30,363 research outputs found
Generalized Network Psychometrics: Combining Network and Latent Variable Models
We introduce the network model as a formal psychometric model,
conceptualizing the covariance between psychometric indicators as resulting
from pairwise interactions between observable variables in a network structure.
This contrasts with standard psychometric models, in which the covariance
between test items arises from the influence of one or more common latent
variables. Here, we present two generalizations of the network model that
encompass latent variable structures, establishing network modeling as parts of
the more general framework of Structural Equation Modeling (SEM). In the first
generalization, we model the covariance structure of latent variables as a
network. We term this framework Latent Network Modeling (LNM) and show that,
with LNM, a unique structure of conditional independence relationships between
latent variables can be obtained in an explorative manner. In the second
generalization, the residual variance-covariance structure of indicators is
modeled as a network. We term this generalization Residual Network Modeling
(RNM) and show that, within this framework, identifiable models can be obtained
in which local independence is structurally violated. These generalizations
allow for a general modeling framework that can be used to fit, and compare,
SEM models, network models, and the RNM and LNM generalizations. This
methodology has been implemented in the free-to-use software package lvnet,
which contains confirmatory model testing as well as two exploratory search
algorithms: stepwise search algorithms for low-dimensional datasets and
penalized maximum likelihood estimation for larger datasets. We show in
simulation studies that these search algorithms performs adequately in
identifying the structure of the relevant residual or latent networks. We
further demonstrate the utility of these generalizations in an empirical
example on a personality inventory dataset.Comment: Published in Psychometrik
Evaluating Data Assimilation Algorithms
Data assimilation leads naturally to a Bayesian formulation in which the
posterior probability distribution of the system state, given the observations,
plays a central conceptual role. The aim of this paper is to use this Bayesian
posterior probability distribution as a gold standard against which to evaluate
various commonly used data assimilation algorithms.
A key aspect of geophysical data assimilation is the high dimensionality and
low predictability of the computational model. With this in mind, yet with the
goal of allowing an explicit and accurate computation of the posterior
distribution, we study the 2D Navier-Stokes equations in a periodic geometry.
We compute the posterior probability distribution by state-of-the-art
statistical sampling techniques. The commonly used algorithms that we evaluate
against this accurate gold standard, as quantified by comparing the relative
error in reproducing its moments, are 4DVAR and a variety of sequential
filtering approximations based on 3DVAR and on extended and ensemble Kalman
filters.
The primary conclusions are that: (i) with appropriate parameter choices,
approximate filters can perform well in reproducing the mean of the desired
probability distribution; (ii) however they typically perform poorly when
attempting to reproduce the covariance; (iii) this poor performance is
compounded by the need to modify the covariance, in order to induce stability.
Thus, whilst filters can be a useful tool in predicting mean behavior, they
should be viewed with caution as predictors of uncertainty. These conclusions
are intrinsic to the algorithms and will not change if the model complexity is
increased, for example by employing a smaller viscosity, or by using a detailed
NWP model
Reliable inference of exoplanet light curve parameters using deterministic and stochastic systematics models
Time-series photometry and spectroscopy of transiting exoplanets allow us to
study their atmospheres. Unfortunately, the required precision to extract
atmospheric information surpasses the design specifications of most general
purpose instrumentation, resulting in instrumental systematics in the light
curves that are typically larger than the target precision. Systematics must
therefore be modelled, leaving the inference of light curve parameters
conditioned on the subjective choice of models and model selection criteria.
This paper aims to test the reliability of the most commonly used systematics
models and model selection criteria. As we are primarily interested in
recovering light curve parameters rather than the favoured systematics model,
marginalisation over systematics models is introduced as a more robust
alternative than simple model selection. This can incorporate uncertainties in
the choice of systematics model into the error budget as well as the model
parameters. Its use is demonstrated using a series of simulated transit light
curves. Stochastic models, specifically Gaussian processes, are also discussed
in the context of marginalisation over systematics models, and are found to
reliably recover the transit parameters for a wide range of systematics
functions. None of the tested model selection criteria - including the BIC -
routinely recovered the correct model. This means that commonly used methods
that are based on simple model selection may underestimate the uncertainties
when extracting transmission and eclipse spectra from real data, and
low-significance claims using such techniques should be treated with caution.
In general, no systematics modelling techniques are perfect; however,
marginalisation over many systematics models helps to mitigate poor model
selection, and stochastic processes provide an even more flexible approach to
modelling instrumental systematics.Comment: 15 pages, 2 figures, published in MNRAS, typo in footnote eq
correcte
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference
Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.
