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100 lines
8.5 KiB
100 lines
8.5 KiB
3 years ago
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\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax
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\babel@toc {english}{}
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\babel@toc {english}{}
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\contentsline {chapter}{List of Figures}{xi}{section*.5}%
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\contentsline {chapter}{List of Tables}{xiii}{section*.7}%
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\contentsline {chapter}{Notational Conventions}{xv}{section*.10}%
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\contentsline {chapter}{Acronyms and Abbreviations}{xvii}{section*.13}%
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\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}%
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\contentsline {section}{\numberline {1.1}Context and motivation}{1}{section.1.1}%
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\contentsline {section}{\numberline {1.2}Survey of related work}{2}{section.1.2}%
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\contentsline {section}{\numberline {1.3}Research objectives and thesis outline}{2}{section.1.3}%
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\contentsline {chapter}{\numberline {2}Background / Theory}{3}{chapter.2}%
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\contentsline {section}{\numberline {2.1}The Bayesian Framework}{3}{section.2.1}%
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\contentsline {subsection}{\numberline {2.1.1}Modeling via Exchangeability}{3}{subsection.2.1.1}%
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\contentsline {section}{\numberline {2.2}Exponential Families}{7}{section.2.2}%
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\contentsline {subsection}{\numberline {2.2.1}Properties of the Canonical Exponential Family}{9}{subsection.2.2.1}%
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\contentsline {subsection}{\numberline {2.2.2}Interpretation as Linearly Constrained Maximum Entropy Distribution}{9}{subsection.2.2.2}%
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\contentsline {subsection}{\numberline {2.2.3}Examples}{9}{subsection.2.2.3}%
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\contentsline {section}{\numberline {2.3}Sufficient Statistics}{9}{section.2.3}%
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\contentsline {section}{\numberline {2.4}Incorporating Prior Knowledge}{11}{section.2.4}%
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\contentsline {subsection}{\numberline {2.4.1}Conjugate Priors}{11}{subsection.2.4.1}%
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\contentsline {subsection}{\numberline {2.4.2}Multinomial Observations}{11}{subsection.2.4.2}%
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\contentsline {subsection}{\numberline {2.4.3}Gaussian Observations}{11}{subsection.2.4.3}%
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\contentsline {subsection}{\numberline {2.4.4}Multivariate Linear Regression Model}{11}{subsection.2.4.4}%
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\contentsline {section}{\numberline {2.5}Graphical Models}{11}{section.2.5}%
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\contentsline {subsection}{\numberline {2.5.1}A Brief Overview}{11}{subsection.2.5.1}%
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\contentsline {subsection}{\numberline {2.5.2}Directed Graphical Models}{11}{subsection.2.5.2}%
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\contentsline {subsection}{\numberline {2.5.3}Undirected Graphical Models}{11}{subsection.2.5.3}%
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\contentsline {subsection}{\numberline {2.5.4}Belief Propagation}{11}{subsection.2.5.4}%
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\contentsline {section}{\numberline {2.6}Hidden Markov Model}{11}{section.2.6}%
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\contentsline {subsection}{\numberline {2.6.1}Forward-Backward Algorithm}{11}{subsection.2.6.1}%
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\contentsline {subsection}{\numberline {2.6.2}Viterbi Algorithm}{11}{subsection.2.6.2}%
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\contentsline {section}{\numberline {2.7}State Space Models}{11}{section.2.7}%
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\contentsline {subsection}{\numberline {2.7.1}Standard Discrete-Time Linear-Gaussian State Space Formulation}{11}{subsection.2.7.1}%
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\contentsline {subsection}{\numberline {2.7.2}Vector Autoregressive Processes}{11}{subsection.2.7.2}%
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\contentsline {subsection}{\numberline {2.7.3}Switching Linear Dynamic Systems}{11}{subsection.2.7.3}%
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\contentsline {subsection}{\numberline {2.7.4}Stochastic Realization Theory}{11}{subsection.2.7.4}%
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\contentsline {subsection}{\numberline {2.7.5}Kalman Filtering and Smoothing}{11}{subsection.2.7.5}%
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\contentsline {section}{\numberline {2.8}Markov Chain Monte Carlo}{11}{section.2.8}%
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\contentsline {subsection}{\numberline {2.8.1}Monte Carlo Integration}{11}{subsection.2.8.1}%
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\contentsline {subsection}{\numberline {2.8.2}The Metropolis-Hastings Algorithm}{11}{subsection.2.8.2}%
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\contentsline {subsection}{\numberline {2.8.3}Gibbs Sampling}{11}{subsection.2.8.3}%
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\contentsline {subsection}{\numberline {2.8.4}Auxiliary, Blocked, and Collapsed Gibbs Samplers}{11}{subsection.2.8.4}%
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\contentsline {section}{\numberline {2.9}Bayesian Nonparametric Methods}{11}{section.2.9}%
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\contentsline {subsection}{\numberline {2.9.1}Dirichlet Processes}{11}{subsection.2.9.1}%
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\contentsline {subsection}{\numberline {2.9.2}Dirichlet Process Mixture Models}{11}{subsection.2.9.2}%
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\contentsline {subsection}{\numberline {2.9.3}Hierarchical Dirichlet Processes}{11}{subsection.2.9.3}%
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\contentsline {subsection}{\numberline {2.9.4}Beta Process}{11}{subsection.2.9.4}%
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\contentsline {chapter}{\numberline {3}Route/Trajectory Prediction}{13}{chapter.3}%
