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53
Adaptive Markov Chain Monte Carlo through Regeneration
, 1998
"... this paper is organized as follows. In Section 2 we introduce the concept of regeneration and adaptation at regeneration, and provide theoretical support. In Section 3, the splitting techniques required for adaptation are reviewed. Section 4 contains four illustrations of adaptive MCMC. Some of the ..."
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Cited by 69 (4 self)
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this paper is organized as follows. In Section 2 we introduce the concept of regeneration and adaptation at regeneration, and provide theoretical support. In Section 3, the splitting techniques required for adaptation are reviewed. Section 4 contains four illustrations of adaptive MCMC. Some of the proofs from Sections 2 and 3 are placed in the Appendix. 2 Regeneration: A Framework for Adaptation
A Simulation Model for Managing Survivability of Networked Information Systems
, 2000
"... ix 1 ..."
A particle migrating randomly on a sphere
 J. Theoretical Prob
, 1997
"... Consider a particle moving on the surface of the unit sphere in R 3 and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for variou ..."
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Cited by 21 (11 self)
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Consider a particle moving on the surface of the unit sphere in R 3 and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for various characteristics of the process including expected travel time to a cap, the limiting distribution, the likelihood ratio and some estimates for parameters appearing in the model. KEY WORDS: Drift; great circle path; likelihood ratio; poleseeking; skew product; spherical Brownian motion; stochastic differential equation; travel time. 1.
Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consi ..."
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Cited by 13 (5 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A
Parameter estimation for multiscale diffusions
 J. Stat. Phys
"... We study the problem of parameter estimation for timeseries possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale data. We demonstrate, numerically and analytically, that if t ..."
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Cited by 13 (6 self)
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We study the problem of parameter estimation for timeseries possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale data. We demonstrate, numerically and analytically, that if the data is sampled too finely then the parameter fit will fail, in that the correct parameters in the homogenized model are not identified. We also show, numerically and analytically, that if the data is subsampled at an appropriate rate then it is possible to estimate the coefficients of the homogenized model correctly.
Elephant Seal Movements: Modelling Migration
"... Elephant seals migrate over vast areas of the eastern North Pacific Ocean between rookeries in Southern California and distant northern foraging areas. Several models of particle movement were evaluated and a model for great circle motion found to give reasonable results for the movement of an adult ..."
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Cited by 10 (8 self)
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Elephant seals migrate over vast areas of the eastern North Pacific Ocean between rookeries in Southern California and distant northern foraging areas. Several models of particle movement were evaluated and a model for great circle motion found to give reasonable results for the movement of an adult female. This model takes specific account of the fact that the movement is on the surface of a sphere and that the animal is apparently heading toward a particular destination. The parameters of the motion were estimated. Such a great circle path of migration may imply that these seals have the ability to assess their position with respect to some global or celestial cues, allowing them to continually adjust their ____________ *The work of DRB supported by the Office of Naval Research Grant N0001494 10042 and the National Science Foundation Grant DMS9625774. Elephant seal dive data were collected in previous studies with partial support of a contract to BSS from the Space and Missile C...
Statistical Aspects of the fractional stochastic calculus
 ANN. STAT
, 2007
"... We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equati ..."
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Cited by 10 (5 self)
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We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of Holderregularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We also prove that a version of the MLE using only discrete observations is still a strongly consistent estimator.
Bayesian analysis of extreme values by mixture modeling
 Extremes
, 2003
"... Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific l ..."
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Cited by 7 (1 self)
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Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a wellknown insurance company over a 15year period.
Extensions of the bifurcating autoregressive model for cell lineage studies
 in "J. Appl. Probab
, 1999
"... ..."
Parameter estimation of a bivariate compound Poisson process
, 2008
"... In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likel ..."
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Cited by 4 (1 self)
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In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likelihood approach. This approach ensures that the estimated model remains in the class of multivariate compound Poisson processes. A simulation study investigates the small sample behaviour of the MLEs, where we also suggest a new simulation algorithm. Finally, we apply our method to the Danish fire insurance data.