Filtering equations for the conditional law of residual lifetimes from a heterogeneous population

2000 ◽  
Vol 37 (3) ◽  
pp. 823-834 ◽  
Author(s):  
A. Gerardi ◽  
F. Spizzichino ◽  
B. Torti
Keyword(s):  
Random Vector ◽  
Probabilistic Model ◽  
Conditional Distribution ◽  
Heterogeneous Population ◽  
Main Assumption ◽  
Stochastic Filtering ◽  
Occupation Numbers ◽  
History Of ◽  
Residual Lifetimes

We consider a probabilistic model of a heterogeneous population P subdivided into homogeneous sub-cohorts. A main assumption is that the frailties give rise to a discrete, exchangeable random vector. We put ourselves in the framework of stochastic filtering to derive the conditional distribution of residual lifetimes of surviving individuals, given an observed history of failures and survivals. As a main feature of our approach, this study is based on the analysis of behaviour of the vector of ‘occupation numbers’.

Filtering equations for the conditional law of residual lifetimes from a heterogeneous population

2000 ◽  
Vol 37 (03) ◽  
pp. 823-834 ◽  
Author(s):  
A. Gerardi ◽  
F. Spizzichino ◽  
B. Torti
Keyword(s):  
Random Vector ◽  
Probabilistic Model ◽  
Conditional Distribution ◽  
Heterogeneous Population ◽  
Main Assumption ◽  
Stochastic Filtering ◽  
Occupation Numbers ◽  
History Of ◽  
Residual Lifetimes

We consider a probabilistic model of a heterogeneous population P subdivided into homogeneous sub-cohorts. A main assumption is that the frailties give rise to a discrete, exchangeable random vector. We put ourselves in the framework of stochastic filtering to derive the conditional distribution of residual lifetimes of surviving individuals, given an observed history of failures and survivals. As a main feature of our approach, this study is based on the analysis of behaviour of the vector of ‘occupation numbers’.

scholarly journals Heterogeneous population dynamical model: a filtering problem

2005 ◽  
Vol 42 (02) ◽  
pp. 346-361 ◽  
Author(s):  
A. Gerardi ◽  
P. Tardelli
Keyword(s):  
Finite Number ◽  
Conditional Distribution ◽  
Heterogeneous Population ◽  
Time Approximation ◽  
Stochastic Filtering ◽  
Discrete Time Approximation ◽  
Different Types ◽  
Number Of Classes ◽  
Filtering Problem ◽  
Over Time

We consider a heterogeneous population of identical particles divided into a finite number of classes according to their level of health. The partition can change over time, and a suitable exchangeability assumption is made to allow for having identical items of different types. The partition is not observed; we only observe the cardinality of a particular class. We discuss the problem of finding the conditional distribution of particle lifetimes, given such observations, using stochastic filtering techniques. In particular, a discrete-time approximation is given.

scholarly journals Heterogeneous population dynamical model: a filtering problem

2005 ◽  
Vol 42 (2) ◽  
pp. 346-361 ◽  
Author(s):  
A. Gerardi ◽  
P. Tardelli
Keyword(s):  
Finite Number ◽  
Conditional Distribution ◽  
Heterogeneous Population ◽  
Time Approximation ◽  
Stochastic Filtering ◽  
Discrete Time Approximation ◽  
Different Types ◽  
Number Of Classes ◽  
Filtering Problem ◽  
Over Time

We consider a heterogeneous population of identical particles divided into a finite number of classes according to their level of health. The partition can change over time, and a suitable exchangeability assumption is made to allow for having identical items of different types. The partition is not observed; we only observe the cardinality of a particular class. We discuss the problem of finding the conditional distribution of particle lifetimes, given such observations, using stochastic filtering techniques. In particular, a discrete-time approximation is given.

scholarly journals One- versus multi-component regular variation and extremes of Markov trees

2020 ◽  
Vol 52 (3) ◽  
pp. 855-878
Author(s):  
Johan Segers
Keyword(s):  
Time Series ◽  
Random Vector ◽  
Regular Variation ◽  
Conditional Independence ◽  
Conditional Distribution ◽  
The Self ◽  
Stationary Time Series ◽  
Markov Tree ◽  
Regularly Varying ◽  
Coupled Random Walks

AbstractA Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of the Markov kernels associated to these pairs, the conditional distribution of the self-normalized random vector when the variable at the root of the tree tends to infinity converges weakly to a random vector of coupled random walks called a tail tree. If, in addition, the conditioning variable has a regularly varying tail, the Markov tree satisfies a form of one-component regular variation. Changing the location of the root, that is, changing the conditioning variable, yields a different tail tree. When the tails of the marginal distributions of the conditioning variables are balanced, these tail trees are connected by a formula that generalizes the time change formula for regularly varying stationary time series. The formula is most easily understood when the various one-component regular variation statements are tied up into a single multi-component statement. The theory of multi-component regular variation is worked out for general random vectors, not necessarily Markov trees, with an eye towards other models, graphical or otherwise.

scholarly journals Generalized contact distributions of inhomogeneous Boolean models

2002 ◽  
Vol 34 (01) ◽  
pp. 21-47 ◽  
Author(s):  
Daniel Hug ◽  
Günter Last ◽  
Wolfgang Weil
Keyword(s):  
Convex Body ◽  
Large Class ◽  
Random Vector ◽  
Boundary Point ◽  
Conditional Distribution ◽  
Boolean Model ◽  
Spatial Density ◽  
Boolean Models ◽  
Grain Distribution ◽  
Contact Distribution

