共查询到20条相似文献,搜索用时 15 毫秒
1.
Abstract. Methodology for Bayesian inference is considered for a stochastic epidemic model which permits mixing on both local and global scales. Interest focuses on estimation of the within- and between-group transmission rates given data on the final outcome. The model is sufficiently complex that the likelihood of the data is numerically intractable. To overcome this difficulty, an appropriate latent variable is introduced, about which asymptotic information is known as the population size tends to infinity. This yields a method for approximate inference for the true model. The methods are applied to real data, tested with simulated data, and also applied to a simple epidemic model for which exact results are available for comparison. 相似文献
2.
Bayesian inference for partially observed stochastic epidemics 总被引:4,自引:0,他引:4
P. D. O'Neill & G. O. Roberts 《Journal of the Royal Statistical Society. Series A, (Statistics in Society)》1999,162(1):121-129
The analysis of infectious disease data is usually complicated by the fact that real life epidemics are only partially observed. In particular, data concerning the process of infection are seldom available. Consequently, standard statistical techniques can become too complicated to implement effectively. In this paper Markov chain Monte Carlo methods are used to make inferences about the missing data as well as the unknown parameters of interest in a Bayesian framework. The methods are applied to real life data from disease outbreaks. 相似文献
3.
Bayesian Inference for Stochastic Epidemics in Populations with Random Social Structure 总被引:1,自引:0,他引:1
A single-population Markovian stochastic epidemic model is defined so that the underlying social structure of the population is described by a Bernoulli random graph. The parameters of the model govern the rate of infection, the length of the infectious period, and the probability of social contact with another individual in the population. Markov chain Monte Carlo methods are developed to facilitate Bayesian inference for the parameters of both the epidemic model and underlying unknown social structure. The methods are applied in various examples of both illustrative and real-life data, with two different kinds of data structure considered. 相似文献
4.
Bayesian Inference for a Stochastic Epidemic Model with Uncertain Numbers of Susceptibles of Several Types 总被引:1,自引:0,他引:1
Yu Hayakawa Philip D. O'Neill Darren Upton Paul S.F. Yip 《Australian & New Zealand Journal of Statistics》2003,45(4):491-502
A stochastic epidemic model with several kinds of susceptible is used to analyse temporal disease outbreak data from a Bayesian perspective. Prior distributions are used to model uncertainty in the actual numbers of susceptibles initially present. The posterior distribution of the parameters of the model is explored via Markov chain Monte Carlo methods. The methods are illustrated using two datasets, and the results are compared where possible to results obtained by previous analyses. 相似文献
5.
Yuan Ji Guosheng Yin Kam-Wah Tsui Mikhail G. Kolonin Jessica Sun Wadih Arap Renata Pasqualini Kim-Anh Do 《Journal of the Royal Statistical Society. Series C, Applied statistics》2007,56(2):139-152
Summary. Phage display is a biological process that is used to screen random peptide libraries for ligands that bind to a target of interest with high affinity. On the basis of a count data set from an innovative multistage phage display experiment, we propose a class of Bayesian mixture models to cluster peptide counts into three groups that exhibit different display patterns across stages. Among the three groups, the investigators are particularly interested in that with an ascending display pattern in the counts, which implies that the peptides are likely to bind to the target with strong affinity. We apply a Bayesian false discovery rate approach to identify the peptides with the strongest affinity within the group. A list of peptides is obtained, among which important ones with meaningful functions are further validated by biologists. To examine the performance of the Bayesian model, we conduct a simulation study and obtain desirable results. 相似文献
6.
G. J. Gibson W. Otten J. A. N. Filipe A. Cook G. Marion C. A. Gilligan 《Statistics and Computing》2006,16(4):391-402
Statistical methods are formulated for fitting and testing percolation-based, spatio-temporal models that are generally applicable
to biological or physical processes that evolve in spatially distributed populations. The approach is developed and illustrated
in the context of the spread of Rhizoctonia solani, a fungal pathogen, in radish but is readily generalized to other scenarios. The particular model considered represents processes
of primary and secondary infection between nearest-neighbour hosts in a lattice, and time-varying susceptibility of the hosts.
