666 research outputs found
Essays in Applied Bayesian Analysis
With continuing rapid developments in computational power, Bayesian statistical methods, because of their user-friendliness and estimation capabilities, have become increasingly popular in a considerable variety of application fields. In this thesis, applied Bayesian methodological topics and empirical examples focusing on nonhomogeneous hidden Markov models (NHMMs) and measurement error models are explored in three chapters. In the first chapter, a subsequence-based variational Bayesian inference framework for NHMMs is proposed in order to address the computational problems encountered when analyzing datasets containing long sequences. The second chapter concentrates on measurement error models, where a Bayesian estimation procedure is proposed for the partial potential impact fraction (pPIF) with the presence of measurement error. The third chapter focuses on an empirical application in marketing, where a coupled nonhomogeneous hidden Markov model (CNHMM) is introduced to provide a novel framework for customer relationship management
A slave mode expansion for obtaining ab-initio interatomic potentials
Here we propose a new approach for performing a Taylor series expansion of
the first-principles computed energy of a crystal as a function of the nuclear
displacements. We enlarge the dimensionality of the existing displacement space
and form new variables (ie. slave modes) which transform like irreducible
representations of the space group and satisfy homogeneity of free space.
Standard group theoretical techniques can then be applied to deduce the
non-zero expansion coefficients a priori. At a given order, the translation
group can be used to contract the products and eliminate terms which are not
linearly independent, resulting in a final set of slave mode products. While
the expansion coefficients can be computed in a variety of ways, we demonstrate
that finite difference is effective up to fourth order. We demonstrate the
power of the method in the strongly anharmonic system PbTe. All anharmonic
terms within an octahedron are computed up to fourth order. A proper unitary
transformation demonstrates that the vast majority of the anharmonicity can be
attributed to just two terms, indicating that a minimal model of phonon
interactions is achievable. The ability to straightforwardly generate
polynomial potentials will allow precise simulations at length and time scales
which were previously unrealizable
A Near-Linear Time Sampler for the Ising Model
We give a near-linear time sampler for the Gibbs distribution of the
ferromagnetic Ising models with edge activities and
external fields (or symmetrically,
) on general graphs with bounded or unbounded maximum
degree.
Our algorithm is based on the field dynamics given in [CLV21]. We prove the
correctness and efficiency of our algorithm by establishing spectral
independence of distribution of the random cluster model and the rapid mixing
of Glauber dynamics on the random cluster model in a low-temperature regime,
which may be of independent interest
Distributed Contingency Analysis over Wide Area Network among Dispatch Centers
Traditionally, a regional dispatch center uses the equivalent method to deal
with external grids, which fails to reflect the interactions among regions.
This paper proposes a distributed N-1 contingency analysis (DCA) solution,
where dispatch centers join a coordinated computation using their private data
and computing resources. A distributed screening method is presented to
determine the Critical Contingency Set (DCCS) in DCA. Then, the distributed
power flow is formulated as a set of boundary equations, which is solved by a
Jacobi-Free Newton-GMRES (JFNG) method. During solving the distributed power
flow, only boundary conditions are exchanged. Acceleration techniques are also
introduced, including reusing preconditioners and optimal resource scheduling
during parallel processing of multiple contingencies. The proposed method is
implemented on a real EMS platform, where tests using the Southwest Regional
Grid of China are carried out to validate its feasibility.Comment: 5 pages, 6 figures, 2017 IEEE PES General Meetin
Competing risks regression for clustered survival data via the marginal additive subdistribution hazards model
A population-averaged additive subdistribution hazards model is proposed to
assess the marginal effects of covariates on the cumulative incidence function
and to analyze correlated failure time data subject to competing risks. This
approach extends the population-averaged additive hazards model by
accommodating potentially dependent censoring due to competing events other
than the event of interest. Assuming an independent working correlation
structure, an estimating equations approach is outlined to estimate the
regression coefficients and a new sandwich variance estimator is proposed. The
proposed sandwich variance estimator accounts for both the correlations between
failure times and between the censoring times, and is robust to
misspecification of the unknown dependency structure within each cluster. We
further develop goodness-of-fit tests to assess the adequacy of the additive
structure of the subdistribution hazards for the overall model and each
covariate. Simulation studies are conducted to investigate the performance of
the proposed methods in finite samples. We illustrate our methods using data
from the STrategies to Reduce Injuries and Develop confidence in Elders
(STRIDE) trial
Model on empirically calibrating stochastic traffic flow fundamental diagram
This paper addresses two shortcomings of the data-driven stochastic fundamental diagram for freeway traffic. The first shortcoming is related to the least-squares methods which have been widely used in establishing traffic flow fundamental diagrams. We argue that these methods are not suitable to generate the percentile-based stochastic fundamental diagrams, because the results generated by least-squares methods represent weighted sample mean, rather than percentile. The second shortcoming is widespread use of independent modeling methodology for a family of percentile-based fundamental diagrams. Existing methods are inadequate to coordinate the fundamental diagrams in the same family, and consequently, are not in alignment with the basic rules in probability theory and statistics. To address these issues, this paper proposes a holistic modeling framework based on the concept of mean absolute error minimization. The established model is convex, but non-differentiable. To efficiently implement the proposed methodology, we further reformulate this model as a linear programming problem which could be solved by the state-of-the-art solvers. Experimental results using real-world traffic flow data validate the proposed method
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