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1.
Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices
Aline Talhouk Arnaud Doucet Kevin Murphy 《Journal of computational and graphical statistics》2013,22(3):739-757
We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials. 相似文献
2.
Chih-Wen Hsu Marick S. Sinay John S. J. Hsu 《Annals of the Institute of Statistical Mathematics》2012,64(2):319-342
Bayesian analysis for a covariance structure has been in use for decades. The commonly adopted Bayesian setup involves the
conjugate inverse Wishart prior specification for the covariance matrix. Here we depart from this approach and adopt a novel
prior specification by considering a multivariate normal prior for the elements of the matrix logarithm of the covariance
structure. This specification allows for a richer class of prior distributions for the covariance structure with respect to
strength of beliefs in prior location hyperparameters and the added ability to model potential correlation amongst the covariance
structure. We provide three computational methods for calculating the posterior moment of the covariance matrix. The moments
of interest are calculated based upon computational results via Importance sampling, Laplacian approximation and Markov Chain
Monte Carlo/Metropolis–Hastings techniques. As a particular application of the proposed technique we investigate educational
test score data from the project talent data set. 相似文献
3.
《Journal of computational and graphical statistics》2013,22(4):897-914
The correlation matrix (denoted by R) plays an important role in many statistical models. Unfortunately, sampling the correlation matrix in Markov chain Monte Carlo (MCMC) algorithms can be problematic. In addition to the positive definite constraint of covariance matrices, correlation matrices have diagonal elements fixed at one. In this article, we propose an efficient two-stage parameter expanded reparameterization and Metropolis-Hastings (PX-RPMH) algorithm for simulating R. Using this algorithm, we draw all elements of R simultaneously by first drawing a covariance matrix from an inverse Wishart distribution, and then translating it back to a correlation matrix through a reduction function and accepting it based on a Metropolis-Hastings acceptance probability. This algorithm is illustrated using multivariate probit (MVP) models and multivariate regression (MVR) models with a common correlation matrix across groups. Via both a simulation study and a real data example, the performance of the PX-RPMH algorithm is compared with those of other common algorithms. The results show that the PX-RPMH algorithm is more efficient than other methods for sampling a correlation matrix. 相似文献
4.
Identifying correlation structure is important to achieving estimation efficiency in analyzing longitudinal data, and is also crucial for drawing valid statistical inference for large-size clustered data. In this article, we propose a nonparametric method to estimate the correlation structure, which is applicable for discrete longitudinal data. We use eigenvector-based basis matrices to approximate the inverse of the empirical correlation matrix and determine the number of basis matrices via model selection. A penalized objective function based on the difference between the empirical and model approximation of the correlation matrices is adopted to select an informative structure for the correlation matrix. The eigenvector representation of the correlation estimation is capable of reducing the risk of model misspecification, and also provides useful information on the specific within-cluster correlation pattern of the data. We show that the proposed method possesses the oracle property and selects the true correlation structure consistently. The proposed method is illustrated through simulations and two data examples on air pollution and sonar signal studies . 相似文献
5.
《Journal of computational and graphical statistics》2013,22(2):262-282
This article proposes a four-pronged approach to efficient Bayesian estimation and prediction for complex Bayesian hierarchical Gaussian models for spatial and spatiotemporal data. The method involves reparameterizing the covariance structure of the model, reformulating the means structure, marginalizing the joint posterior distribution, and applying a simplex-based slice sampling algorithm. The approach permits fusion of point-source data and areal data measured at different resolutions and accommodates nonspatial correlation and variance heterogeneity as well as spatial and/or temporal correlation. The method produces Markov chain Monte Carlo samplers with low autocorrelation in the output, so that fewer iterations are needed for Bayesian inference than would be the case with other sampling algorithms. Supplemental materials are available online. 相似文献
6.
Nonlinear dynamical stochastic models are ubiquitous in different
areas. Their statistical properties are often of great interest, but
are also very challenging to compute. Many excitable media models
belong to such types of complex systems with large state dimensions
and the associated covariance matrices have localized structures. In
this article, a mathematical framework to understand the spatial
localization for a large class of stochastically coupled nonlinear
systems in high dimensions is developed. Rigorous \linebreak
mathematical analysis shows that the local effect from the diffusion
results in an exponential decay of the components in the covariance
matrix as a function of the distance while the global effect due to
the mean field interaction synchronizes different components and
contributes to a global covariance. The analysis is based on a
comparison with an appropriate linear surrogate model, of which the
covariance propagation can be computed explicitly. Two important
applications of these theoretical results are discussed. They are
the spatial averaging strategy for efficiently sampling the
covariance matrix and the localization technique in data
assimilation. Test examples of a linear model and a stochastically
coupled FitzHugh-Nagumo model for excitable media are adopted to
validate the theoretical results. The latter is also used for a
systematical study of the spatial averaging strategy in efficiently
sampling the covariance matrix in different dynamical regimes. 相似文献
7.
