Dissertation - Elijah DePalma

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Transcript of Dissertation - Elijah DePalma

UNIVERSITY OF CALIFORNIA RIVERSIDE

Sequential Hypothesis Testing With Spatially Correlated Presence-Absence Data and the Corridor Problem

A Dissertation submitted in partial satisfaction of the requirements for the degree of

Doctor of Philosophy in Applied Statistics by Elijah Daniel DePalma December 2011

Dissertation Committee:Dr. Dr. Dr. Dr. Richard Arnott, Co-Chairperson Daniel Jeske, Co-Chairperson Matthew Barth James Flegal

Copyright by Elijah Daniel DePalma 2011

The Dissertation of Elijah Daniel DePalma is approved:

Committee Co-Chairperson

Committee Co-Chairperson

University of California, Riverside

AcknowledgmentsI am grateful to Professor Richard Arnott and Professor Daniel Jeske for their guidance and support, and for the research opportunities they have provided over the last few years. I am grateful to Professor Matthew Barth for allowing me to participate in his research group, and to his research assistants Kanok Boriboonsomsin, Alex Vu and Guoyuan Wu. I am especially grateful to Professor Alex Skabardonis for granting me permission to obtain the PeMS data used in this dissertation. The text appearing in Chapter 2 of this dissertation, in part or in full, has been submitted as a working paper for publication to Journal of Economic Entomology. The co-author Daniel R. Jeske listed in that working paper directed and supervised the research which forms the basis for this dissertation. The co-authors Jesus R. Lara and Mark S. Hoddle listed in that working paper contributed empirical data, editorial assistance, the graph appearing in Figure 2.1, a portion of the Discussion section, and general research collaboration. This joint work was supported in part by a USDA-NIFA Regional Integrated Pest Management Competitive Grants Program Western Region Grant 2010-34103-21202 to Mark S. Hoddle and Daniel R. Jeske. The text appearing in Chapter 3 of this dissertation, in part or in full, is a reprint of the material as is appears in Transportation Research Part B (2011), 45:743 768. The co-author Richard Arnott listed in that publication directed and supervised the research which forms the basis for this dissertation. We are indebted to Caltrans and the USDOT for research award UCTC FY 09-10, awarded under Caltrans for transfer to USDOT. The text appearing in Chapter 4 of this dissertation, in part or in full, has

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been submitted as a working paper for publication to Transportation Research Part B. The co-author Richard Arnott listed in that working paper directed and supervised the research which forms the basis for this dissertation. We are grateful to the US Department of Transportation, grant #DTRT07-G-0009, and the California Department of Transportation, grant #65A0216, through the University of California Transportation Center (UCTC) at UC Berkeley, and the dissertation fellowship award through the University of California Transportation Center (UCTC).

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To Professor Richard Arnott and Professor Daniel Jeske... ...for their continuing guidance and innovation.

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ABSTRACT OF THE DISSERTATION

Sequential Hypothesis Testing With Spatially Correlated Presence-Absence Data and the Corridor Problem by Elijah Daniel DePalma Doctor of Philosophy, Graduate Program in Applied Statistics University of California, Riverside, December 2011 Dr. Richard Arnott, Co-Chairperson Dr. Daniel Jeske, Co-Chairperson

Firstly, we develop a sampling methodology for making pest treatment decisions based on mean pest density. Previous research assumes pest densities are uniformly distributed over space, and advocates using sequential, presence-absence sampling plans for making treatment decisions. Here we develop a spatial sampling plan which accomodates pest densities which vary over space and which exhibit spatial correlation, and we demonstrate the eectiveness of our proposed methodology using parameter values calibrated from empirical data on Oligonychus perseae, a mite pest of avocados. To our knowledge, this research is the rst to combine sequential hypothesis testing techniques with presence-absence sampling strategies which account for spatially correlated pest densities. Secondly, we investigate The Corridor Problem, a model of morning trac ow along a corridor to a central business district (CBD). We consider travel time cost and schedule delay (time early) cost, and we assume that a xed number of identical commuters have the same desired work start-time at the CBD and that late arrivals are prohibited. Trac ow along the corridor is subject to LWR ow congestion with

