovskite oxide thin films and superlattices.Comment: 10 page
Predicting polarization enhancement in multicomponent ferroelectric superlattices
Ab initio calculations are utilized as an input to develop a simple model of
polarization in epitaxial short-period CaTiO3/SrTiO3/BaTiO3 superlattices grown
on a SrTiO3 substrate. The model is then combined with a genetic algorithm
technique to optimize the arrangement of individual CaTiO3, SrTiO3 and BaTiO3
layers in a superlattice, predicting structures with the highest possible
polarization and a low in-plane lattice constant mismatch with the substrate.
This modelling procedure can be applied to a wide range of layered
perovskite-oxide nanostructures providing guidance for experimental development
of nanoelectromechanical devices with substantially improved polar properties.Comment: 4 pages, submitted to PR
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