Summary Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the
definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust)
correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared
with the more traditional approach to robust canonical correlation via covariance matrix estimates. A simulation study compares
the performance of the different estimators under several kinds of sampling schemes. Robustness is studied as well by breakdown
plots. 相似文献
8.
Rapisarda Francesco; Brigo Damiano; Mercurio Fabio 《IMA Journal of Management Mathematics》2007,18(1):55-73
** Email: francesco.rapisarda{at}ubs.com
In this paper, we present a new interpretation of the parameterizationof a correlation matrix proposed earlier by some authors (Jäckel& Rebonato, 1999). This interpretation is based on viewingany correlation matrix as the result of the scalar productsof a suitable set of unit vectors in a multidimensional space,each rotated from all the others by generalized Euler angles.It is possible to exploit the intuitive nature of this approachin order to obtain more efficient optimization schemes whencalibrating a reduced-form model to a desired correlation structure. 相似文献
9.
We study the role of partial autocorrelations in the reparameterization and parsimonious modeling of a covariance matrix. The work is motivated by and tries to mimic the phenomenal success of the partial autocorrelations function (PACF) in model formulation, removing the positive-definiteness constraint on the autocorrelation function of a stationary time series and in reparameterizing the stationarity-invertibility domain of ARMA models. It turns out that once an order is fixed among the variables of a general random vector, then the above properties continue to hold and follow from establishing a one-to-one correspondence between a correlation matrix and its associated matrix of partial autocorrelations. Connections between the latter and the parameters of the modified Cholesky decomposition of a covariance matrix are discussed. Graphical tools similar to partial correlograms for model formulation and various priors based on the partial autocorrelations are proposed. We develop frequentist/Bayesian procedures for modelling correlation matrices, illustrate them using a real dataset, and explore their properties via simulations. 相似文献
10.
We study a lattice model that is closely related to the Ising model and can be regarded as describing diffusion of loops in two dimensions. The time development is given by a transfer matrix for a random surface model on a three-dimensional lattice. The transfer matrix is indexed by loops and is invariant under a group of motions in the loop space. The eigenvalues of the transfer matrix are calculated in terms of the partition function and the correlation functions of the Ising model. 相似文献
11.
Susana Rubin-Bleuer 《Journal of multivariate analysis》2011,102(5):884-895
Data from most complex surveys are subject to selection bias and clustering due to the sampling design. Results developed for a random sample from a super-population model may not apply. Ignoring the survey sampling weights may cause biased estimators and erroneous confidence intervals. In this paper, we use the design approach for fitting the proportional hazards (PH) model and prove formally the asymptotic normality of the sample maximum partial likelihood (SMPL) estimators under the PH model for both stochastically independent and clustered failure times. In the first case, we use the central limit theorem for martingales in the joint design-model space, and this enables us to obtain results for a general multistage sampling design under mild and easily verifiable conditions. In the case of clustered failure times, we require asymptotic normality in the sampling design space directly, and this holds for fewer sampling designs than in the first case. We also propose a variance estimator of the SMPL estimator. A key property of this variance estimator is that we do not have to specify the second-stage correlation model. 相似文献
12.
Hiroshi Kurata 《Journal of multivariate analysis》1998,67(2):297-305
This paper presents a generalization of Rao's covariance structure. In a general linear regression model, we classify the error covariance structure into several categories and investigate the efficiency of the ordinary least squares estimator (OLSE) relative to the Gauss–Markov estimator (GME). The classification criterion considered here is the rank of the covariance matrix of the difference between the OLSE and the GME. Hence our classification includes Rao's covariance structure. The results are applied to models with special structures: a general multivariate analysis of variance model, a seemingly unrelated regression model, and a serial correlation model. 相似文献
13.
The case-cohort design is widely used in large epidemiological studies and prevention trials for cost reduction. In such a design, covariates are assembled only for a subcohort which is a random subset of the entire cohort and any additional cases outside the subcohort. In this paper, we discuss the case-cohort analysis with a class of general additive-multiplicative hazard models which includes the commonly used Cox model and additive hazard model as special cases. Two sampling schemes for the subcohort, Bernoulli sampling with arbitrary selection probabilities and stratified simple random sampling with fixed subcohort sizes, are discussed. In each setting, an estimating function is constructed to estimate the regression parameters. The resulting estimator is shown to be consistent and asymptotically normally distributed. The limiting variance-covariance matrix can be consistently estimated by the case-cohort data. A simulation study is conducted to assess the finite sample performances of the proposed method and a real example is provided. 相似文献
14.
