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  总被引:5,自引:0,他引:5  
Vounatsou and Smith (1995, Biometrics 51, 687-708) describe the modern Bayesian analysis of ring-recovery data. Here we discuss and extend their work. We draw different conclusions from two major data analyses. We emphasize the extreme sensitivity of certain parameter estimates to the choice of prior distribution and conclude that naive use of Bayesian methods in this area can be misleading. Additionally, we explain the discrepancy between the Bayesian and classical analyses when the likelihood surface has a flat ridge. In this case, when there is no unique maximum likelihood estimate, the Bayesian estimators are remarkably precise.  相似文献   

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Estimation of a covariance matrix with zeros   总被引:1,自引:0,他引:1  
We consider estimation of the covariance matrix of a multivariaterandom vector under the constraint that certain covariancesare zero. We first present an algorithm, which we call iterativeconditional fitting, for computing the maximum likelihood estimateof the constrained covariance matrix, under the assumption ofmultivariate normality. In contrast to previous approaches,this algorithm has guaranteed convergence properties. Droppingthe assumption of multivariate normality, we show how to estimatethe covariance matrix in an empirical likelihood approach. Theseapproaches are then compared via simulation and on an exampleof gene expression.  相似文献   

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For analyzing longitudinal binary data with nonignorable and nonmonotone missing responses, a full likelihood method is complicated algebraically, and often requires intensive computation, especially when there are many follow-up times. As an alternative, a pseudolikelihood approach has been proposed in the literature under minimal parametric assumptions. This formulation only requires specification of the marginal distributions of the responses and missing data mechanism, and uses an independence working assumption. However, this estimator can be inefficient for estimating both time-varying and time-stationary effects under moderate to strong within-subject associations among repeated responses. In this article, we propose an alternative estimator, based on a bivariate pseudolikelihood, and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudolikelihood obtained under the assumption of independence. We illustrate the method using longitudinal data on CD4 counts from two clinical trials of HIV-infected patients.  相似文献   

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A generalized mover-stayer model for panel data   总被引:1,自引:0,他引:1  
A generalized mover-stayer model is described for conditionally Markov processes under panel observation. Marginally the model represents a mixture of nested continuous-time Markov processes in which sub-models are defined by constraining some transition intensities to zero between two or more states of a full model. A Fisher scoring algorithm is described which facilitates maximum likelihood estimation based only on the first derivatives of the transition probability matrices. The model is fit to data from a smoking prevention study and is shown to provide a significant improvement in fit over a time-homogeneous Markov model. Extensions are developed which facilitate examination of covariate effects on both the transition intensities and the mover-stayer probabilities.  相似文献   

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Sundberg  Rolf 《Biometrika》2002,89(2):478-483
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Data on the presence of a number of vegetation states (defined in terms of species dominance in areas of 10×10 cm) and transition probabilities were derived from permanent quadrats in a number of recently burned heath stands. Data were taken from a species-rich community, a species-poor type and a high-level Calluna-Eriophorum bog. Simple Markovian models were constructed using these data, and the model predictions were compared with known or expected trends. Models for species-rich heath yielded poor simulations of expected trends since matrices derived from data for the first years after fire did not contain sufficient information on transitions to states important later in the developmental sequence. Model results for the simpler species-poor and bog communities were more satisfactory and simulated expected trends. In these types all species recovered quickly after fire and less rearrangement of species abundances took place. Maximum likelihood statistics carried out on the transition matrices produced inconclusive results for the species-rich and species-poor types, but indicated that the data from the Calluna-Eriophorum bog approximated a first-order time-homogeneous Markov chain. It was concluded that Markov models lack predictive ability except in relatively simple systems, but that they may be useful in illustrating variations in short-term community dynamics.Nomenclature follows Tutin et al. (1964–80) for vascular plants and Smith (1978) for mosses.I am grateful to Prof. C. H. Gimingham for help and advice during this study, which was carried out during tenure of a Natural Environment Research Council studentship. Thanks are also due to Dr M. B. Usher and an anonymous referee for their comments on the draft.  相似文献   

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Analysis of multivariate probit models   总被引:13,自引:0,他引:13  
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The behaviour of many biological systems can be attributed to that of a large number of units, with each unit swinging between two competing states. During the past few years efforts have been made (e.g., Chung and Kennedy , 1996) to describe such discrete systems using a multiple binary Markov chain model. Here we explore the gamut of these models and classify their behaviour into five qualitatively distinct types, corresponding to subregions of the parameter space. It is suggested that these model behaviours may correspond to behaviours observed in nature. A simple method for fitting the model to data is presented.  相似文献   

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The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.  相似文献   