Bayesian methods for fitting the model to observations of disease spread through space and time in replicate populations are
developed. These use Markov chain Monte Carlo methods to overcome the problems associated with partial observation of the
process. We also consider how model testing can be achieved by embedding classical methods within the Bayesian analysis. In
particular we show how a residual process, with known sampling distribution, can be defined. Model fit is then examined by
generating samples from the posterior distribution of the residual process, to which a classical test for consistency with
the known distribution is applied, enabling the posterior distribution of the P-value of the test used to be estimated. For the Rhizoctonia-radish system the methods confirm the findings of earlier non-spatial analyses regarding the dynamics of disease transmission
and yield new evidence of environmental heterogeneity in the replicate experiments. 相似文献
7.
C. P. Robert T. Rydén & D. M. Titterington 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2000,62(1):57-75
Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data from finance, meteorology and geomagnetism. 相似文献
8.
《Journal of Statistical Computation and Simulation》2012,82(7):1295-1319
This paper extends stochastic conditional duration (SCD) models for financial transaction data to allow for correlation between error processes and innovations of observed duration process and latent log duration process. Suitable algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting SCD models under various distributional assumptions about the innovation of the measurement equation. Unlike the estimation methods commonly used to estimate the SCD models in the literature, we work with the original specification of the model, without subjecting the observation equation to a logarithmic transformation. Results of simulation studies suggest that our proposed models and corresponding estimation methodology perform quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts of the fitted models. Applications to the IBM transaction data allow comparison of our models and methods to those existing in the literature. 相似文献
9.
In this paper we present a review of population-based simulation for static inference problems. Such methods can be described as generating a collection of random variables {X
n
}
n=1,…,N
in parallel in order to simulate from some target density π (or potentially sequence of target densities). Population-based simulation is important as many challenging sampling problems
in applied statistics cannot be dealt with successfully by conventional Markov chain Monte Carlo (MCMC) methods. We summarize
population-based MCMC (Geyer, Computing Science and Statistics: The 23rd Symposium on the Interface, pp. 156–163, 1991; Liang and Wong, J. Am. Stat. Assoc. 96, 653–666, 2001) and sequential Monte Carlo samplers (SMC) (Del Moral, Doucet and Jasra, J. Roy. Stat. Soc. Ser. B 68, 411–436, 2006a), providing a comparison of the approaches. We give numerical examples from Bayesian mixture modelling (Richardson and Green,
J. Roy. Stat. Soc. Ser. B 59, 731–792, 1997). 相似文献
10.
《Journal of the Korean Statistical Society》2014,43(1):31-45
Monte Carlo methods for the exact inference have received much attention recently in complete or incomplete contingency table analysis. However, conventional Markov chain Monte Carlo, such as the Metropolis–Hastings algorithm, and importance sampling methods sometimes generate the poor performance by failing to produce valid tables. In this paper, we apply an adaptive Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm (SAMC; Liang, Liu, & Carroll, 2007), to the exact test of the goodness-of-fit of the model in complete or incomplete contingency tables containing some structural zero cells. The numerical results are in favor of our method in terms of quality of estimates. 相似文献
11.
Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods 总被引:1,自引:0,他引:1
Philip D. O'Neill David J. Balding Niels G. Becker Mervi Eerola & Denis Mollison 《Journal of the Royal Statistical Society. Series C, Applied statistics》2000,49(4):517-542
The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis–Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses. 相似文献
12.
Marcelo Hartmann 《统计学通讯:模拟与计算》2017,46(7):5285-5302
In this article, we propose to evaluate and compare Markov chain Monte Carlo (MCMC) methods to estimate the parameters in a generalized extreme value model. We employed the Bayesian approach using traditional Metropolis-Hastings methods, Hamiltonian Monte Carlo (HMC), and Riemann manifold HMC (RMHMC) methods to obtain the approximations to the posterior marginal distributions of interest. Applications to real datasets and simulation studies provide evidence that the extra analytical work involved in Hamiltonian Monte Carlo algorithms is compensated by a more efficient exploration of the parameter space. 相似文献
13.