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Greenshields Relation (i.e., mass conservation for a uid coupled with a negative linear relationship between velocity and density), and we seek to characterize the no-toll equilibrium or user optimum (UO) solution, in which no commuter can reduce their trip cost, and the social optimum (SO) solution, in which the total population trip cost is minimized. Allowing for a continuum of entry-points into the corridor we develop a numerical algorithm for constructing a UO solution. Restricting to a single entry-point we provide complete characterizations of the SO and UO, with numerical examples and quasi-analytic solutions. Finally, we develop a stochastic model of incident occurrence on a corridor, calibrated using a recently developed change-point detection algorithm applied to trac data along a San Diego freeway over the course of a year, coupled with Hierarchical Generalized Linear Model (HGLM) tting techniques. We use the calibrated incident model in a simulation study to determine the eect of stochastic incidents on the equilibrium solutions to the single-entry point Corridor Problem.

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ContentsList of Figures List of Tables 1 Introduction 2 Sequential Hypothesis Testing With Spatially Correlated PresenceAbsence Data 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Mean-Proportion Relationship . . . . . . . . . . . . . . . . . . . 2.2.2 Presence-Absence Sampling Hypothesis Test . . . . . . . . . . . 2.2.3 Spatial GLMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Spatial GLMM Hypothesis Test . . . . . . . . . . . . . . . . . . . 2.2.5 Bartletts SPRT . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Leaf-Selection Rules and Sampling Cost . . . . . . . . . . . . . . 2.2.7 Sequential Maximin Tree-Selection Rule . . . . . . . . . . . . . . 2.2.8 Evaluation of Proposed Methodology . . . . . . . . . . . . . . . . 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Illustrated Examples: Sample Parameter Estimates . . . . . . . . 2.3.2 Leaf-Selection Rules: Outcome . . . . . . . . . . . . . . . . . . . 2.3.3 Evaluation of Proposed Methodology: Outcome . . . . . . . . . . 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Corridor Problem: Preliminary Results on the No-toll Equilibrium 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Trip Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Trip-Timing Condition (TT) . . . . . . . . . . . . . . . . . . . . 3.3 Implications of the Trip-Timing Condition . . . . . . . . . . . . . . . . . 3.3.1 Relation between Arrival and Departure Times . . . . . . . . . . 3.3.2 Constant Departure Rate within Interior of Departure Set . . . . 3.4 Proposed Departure Set . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii xix 1

5 6 9 9 11 12 14 14 17 18 19 22 22 22 23 27 30

33 34 38 39 39 40 41 41 42 44

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3.4.1 General Properties of the Departure Set . . . . . . . . . . . 3.4.2 Proposed Departure Set . . . . . . . . . . . . . . . . . . . . 3.5 Mathematical Analysis: Analytic Results . . . . . . . . . . . . . . 3.5.1 Continuity Equation: Method of Characteristics . . . . . . 3.5.2 Region I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Region II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Parametrization of Lower Boundary Curve . . . . . . . . . 3.5.5 Arrival Flow Rate . . . . . . . . . . . . . . . . . . . . . . . 3.5.6 Modication of Proposed Departure Set . . . . . . . . . . . 3.5.7 Three Governing Equations: Summary . . . . . . . . . . . . 3.5.8 Derivation of the Three Governing Equations . . . . . . . . 3.6 Numerical Analysis (Greenshields) . . . . . . . . . . . . . . . . . . 3.6.1 Greenshields Velocity-Density Relation . . . . . . . . . . . 3.6.2 Scale Parameters and Notation . . . . . . . . . . . . . . . . 3.6.3 Overview of Numerical Solution . . . . . . . . . . . . . . . . 3.6.4 Iterated Sequence of Discretized Flow Values . . . . . . . . 3.6.5 Discretization of the First and Third Governing Equations . 3.6.6 Iterative Procedure . . . . . . . . . . . . . . . . . . . . . . . 3.6.7 Initializing Seed Values . . . . . . . . . . . . . . . . . . . . 3.6.8 Final Segment . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Numerical Results (Greenshields) . . . . . . . . . . . . . . . . . . . 3.7.1 Departure Set Solutions . . . . . . . . . . . . . . . . . . . . 3.7.2 Corresponding Population Densities . . . . . . . . . . . . . 3.7.3 Interpretation of Results . . . . . . . . . . . . . . . . . . . . 3.7.4 Comparison with Empirical Data . . . . . . . . . . . . . . . 3.8 Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . 3.8.1 Directions for Future Research . . . . . . . . . . . . . . . . 3.8.2 Conclusion . . . . . . . . . . . . . . . . . . .