642 research outputs found
A Bayesian Nonparametric Markovian Model for Nonstationary Time Series
Stationary time series models built from parametric distributions are, in
general, limited in scope due to the assumptions imposed on the residual
distribution and autoregression relationship. We present a modeling approach
for univariate time series data, which makes no assumptions of stationarity,
and can accommodate complex dynamics and capture nonstandard distributions. The
model for the transition density arises from the conditional distribution
implied by a Bayesian nonparametric mixture of bivariate normals. This implies
a flexible autoregressive form for the conditional transition density, defining
a time-homogeneous, nonstationary, Markovian model for real-valued data indexed
in discrete-time. To obtain a more computationally tractable algorithm for
posterior inference, we utilize a square-root-free Cholesky decomposition of
the mixture kernel covariance matrix. Results from simulated data suggest the
model is able to recover challenging transition and predictive densities. We
also illustrate the model on time intervals between eruptions of the Old
Faithful geyser. Extensions to accommodate higher order structure and to
develop a state-space model are also discussed
A Fully Nonparametric Modelling Approach to Binary Regression
We propose a general nonparametric Bayesian framework for binary regression,
which is built from modeling for the joint response-covariate distribution. The
observed binary responses are assumed to arise from underlying continuous
random variables through discretization, and we model the joint distribution of
these latent responses and the covariates using a Dirichlet process mixture of
multivariate normals. We show that the kernel of the induced mixture model for
the observed data is identifiable upon a restriction on the latent variables.
To allow for appropriate dependence structure while facilitating
identifiability, we use a square-root-free Cholesky decomposition of the
covariance matrix in the normal mixture kernel. In addition to allowing for the
necessary restriction, this modeling strategy provides substantial
simplifications in implementation of Markov chain Monte Carlo posterior
simulation. We present two data examples taken from areas for which the
methodology is especially well suited. In particular, the first example
involves estimation of relationships between environmental variables, and the
second develops inference for natural selection surfaces in evolutionary
biology. Finally, we discuss extensions to regression settings with
multivariate ordinal responses
Bayesian spectral modeling for multiple time series
We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single spectral density, we develop a hierarchical extension for multiple time series. Specifically, we set the mean functions to be common to all spectral densities and make the weights specific to the time series through the parameters of the logit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation is that it allows for ready posterior simulation through a Gibbs sampler with closed form full conditional distributions for all model parameters. The modeling approach is illustrated with simulated datasets, and used for spectral analysis of multichannel electroencephalographic recordings (EEGs), which provides a key motivating application for the proposed methodology
USAF Pilot Perceptions of Workload Assessment in a Combat or High-Threat Environment
This study analyzed the self-reported survey responses of 219 Air Force Pilots concerning their perceptions of workload assessment in a combat or a high threat environment. The first objective of this study was to determine and compare the combat workload factors of varying importance in combat workload assessment by aircraft and mission type flown. The second objective was to examine the pilots\u27 perception of combat mission inflight workload. A stepwise regression model to predict the pilots\u27 perceptions of inflight workload using pilots\u27 characteristics data was explored. Research conclusion varied among aircraft types. Combat workload items indicated as distractingly important were similar for all aircraft types, while items in lower level of importance were impacted by aircraft type. Mean Combat Workload (CWL) scores of pilots from each aircraft type were not significantly different. Overall, it was concluded that surveying pilots who had flown in combat or high threat environments provided useful responses to assess pilot workload; however, findings based on subjective assessments, provide tentative grounds for further research
The Neutron Star Mass Distribution
In recent years, the number of pulsars with secure mass measurements has
increased to a level that allows us to probe the underlying neutron star (NS)
mass distribution in detail. We critically review the radio pulsar mass
measurements. For the first time, we are able to analyze a sizable population
of NSs with a flexible modeling approach that can effectively accommodate a
skewed underlying distribution and asymmetric measurement errors. We find that
NSs that have evolved through different evolutionary paths reflect distinctive
signatures through dissimilar distribution peak and mass cutoff values. NSs in
double neutron star and neutron star-white dwarf systems show consistent
respective peaks at 1.33 Msun and 1.55 Msun suggesting significant mass
accretion (delta m~0.22 Msun) has occurred during the spin-up phase. The width
of the mass distribution implied by double NS systems is indicative of a tight
initial mass function while the inferred mass range is significantly wider for
NSs that have gone through recycling. We find a mass cutoff at ~2.1 Msun for
NSs with white dwarf companions which establishes a firm lower bound for the
maximum NS mass. This rules out the majority of strange quark and soft equation
of state models as viable configurations for NS matter. The lack of truncation
close to the maximum mass cutoff along with the skewed nature of the inferred
mass distribution both enforce the suggestion that the 2.1 Msun limit is set by
evolutionary constraints rather than nuclear physics or general relativity, and
the existence of rare super-massive NSs is possible.Comment: 13 pages, 4 figures, 2 tables. ApJ in press. A completely new and
more flexible statistical model applied. Astrophysical results remained same
as arXiv:1011.429
State v. Fordsham, 362 P.2d 413 (Mont. 1961)
State v. Fordsha
Structured Mixture of Continuation-ratio Logits Models for Ordinal Regression
We develop a nonparametric Bayesian modeling approach to ordinal regression
based on priors placed directly on the discrete distribution of the ordinal
responses. The prior probability models are built from a structured mixture of
multinomial distributions. We leverage a continuation-ratio logits
representation to formulate the mixture kernel, with mixture weights defined
through the logit stick-breaking process that incorporates the covariates
through a linear function. The implied regression functions for the response
probabilities can be expressed as weighted sums of parametric regression
functions, with covariate-dependent weights. Thus, the modeling approach
achieves flexible ordinal regression relationships, avoiding linearity or
additivity assumptions in the covariate effects. A key model feature is that
the parameters for both the mixture kernel and the mixture weights can be
associated with a continuation-ratio logits regression structure. Hence, an
efficient and relatively easy to implement posterior simulation method can be
designed, using P\'olya-Gamma data augmentation. Moreover, the model is built
from a conditional independence structure for category-specific parameters,
which results in additional computational efficiency gains through partial
parallel sampling. In addition to the general mixture structure, we study
simplified model versions that incorporate covariate dependence only in the
mixture kernel parameters or only in the mixture weights. For all proposed
models, we discuss approaches to prior specification and develop Markov chain
Monte Carlo methods for posterior simulation. The methodology is illustrated
with several synthetic and real data examples
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