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Table of contents
Introduction
1 Graphs and graphical models frameworks
1.1 Introduction to graph theory
1.1.1 Definitions
1.1.2 Drawings
1.1.3 Graph properties
1.2 Graphical model framework
1.2.1 Random vectors and independencies
1.2.2 From graphs to distributions
1.2.3 From distributions to graphs
1.3 Gaussian graphical models
1.3.1 Parametrizations
1.3.2 Inference
References
2 Tree-indexed data and Markov Tree (MT) models
2.1 Introduction to tree-indexed data
2.1.1 Definitions
2.1.2 Drawing tree-indexed data
2.2 Tree-indexed data and plants
2.2.1 Tree-indexed data on a cellular scale
2.2.2 Tree-indexed data on the whole plant scale
2.3 Markov models for tree indexed-data
2.3.1 Markov models
2.3.2 Hidden Markov Tree (HMT) models
References
3 Semi-parametric Hidden Markov Out-Tree (HMOT) models for cell lineage analysis
3.1 Introduction
3.2 Definitions
3.2.1 Markov Out-Tree (MOT) models
3.2.2 Hidden Markov Tree (HMT) models
3.3 Computational methods for Hidden Markov Out-Tree (HMOT) models
3.3.1 Upward-downward smoothing algorithm
3.3.2 Application of the EM algorithm
3.3.3 Dynamic programming restoration algorithm
3.4 Application to cell lineage trees
3.4.1 Results
3.4.2 Discussions
References
4 Inference ofMixed Acyclic GraphicalModels (MAGMs) inMulti-Type Branching Processes (MTBPs)
4.1 Introduction
4.2 Definitions
4.2.1 Multi-Type Branching Processes (MTBPs)
4.2.2 Poisson Mixed Acyclic Graphical Models (PMAGMs)
4.2.3 Discrete Parametric Mixed Acyclic Graphical Models (DPMAGMs)
4.3 Discrete Parametric Mixed Acyclic Graphical Models (DPMAGMs) inference
4.3.1 Parameter inference
4.3.2 Structure inference
4.4 Application to Multi-Type Branching Processes (MTBPs): the case of mango tree asynchronisms
4.5 Concluding remarks
References
5 Quantification of plant patchiness via tree-structured statistical mod- els: a tree-segmentation/clustering approach
5.1 Introduction
5.2 Material and methods
5.2.1 Tree-structured representation of plants
5.2.2 Modeling plant patchiness with tree segmentation/clustering models
5.2.3 Plant material
5.3 Results
5.3.1 Tree segmentation
5.3.2 Subtree clustering
5.3.3 Cultivar comparisons
5.4 Discussion
References
Work in progress and perspectives
StatisKit: graphical model inference in C++ and Python
Hidden Markov In-Tree (HMIT) models
Multivariate mixture models in Multi-Type Branching Processes (MTBPs)
Integrative models for deciphering mango tree asynchronisms
References
Index of references
