Search results for "Tree"
showing 10 items of 1841 documents
Variable Length Memory Chains: Characterization of stationary probability measures
2021
Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability theory. The question of the existence of stationary probability measures leads us to introduce a key combinatorial structure for words produced by a VLMC: the Longest Internal Suffix. This notion allows us to state a necessary and sufficient condition for a general VLMC to admit a unique invariant probability measure. This condition turns out to get a much simpler form for a subclass of VLMC: the stable VLMC. This natural subclass, unlike the general case, enj…
On statistical inference for the random set generated Cox process with set-marking.
2007
Cox point process is a process class for hierarchical modelling of systems of non-interacting points in ℝd under environmental heterogeneity which is modelled through a random intensity function. In this work a class of Cox processes is suggested where the random intensity is generated by a random closed set. Such heterogeneity appears for example in forestry where silvicultural treatments like harvesting and site-preparation create geometrical patterns for tree density variation in two different phases. In this paper the second order property, important both in data analysis and in the context of spatial sampling, is derived. The usefulness of the random set generated Cox process is highly…
Basic networks: Definition and applications
2009
7 pages, 4 figures, 1 table.-- PMID: 19490867 [PubMed]
MODERATE DEVIATION PRINCIPLES FOR BIFURCATING MARKOV CHAINS: CASE OF FUNCTIONS DEPENDENT OF ONE VARIABLE
2021
The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be seen as the models which represent the evolution of a trait along a population where each individual has two offsprings. Unlike the previous results of Bitseki, Djellout \& Guillin (2014), we consider here the case of functions which depend only on one variable. So, mainly inspired by the recent works of Bitseki \& Delmas (2020) about the central limit theorem for general additive functionals of bifurcating Markov chains, we give here a moderate deviatio…
Deducing self-interaction in eye movement data using sequential spatial point processes
2016
Eye movement data are outputs of an analyser tracking the gaze when a person is inspecting a scene. These kind of data are of increasing importance in scientific research as well as in applications, e.g. in marketing and man-machine interface planning. Thus the new areas of application call for advanced analysis tools. Our research objective is to suggest statistical modelling of eye movement sequences using sequential spatial point processes, which decomposes the variation in data into structural components having interpretation. We consider three elements of an eye movement sequence: heterogeneity of the target space, contextuality between subsequent movements, and time-dependent behaviou…
Contributed discussion on article by Pratola
2016
The author should be commended for his outstanding contribution to the literature on Bayesian regression tree models. The author introduces three innovative sampling approaches which allow for efficient traversal of the model space. In this response, we add a fourth alternative.
Recent applications of point process methods in forestry statistics
2000
Forestry statistics is an important field of applied statistics with a long tradition. Many forestry problems can be solved by means of point processes or marked point processes. There, the "points" are tree locations and the "marks" are tree characteristics such as diameter at breast height or degree of damage by environmental factors. Point pro- cess characteristics are valuable tools for exploratory data analysis in forestry, for describing the variability of forest stands and for under- standing and quantifying ecological relationships. Models of point pro- cesses are also an important basis of modern single-tree modeling, that gives simulation tools for the investigation of forest stru…