The conditional autoregressive model is a routinely used statistical model for areal data thatarise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregr...The conditional autoregressive model is a routinely used statistical model for areal data thatarise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have also been extensively studied in the literatureand it has been shown that extending from the univariate case to the multivariate case is nottrivial. The difficulties lie in many aspects, including validity, interpretability, flexibility and computational feasibility of the model. In this paper, we approach the multivariate modelling froman element-based perspective instead of the traditional vector-based perspective. We focus onthe joint adjacency structure of elements and discuss graphical structures for both the spatialand non-spatial domains. We assume that the graph for the spatial domain is generally knownand fixed while the graph for the non-spatial domain can be unknown and random. We proposea very general specification for the multivariate conditional modelling and then focus on threespecial cases, which are linked to well-known models in the literature. Bayesian inference forparameter learning and graph learning is provided for the focused cases, and finally, an examplewith public health data is illustrated.展开更多
Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studie...Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.展开更多
针对传统高斯混合模型(GMM,Gaussian mixture model)难以自动获取类属数和对噪声敏感问题,提出了一种基于可变类空间约束GMM的遥感图像分割方法。首先在构建的GMM中,将像素类属性建模为马尔可夫随机场(MRF,Markov random field),并在此...针对传统高斯混合模型(GMM,Gaussian mixture model)难以自动获取类属数和对噪声敏感问题,提出了一种基于可变类空间约束GMM的遥感图像分割方法。首先在构建的GMM中,将像素类属性建模为马尔可夫随机场(MRF,Markov random field),并在此基础上定义其先验概率;结合邻域像素类属性的后验概率和先验概率,定义噪声平滑因子,以提高算法的抗噪性;在参数求解过程中,分别采用可逆跳变马尔可夫链蒙特卡罗(RJMCMC,reversible jump Markov chain Monte Carlo)方法和最大似然(ML,maximum likelihood)方法估计类属数和模型参数;最后以最小化噪声平滑因子为准则获取最终分割结果。为了验证提出的分割方法,分别对模拟图像和全色遥感图像进行了可变类分割实验。实验结果表明提出方法的可行性和有效性。展开更多
A Bayesian estimation method to separate multicomponent signals with single channel observation is presented in this paper. By using the basis function projection, the component separation becomes a problem of limited...A Bayesian estimation method to separate multicomponent signals with single channel observation is presented in this paper. By using the basis function projection, the component separation becomes a problem of limited parameter estimation. Then, a Bayesian model for estimating parameters is set up. The reversible jump MCMC （Monte Carlo Markov Chain） algorithmis adopted to perform the Bayesian computation. The method can jointly estimate the parameters of each component and the component number. Simulation results demonstrate that the method has low SNR threshold and better performance.展开更多
文摘The conditional autoregressive model is a routinely used statistical model for areal data thatarise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have also been extensively studied in the literatureand it has been shown that extending from the univariate case to the multivariate case is nottrivial. The difficulties lie in many aspects, including validity, interpretability, flexibility and computational feasibility of the model. In this paper, we approach the multivariate modelling froman element-based perspective instead of the traditional vector-based perspective. We focus onthe joint adjacency structure of elements and discuss graphical structures for both the spatialand non-spatial domains. We assume that the graph for the spatial domain is generally knownand fixed while the graph for the non-spatial domain can be unknown and random. We proposea very general specification for the multivariate conditional modelling and then focus on threespecial cases, which are linked to well-known models in the literature. Bayesian inference forparameter learning and graph learning is provided for the focused cases, and finally, an examplewith public health data is illustrated.
文摘Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.
文摘A Bayesian estimation method to separate multicomponent signals with single channel observation is presented in this paper. By using the basis function projection, the component separation becomes a problem of limited parameter estimation. Then, a Bayesian model for estimating parameters is set up. The reversible jump MCMC （Monte Carlo Markov Chain） algorithmis adopted to perform the Bayesian computation. The method can jointly estimate the parameters of each component and the component number. Simulation results demonstrate that the method has low SNR threshold and better performance.
