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

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

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

Traveling wavefronts of a prey–predator diffusion system with stage-structure and harvesting

AbstractFrom a biological point of view, we consider a prey–predator-type free diffusion fishery model with stage-structure and harvesting. First, we study the stability of the nonnegative constant equilibria. In particular, the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation. Then, employing the upper and lower solution method, we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system. Numerical simulation is also carried out to illustrate the main result