Gareth O. Roberts Omiros Papaspiliopoulos Petros Dellaportas 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2004,66(2):369-393
Summary. We develop Markov chain Monte Carlo methodology for Bayesian inference for non-Gaussian Ornstein–Uhlenbeck stochastic volatility processes. The approach introduced involves expressing the unobserved stochastic volatility process in terms of a suitable marked Poisson process. We introduce two specific classes of Metropolis–Hastings algorithms which correspond to different ways of jointly parameterizing the marked point process and the model parameters. The performance of the methods is investigated for different types of simulated data. The approach is extended to consider the case where the volatility process is expressed as a superposition of Ornstein–Uhlenbeck processes. We apply our methodology to the US dollar–Deutschmark exchange rate. 相似文献
14.
Ole F. Christensen Gareth O. Roberts Jeffrey S. Rosenthal 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2005,67(2):253-268
Summary. The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory. 相似文献
15.
Kim E. Andersen Stephen P. Brooks Martin B. Hansen 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2003,65(3):619-642
Summary. Enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling. To interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures. We use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the Earth and we contrast our approach with earlier methods based on smooth Gaussian fields. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid Metropolis–coupled Markov chain Monte Carlo methods and illustrate the method on a set of field data. 相似文献
16.
Bayesian inference for generalized additive mixed models based on Markov random field priors 总被引:9,自引:0,他引:9
Ludwig Fahrmeir & Stefan Lang 《Journal of the Royal Statistical Society. Series C, Applied statistics》2001,50(2):201-220
Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications. 相似文献
17.
This article presents a Bayesian approach to the regression analysis of truncated data, with a focus on zero-truncated counts from the Poisson distribution. The approach provides inference not only on the regression coefficients but also on the total sample size and the parameters of the covariate distribution. The theory is applied to some illegal immigrant data from The Netherlands. Several models are fitted with the aid of Markov chain Monte Carlo methods and assessed via posterior predictive p-values. Inferences are compared with those obtained elsewhere using other approaches. 相似文献
18.
P. J. Lenk 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1999,61(4):863-879
This paper presents the Bayesian analysis of a semiparametric regression model that consists of parametric and nonparametric components. The nonparametric component is represented with a Fourier series where the Fourier coefficients are assumed a priori to have zero means and to decay to 0 in probability at either algebraic or geometric rates. The rate of decay controls the smoothness of the response function. The posterior analysis automatically selects the amount of smoothing that is coherent with the model and data. Posterior probabilities of the parametric and semiparametric models provide a method for testing the parametric model against a non-specific alternative. The Bayes estimator's mean integrated squared error compares favourably with the theoretically optimal estimator for kernel regression. 相似文献
19.
We introduce a class of spatial random effects models that have Markov random fields (MRF) as latent processes. Calculating
the maximum likelihood estimates of unknown parameters in SREs is extremely difficult, because the normalizing factors of
MRFs and additional integrations from unobserved random effects are computationally prohibitive. We propose a stochastic approximation
expectation-maximization (SAEM) algorithm to maximize the likelihood functions of spatial random effects models. The SAEM
algorithm integrates recent improvements in stochastic approximation algorithms; it also includes components of the Newton-Raphson
algorithm and the expectation-maximization (EM) gradient algorithm. The convergence of the SAEM algorithm is guaranteed under
some mild conditions. We apply the SAEM algorithm to three examples that are representative of real-world applications: a
state space model, a noisy Ising model, and segmenting magnetic resonance images (MRI) of the human brain. The SAEM algorithm
gives satisfactory results in finding the maximum likelihood estimate of spatial random effects models in each of these instances. 相似文献
20.
Mogens Bladt Michael Sørensen 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2005,67(3):395-410
Summary. Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Markov chain Monte Carlo procedure. When the maximum likelihood estimator does not exist, an estimator can be obtained by using a penalized likelihood function or by the Markov chain Monte Carlo procedure with a suitable prior. The methodology and its implementation are illustrated by examples and simulation studies. 相似文献