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Uhlenbeck Process (uhlenbeck + process)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Bayesian analysis of single-molecule experimental data

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 3 2005
S. C. Kou
Summary., Recent advances in experimental technologies allow scientists to follow biochemical processes on a single-molecule basis, which provides much richer information about chemical dynamics than traditional ensemble-averaged experiments but also raises many new statistical challenges. The paper provides the first likelihood-based statistical analysis of the single-molecule fluorescence lifetime experiment designed to probe the conformational dynamics of a single deoxyribonucleic acid (DNA) hairpin molecule. The conformational change is initially treated as a continuous time two-state Markov chain, which is not observable and must be inferred from changes in photon emissions. This model is further complicated by unobserved molecular Brownian diffusions. Beyond the simple two-state model, a competing model that models the energy barrier between the two states of the DNA hairpin as an Ornstein,Uhlenbeck process has been suggested in the literature. We first derive the likelihood function of the simple two-state model and then generalize the method to handle complications such as unobserved molecular diffusions and the fluctuating energy barrier. The data augmentation technique and Markov chain Monte Carlo methods are developed to sample from the posterior distribution desired. The Bayes factor calculation and posterior estimates of relevant parameters indicate that the fluctuating barrier model fits the data better than the simple two-state model. [source]

Optimal designs for parameter estimation of the Ornstein,Uhlenbeck process

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009
Maroussa Zagoraiou
Abstract This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein,Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend µ and the correlation parameter , using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388,1396). We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for µ conflicts with the one for ,, since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation's precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Shrinkage drift parameter estimation for multi-factor Ornstein,Uhlenbeck processes

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 2 2010
Sévérien Nkurunziza
Abstract We consider some inference problems concerning the drift parameters of multi-factors Vasicek model (or multivariate Ornstein,Uhlebeck process). For example, in modeling for interest rates, the Vasicek model asserts that the term structure of interest rate is not just a single process, but rather a superposition of several analogous processes. This motivates us to develop an improved estimation theory for the drift parameters when homogeneity of several parameters may hold. However, the information regarding the equality of these parameters may be imprecise. In this context, we consider Stein-rule (or shrinkage) estimators that allow us to improve on the performance of the classical maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, their relative dominance is explored and assessed. We illustrate the suggested methods by analyzing interbank interest rates of three European countries. Further, a simulation study illustrates the behavior of the suggested method for observation periods of small and moderate lengths of time. Our analytical and simulation results demonstrate that shrinkage estimators (SEs) provide excellent estimation accuracy and outperform the MLE uniformly. An over-ridding theme of this paper is that the SEs provide powerful extensions of their classical counterparts. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets

BIOMETRICS, Issue 2 2009
Andrew O. Finley
Summary This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein,Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability. [source]