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Statistics and Soccer
OneTopicsgoals in soccer of the reasons why people are fascinated by soccer is the fact that chance plays a greater role here than in many other...
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Eigenvalues of Stochastic Blockmodel Graphs and Random Graphs with Low-Rank Edge Probability Matrices
We derive the limiting distribution for the outlier eigenvalues of the adjacency matrix for random graphs with independent edges whose edge...
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Combining assumptions and graphical network into gene expression data analysis
BackgroundAnalyzing gene expression data rigorously requires taking assumptions into consideration but also relies on using information about network...
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Scan Statistics on Graphs and Networks
This article summarizes modern research of scan statistics on graphs and networks. These statistics arise naturally in the scanning of time and space...
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Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model
We are interested here in a theoretical and practical approach for detecting atypical segments in a multi-state sequence. We prove in this article...
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Extremal clustering in non-stationary random sequences
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically...
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Functionals of Telegraph Process
This chapter is devoted to the various functionals of telegraph processes. First, we present well-known results on distributions of the telegraph...
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Financial Modelling Based on Telegraph Processes
This last chapter of the book is devoted to financial applications of the previously described results. After brief preliminaries, the chapter opens...
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A general stochastic model for bivariate episodes driven by a gamma sequence
We propose a new stochastic model describing the joint distribution of ( X , N ), where N is a counting variable while X is the sum of N independent...
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Order Statistics
In this chapter, recollecting the notion of order statistics introduced in Sect. 1.4 , we discuss the...
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Asymmetric Jump-Telegraph Processes
The concepts and results of Chap. 2 are generalised, first, to asymmetric processes equipped with jumps (of...
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Refining Invariant Coordinate Selection via Local Projection Pursuit
Invariant coordinate selection (ICS), introduced by Tyler et al. (J. Roy. Stat. Soc. B 71(3):549–592, 2009), is a powerful tool to find potentially...
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Preliminaries
In this chapter, we address and review key concepts that will be used in later chapters. In Sect. 1.1, we review briefly the key notions of...
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Digression on Multiple Testing: False Discovery Rates
A classical single hypothesis test proceeds by specifying...
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Improvements on SCORE, Especially for Weak Signals
A network may have weak signals and severe degree heterogeneity, and may be very sparse in one occurrence but very dense in another. SCORE (Ann....
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Inference on extremal dependence in the domain of attraction of a structured Hüsler–Reiss distribution motivated by a Markov tree with latent variables
A Markov tree is a probabilistic graphical model for a random vector indexed by the nodes of an undirected tree encoding conditional independence...
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Rank Statistics
Ranks and magnitude ranks are closely related with order and magnitude order statistics discussed in Chap. 2 ,...
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Solving Elliptic Equations with Brownian Motion: Bias Reduction and Temporal Difference Learning
The Feynman-Kac formula provides a way to understand solutions to elliptic partial differential equations in terms of expectations of continuous time...
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A New Copula-Based Approach for Counting: The Distorted and the Limiting Case
The purpose of this chapter is to examine in depth the new algorithm for counting with dependence, assuming at first to have a hierarchy in the...
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A new trivariate model for stochastic episodes
We study the joint distribution of stochastic events described by ( X , Y , N ), where N has a 1-inflated (or deflated) geometric distribution and X , Y are...