To understand and predict chronological dependence in the second‐order moments of asset returns, this paper considers a multivariate hysteretic autoregressive (HAR) model with generalized autoregressive conditional heteroskedasticity (GARCH) specification and time‐varying correlations, by providing a new method to describe a nonlinear dynamic structure of the target time series. The hysteresis variable governs the nonlinear dynamics of the proposed model in which the regime switch can be delayed if the hysteresis variable lies in a hysteresis zone. The proposed setup combines three useful model components for modeling economic and financial data: (1) the multivariate HAR model, (2) the multivariate hysteretic volatility models, and (3) a dynamic conditional correlation structure. This research further incorporates an adapted multivariate Student t innovation based on a scale mixture normal presentation in the HAR model to tolerate for dependence and different shaped innovation components. This study carries out bivariate volatilities, Value at Risk, and marginal expected shortfall based on a Bayesian sampling scheme through adaptive Markov chain Monte Carlo (MCMC) methods, thus allowing to statistically estimate all unknown model parameters and forecasts simultaneously. Lastly, the proposed methods herein employ both simulated and real examples that help to jointly measure for industry downside tail risk. 相似文献
15.
This paper considers principal component analysis (PCA) in familial models, where the number of siblings can differ among families. S. Konishi and C. R. Rao (1992, Biometrika79, 631–641) used the unified estimator of S. Konishi and C. G. Khatri (1990, Ann. Inst. Statist. Math.42, 561–580) to develop a PCA derived from the covariance matrix. However, because of the lack of invariance to componentwise change of scale, an analysis based on the correlation matrix is often preferred. The asymptotic distribution of the estimated eigenvalues and eigenvectors of the correlation matrix are derived under elliptical sampling. A Monte Carlo simulation shows the usefulness of the asymptotic expressions for samples as small as N=25 families. 相似文献
16.
本文提出Toeplitz矩阵填充的四种流形逼近算法。在左奇异向量空间中对已知部分运用最小二乘法逼近,形成新的可行矩阵;并将对角线上的元素分别用均值,l1范数,l∞范数和中间数四种方法逼近使得迭代后的矩阵仍保持Toeplitz结构,节约了奇异向量空间的分解时间。最终找到合理的低秩矩阵来逼近未知的高秩矩阵,进而精确地完成Toeplitz矩阵的填充。理论上,分析了在一定条件下算法的收敛性。实验上,通过取不同的采样密度进行数值实验展示了四种算法的优劣。实验结果说明均值算法和l∞范数算法大多用的时间较少,但是当采样密度和矩阵规模较大时,中间数算法的精度较高。 相似文献
17.
灰色面板数据包含研究对象诸多信息,由于数据类型和结构较为复杂,目前还没有测度其相似性和接近性的关联度模型,针对这一问题。首先,通过投影方法将灰色面板数据转化为样本关于指标的时间序列行为矩阵,矩阵每行为指标的时间序列;然后,定义一般灰数的距离测度和运算法则;最后,基于两折线间斜率与面积的视角,测度相似性和接近性关联系数。进而构建灰色面板数据的相似性和接近性关联度模型,并研究了该模型的性质。实例表明该模型在测度面板数据类型为一般灰数时的相似性和接近性方面具有良好的效果。 相似文献
18.
Summary This paper presents a heuristic approach for multivariate random number generation. Our aim is to generate multivariate samples
with specified marginal distributions and correlation matrix, which can be incorporated into risk analysis models to conduct
simulation studies. The proposed sampling approach involves two distinct steps: first a univariate random sample from each
specified probability distribution is generated; then a heuristic combinatorial optimization procedure is used to rearrange
the generated univariate samples, in order to obtain the desired correlations between them. The combinatorial optimization
step is performed with a simulated annealing algorithm, which changes only the positions and not the values of the numbers
generated in the first step. The proposed multivariate sampling approach can be used with any type of marginal distributions:
continuous or discrete, parametric or non-parametric, etc. 相似文献
19.
随着金融资产种类的增加,特别是考虑大规模投资组合问题时,很可能出现资产间的多重共线性或相关性,从而出现协方差阵奇异的情况。然而,目前关于投资组合的均值—方差分析大都是在协方差阵正定的条件下得到的,因此,不适用于奇异协方差阵的情形。针对这一问题,利用广义逆矩阵研究了协方差阵奇异时的均值—方差投资组合模型,在不同借贷利率条件下得到了前沿组合和组合前沿的解析解,突破了传统方法中要求协方差阵可逆的限制,推广了经典Markowitz模型。 相似文献