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ ℝ d and a gauge body B ⊂ ℝ d , such a generalized contact distribution is the conditional distribution of the random vector (d B (L,Z),u B (L,Z),p B (L,Z),l B (L,Z)) given that Z∩L = ∅, where Z is a Boolean model, d B (L,Z) is the distance of L from Z with respect to B, p B (L,Z) is the boundary point in L realizing this distance (if it exists uniquely), u B (L,Z) is the corresponding boundary point of B (if it exists uniquely) and l B (L,·) may be taken from a large class of locally defined functionals. In particular, we pursue the question of the extent to which the spatial density and the grain distribution underlying an inhomogeneous Boolean model Z are determined by the generalized contact distributions of Z.

scholarly journals Tempo and mode in karyotype evolution revealed by a probabilistic model incorporating both chromosome number and morphology

PLoS Genetics ◽  
2021 ◽  
Vol 17 (4) ◽  
pp. e1009502
Author(s):  
Kohta Yoshida ◽  
Jun Kitano
Keyword(s):  
Probabilistic Model ◽  
Karyotype Evolution ◽  
Dimensional Space ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Centric Fusion ◽  
Extinction Rates ◽  
Plant Group ◽  
History Of ◽  
Taxonomic Groups

Karyotype, including the chromosome and arm numbers, is a fundamental genetic characteristic of all organisms and has long been used as a species-diagnostic character. Additionally, karyotype evolution plays an important role in divergent adaptation and speciation. Centric fusion and fission change chromosome numbers, whereas the intra-chromosomal movement of the centromere, such as pericentric inversion, changes arm numbers. A probabilistic model simultaneously incorporating both chromosome and arm numbers has not been established. Here, we built a probabilistic model of karyotype evolution based on the “karyograph”, which treats karyotype evolution as a walk on the two-dimensional space representing the chromosome and arm numbers. This model enables analysis of the stationary distribution with a stable karyotype for any given parameter. After evaluating their performance using simulated data, we applied our model to two large taxonomic groups of fish, Eurypterygii and series Otophysi, to perform maximum likelihood estimation of the transition rates and reconstruct the evolutionary history of karyotypes. The two taxa significantly differed in the evolution of arm number. The inclusion of speciation and extinction rates demonstrated possibly high extinction rates in species with karyotypes other than the most typical karyotype in both groups. Finally, we made a model including polyploidization rates and applied it to a small plant group. Thus, the use of this probabilistic model can contribute to a better understanding of tempo and mode in karyotype evolution and its possible role in speciation and extinction.

scholarly journals Generalized contact distributions of inhomogeneous Boolean models

2002 ◽  
Vol 34 (1) ◽  
pp. 21-47 ◽  
Author(s):  
Daniel Hug ◽  
Günter Last ◽  
Wolfgang Weil
Keyword(s):  
Convex Body ◽  
Large Class ◽  
Random Vector ◽  
Boundary Point ◽  
Conditional Distribution ◽  
Boolean Model ◽  
Spatial Density ◽  
Boolean Models ◽  
Grain Distribution ◽  
Contact Distribution

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ ℝd and a gauge body B ⊂ ℝd, such a generalized contact distribution is the conditional distribution of the random vector (dB(L,Z),uB(L,Z),pB(L,Z),lB(L,Z)) given that Z∩L = ∅, where Z is a Boolean model, dB(L,Z) is the distance of L from Z with respect to B, pB(L,Z) is the boundary point in L realizing this distance (if it exists uniquely), uB(L,Z) is the corresponding boundary point of B (if it exists uniquely) and lB(L,·) may be taken from a large class of locally defined functionals. In particular, we pursue the question of the extent to which the spatial density and the grain distribution underlying an inhomogeneous Boolean model Z are determined by the generalized contact distributions of Z.

scholarly journals Conditional tail independence in Archimedean copula models

2019 ◽  
Vol 56 (3) ◽  
pp. 858-869
Author(s):  
Michael Falk ◽  
Simone A. Padoan ◽  
Florian Wisheckel
Keyword(s):  
Distribution Function ◽  
Random Vector ◽  
Mild Condition ◽  
Conditional Distribution ◽  
Archimedean Copula ◽  
Tail Behavior ◽  
Copula Models ◽  
Generator Function

AbstractConsider a random vector $\textbf{U}$ whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $\textbf{U}$ , conditional on one of its components, has under a mild condition on the generator function independent upper tails, no matter what the unconditional tail behavior is. This finding is extended to Archimax copulas.

Lattice Boltzmann Models with Underlying Boolean Microdynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Kinetic Theory ◽  
Lattice Boltzmann ◽  
Degrees Of Freedom ◽  
Time History ◽  
Lattice Boltzmann Model ◽  
Occupation Numbers ◽  
History Of ◽  
Lattice Boltzmann Models ◽  
Boltzmann Model ◽  
Statistical Noise

This chapter takes a walk into the Jurassics of LBE, namely the earliest Lattice Boltzmann model that grew up out in response to the main drawbacks of the underlying LGCA. The earliest LBE was first proposed by G. McNamara and G. Zanetti in 1988, with the explicit intent of sidestepping the statistical noise problem plaguing its LGCA ancestor. The basic idea is simple: just replace the Boolean occupation Numbers with the corresponding ensemble-averaged population. The change in perspective is exactly the same as in Continuum Kinetic Theory (CKT); instead of tracking single Boolean molecules, one contents himself with the time history of a collective population representing a “cloud” of microscopic degrees of freedom.

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