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\contentsline {section}{\numberline {3.1}Section}{13}{section.3.1}%
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\contentsline {subsection}{\numberline {3.1.1}Subsection}{13}{subsection.3.1.1}%
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\contentsline {chapter}{\numberline {4}Prediction of driver influenced parameter (velocity and longitudinal and lateral acceleration)}{15}{chapter.4}%
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\contentsline {section}{\numberline {4.1}Section}{15}{section.4.1}%
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\contentsline {subsection}{\numberline {4.1.1}Subsection}{15}{subsection.4.1.1}%
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\contentsline {chapter}{\numberline {5}Fifth Chapter}{17}{chapter.5}%
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\contentsline {section}{\numberline {5.1}Section}{17}{section.5.1}%
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\contentsline {subsection}{\numberline {5.1.1}Subsection}{17}{subsection.5.1.1}%
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\contentsline {chapter}{\numberline {6}Conclusion}{19}{chapter.6}%
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\contentsline {section}{\numberline {6.1}Section}{19}{section.6.1}%
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\contentsline {subsection}{\numberline {6.1.1}Subsection}{19}{subsection.6.1.1}%
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\contentsline {chapter}{\numberline {7}Test Chapter}{21}{chapter.7}%
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\contentsline {section}{\numberline {7.1}ToDo's}{21}{section.7.1}%
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\contentsline {section}{\numberline {7.2}Notes}{22}{section.7.2}%
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\contentsline {section}{\numberline {7.3}FixMe}{22}{section.7.3}%
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\contentsline {section}{\numberline {7.4}Cite}{23}{section.7.4}%
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\contentsline {section}{\numberline {7.5}Glossaries}{23}{section.7.5}%
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\contentsline {section}{\numberline {7.6}Reference}{23}{section.7.6}%
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\contentsline {section}{\numberline {7.7}Macros}{23}{section.7.7}%
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\contentsline {subsection}{\numberline {7.7.1}Equations}{23}{subsection.7.7.1}%
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\contentsline {subsection}{\numberline {7.7.2}Function}{24}{subsection.7.7.2}%
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\contentsline {section}{\numberline {7.8}Table}{24}{section.7.8}%
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\contentsline {section}{\numberline {7.9}Figures}{25}{section.7.9}%
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\contentsline {chapter}{\numberline {8}Heading on level\xspace 0 (chapter)}{29}{chapter.8}%
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\contentsline {section}{\numberline {8.1}Heading on level\xspace 1 (section)}{29}{section.8.1}%
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\contentsline {subsection}{\numberline {8.1.1}Heading on level\xspace 2 (subsection)}{29}{subsection.8.1.1}%
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\contentsline {subsubsection}{\nonumberline Heading on level\xspace 3 (subsubsection)}{30}{section*.21}%
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\contentsline {paragraph}{\nonumberline Heading on level\xspace 4 (paragraph)}{30}{section*.22}%
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\contentsline {section}{\numberline {8.2}Lists}{30}{section.8.2}%
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\contentsline {subsection}{\numberline {8.2.1}Example for list\xspace (itemize)}{30}{subsection.8.2.1}%
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\contentsline {subsubsection}{\nonumberline Example for list\xspace (4*itemize)}{31}{section*.23}%
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\contentsline {subsection}{\numberline {8.2.2}Example for list\xspace (enumerate)}{31}{subsection.8.2.2}%
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\contentsline {subsubsection}{\nonumberline Example for list\xspace (4*enumerate)}{31}{section*.24}%
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\contentsline {subsection}{\numberline {8.2.3}Example for list\xspace (description)}{32}{subsection.8.2.3}%
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\contentsline {subsubsection}{\nonumberline Example for list\xspace (4*description)}{32}{section*.25}%
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\contentsline {chapter}{\numberline {9}Heading on level\xspace 0 (chapter)}{33}{chapter.9}%
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\contentsline {section}{\numberline {9.1}Heading on level\xspace 1 (section)}{33}{section.9.1}%
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\contentsline {subsection}{\numberline {9.1.1}Heading on level\xspace 2 (subsection)}{34}{subsection.9.1.1}%
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\contentsline {subsubsection}{\nonumberline Heading on level\xspace 3 (subsection)}{36}{section*.26}%
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\contentsline {paragraph}{\nonumberline Heading on level\xspace 4 (paragraph)}{37}{section*.27}%
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\contentsline {section}{\numberline {9.2}Lists}{38}{section.9.2}%
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\contentsline {subsection}{\numberline {9.2.1}Example for list\xspace (itemize)}{38}{subsection.9.2.1}%
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\contentsline {subsubsection}{\nonumberline Example for list\xspace (4*itemize)}{39}{section*.28}%
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\contentsline {subsection}{\numberline {9.2.2}Example for list\xspace (enumerate)}{42}{subsection.9.2.2}%
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\contentsline {subsubsection}{\nonumberline Example for list\xspace (4*enumerate)}{43}{section*.29}%
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\contentsline {subsection}{\numberline {9.2.3}Example for list\xspace (description)}{45}{subsection.9.2.3}%
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\contentsline {subsubsection}{\nonumberline Example for list\xspace (4*description)}{47}{section*.30}%
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\contentsline {chapter}{\numberline {A}Appendix}{55}{appendix.A}%
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\contentsline {chapter}{Bibliography}{XIX}{section*.31}%
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\contentsfinish
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