New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.
Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference.
Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain.
Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.
Keywords: Granger causality, vector autoregressive modelling, time series analysi
PICACS: self-consistent modelling of galaxy cluster scaling relations
In this paper, we introduce PICACS, a physically-motivated, internally
consistent model of scaling relations between galaxy cluster masses and their
observable properties. This model can be used to constrain simultaneously the
form, scatter (including its covariance) and evolution of the scaling
relations, as well as the masses of the individual clusters. In this framework,
scaling relations between observables (such as that between X-ray luminosity
and temperature) are modelled explicitly in terms of the fundamental
mass-observable scaling relations, and so are fully constrained without being
fit directly. We apply the PICACS model to two observational datasets, and show
that it performs as well as traditional regression methods for simply measuring
individual scaling relation parameters, but reveals additional information on
the processes that shape the relations while providing self-consistent mass
constraints. Our analysis suggests that the observed combination of slopes of
the scaling relations can be described by a deficit of gas in low-mass clusters
that is compensated for by elevated gas temperatures, such that the total
thermal energy of the gas in a cluster of given mass remains close to
self-similar expectations. This is interpreted as the result of AGN feedback
removing low entropy gas from low mass systems, while heating the remaining
gas. We deconstruct the luminosity-temperature (LT) relation and show that its
steepening compared to self-similar expectations can be explained solely by
this combination of gas depletion and heating in low mass systems, without any
additional contribution from a mass dependence of the gas structure. Finally,
we demonstrate that a self-consistent analysis of the scaling relations leads
to an expectation of self-similar evolution of the LT relation that is
significantly weaker than is commonly assumed.Comment: Updated to match published version. Improvements to presentation of
results, and treatment of scatter and covariance. Main conclusions unchange
Supernova Constraints and Systematic Uncertainties from the First Three Years of the Supernova Legacy Survey
We combine high-redshift Type Ia supernovae from the first three years of the Supernova Legacy Survey (SNLS) with other supernova (SN) samples, primarily at lower redshifts, to form a high-quality joint sample of 472 SNe (123 low-z, 93 SDSS, 242 SNLS, and 14 Hubble Space Telescope). SN data alone require cosmic acceleration at >99.999% confidence, including systematic effects. For the dark energy equation of state parameter (assumed constant out to at least z = 1.4) in a flat universe, we find w = –0.91^(+0.16)_(–0.20)(stat)^(+0.07)_(–0.14)(sys) from SNe only, consistent with a cosmological constant. Our fits include a correction for the recently discovered relationship between host-galaxy mass and SN absolute brightness. We pay particular attention to systematic uncertainties, characterizing them using a systematic covariance matrix that incorporates the redshift dependence of these effects, as well as the shape-luminosity and color-luminosity relationships. Unlike previous work, we include the effects of systematic terms on the empirical light-curve models. The total systematic uncertainty is dominated by calibration terms. We describe how the systematic uncertainties can be reduced with soon to be available improved nearby and intermediate-redshift samples, particularly those calibrated onto USNO/SDSS-like systems
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimation
In this paper, we present the optimization formulation of the Kalman
filtering and smoothing problems, and use this perspective to develop a variety
of extensions and applications. We first formulate classic Kalman smoothing as
a least squares problem, highlight special structure, and show that the classic
filtering and smoothing algorithms are equivalent to a particular algorithm for
solving this problem. Once this equivalence is established, we present
extensions of Kalman smoothing to systems with nonlinear process and
measurement models, systems with linear and nonlinear inequality constraints,
systems with outliers in the measurements or sudden changes in the state, and
systems where the sparsity of the state sequence must be accounted for. All
extensions preserve the computational efficiency of the classic algorithms, and
most of the extensions are illustrated with numerical examples, which are part
of an open source Kalman smoothing Matlab/Octave package.Comment: 46 pages, 11 figure
Structural Constant Conditional Correlation
A small strand of recent literature is occupied with identifying simultaneity in multiple equation systems through autoregressive conditional heteroscedasticity. Since this approach assumes that the structural innovations are uncorrelated, any contemporaneous connection of the endogenous variables needs to be exclusively explained by mutual spillover effects. In contrast, this paper allows for instantaneous covariances, which become identifiable by imposing the constraint of structural constant conditional correlation (SCCC). In this, common driving forces can be modelled in addition to simultaneous transmission effects. The new methodology is applied to the Dow Jones and Nasdaq Composite indexes in a small empirical example, illuminating scope and functioning of the SCCC model.Simultaneity, Identification, EGARCH, CCC
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