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Yang J  Wu R  Casella G 《Biometrics》2009,65(1):30-39
Summary .  Functional mapping is a useful tool for mapping quantitative trait loci (QTL) that control dynamic traits. It incorporates mathematical aspects of biological processes into the mixture model-based likelihood setting for QTL mapping, thus increasing the power of QTL detection and the precision of parameter estimation. However, in many situations there is no obvious functional form and, in such cases, this strategy will not be optimal. Here we propose to use nonparametric function estimation, typically implemented with B-splines, to estimate the underlying functional form of phenotypic trajectories, and then construct a nonparametric test to find evidence of existing QTL. Using the representation of a nonparametric regression as a mixed model, the final test statistic is a likelihood ratio test. We consider two types of genetic maps: dense maps and general maps, and the power of nonparametric functional mapping is investigated through simulation studies and demonstrated by examples.  相似文献   

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Maximum likelihood estimation of oncogenetic tree models   总被引:2,自引:0,他引:2  
We present a new approach for modelling the dependences between genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumour development and progression is assumed to follow a probabilistic tree model. We show how maximum likelihood estimation can be used to reconstruct a tree model for the dependences between genetic alterations in a given tumour type. We illustrate the use of the proposed method by applying it to cytogenetic data from 173 cases of clear cell renal cell carcinoma, arriving at a model for the karyotypic evolution of this tumour.  相似文献   

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Single ion channel currents can be analysed by hidden or aggregated Markov models. A classical result from Fredkin et al. (Proceedings of the Berkeley conference in honor of Jerzy Neyman and Jack Kiefer, vol I, pp 269–289, 1985) states that the maximum number of identifiable parameters is bounded by 2nonc, where no and nc denote the number of open and closed states, respectively. We show that this bound can be overcome when the probabilities of the initial distribution are known and the data consist of several sweeps.  相似文献   

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There has been considerable interest in the problem of making maximum likelihood (ML) evolutionary trees which allow insertions and deletions. This problem is partly one of formulation: how does one define a probabilistic model for such trees which treats insertion and deletion in a biologically plausible manner? A possible answer to this question is proposed here by extending the concept of a hidden Markov model (HMM) to evolutionary trees. The model, called a tree-HMM, allows what may be loosely regarded as learnable affine-type gap penalties for alignments. These penalties are expressed in HMMs as probabilities of transitions between states. In the tree-HMM, this idea is given an evolutionary embodiment by defining trees of transitions. Just as the probability of a tree composed of ungapped sequences is computed, by Felsenstein's method, using matrices representing the probabilities of substitutions of residues along the edges of the tree, so the probabilities in a tree-HMM are computed by substitution matrices for both residues and transitions. How to define these matrices by a ML procedure using an algorithm that learns from a database of protein sequences is shown here. Given these matrices, one can define a tree-HMM likelihood for a set of sequences, assuming a particular tree topology and an alignment of the sequences to the model. If one could efficiently find the alignment which maximizes (or comes close to maximizing) this likelihood, then one could search for the optimal tree topology for the sequences. An alignment algorithm is defined here which, given a particular tree topology, is guaranteed to increase the likelihood of the model. Unfortunately, it fails to find global optima for realistic sequence sets. Thus further research is needed to turn the tree-HMM into a practical phylogenetic tool.  相似文献   

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Hierarchical likelihood approach for frailty models   总被引:5,自引:0,他引:5  
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We point out a general problem in fitting continuous time spatially explicit models to a temporal sequence of spatial data observed at discrete times. To illustrate the problem, we examined the continuous time Markov model for forest gap dynamics. A forest is assumed to be apportioned into discrete cells (or sites) arranged in a regular square lattice. Each site is characterized as either a gap or a non-gap site according to the vegetation height of trees. The model incorporates the influence of neighboring sites on transition rate: transition rate from a non-gap to a gap site increases linearly with the number of neighbors that are currently in the gap state, and vice versa. We fitted the model to the spatiotemporal data of canopy height observed at the permanent plot in Barro Colorado Island (BCI). When we used the approximate maximum likelihood method to estimate the parameters of the model, the estimated transition rates included a large bias-in particular, the strength of interaction between nearby sites was underestimated. This bias originated from the assumption that each transition between two observation times is independent. The interaction between sites at local scale creates a long chain of transitions within a single census interval, which violates the independence of each transition. We show that a computer-intensive method, called Monte Carlo bias correction (MCBC), is very effective in removing the bias included in the estimate. The global and local gap densities measuring spatial aggregation of gap sites were computed from simulated and real gap dynamics to assess the model. When the approximate likelihood estimates were applied to the model, the predicted local gap density was clearly lower than the observed one. The use of MCBC estimates, suggesting a strong interaction between sites, improved this discrepancy.  相似文献   

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