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201.
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations 总被引:7,自引:0,他引:7
Håvard Rue Sara Martino Nicolas Chopin 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2009,71(2):319-392
Summary. Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. 相似文献
202.
Howard D. Bondell Lexin Li 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2009,71(1):287-299
Summary. The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis. 相似文献
203.
On distribution-weighted partial least squares with diverging number of highly correlated predictors
Li-Ping Zhu Li-Xing Zhu 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2009,71(2):525-548
Summary. Because highly correlated data arise from many scientific fields, we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. For this, we first develop a distribution-weighted least squares estimator that can recover directions in the central subspace, then use the distribution-weighted least squares estimator as a seed vector and project it onto a Krylov space by partial least squares to avoid computing the inverse of the covariance of predictors. Thus, distrbution-weighted partial least squares can handle the cases with high dimensional and highly correlated predictors. Furthermore, we also suggest an iterative algorithm for obtaining a better initial value before implementing partial least squares. For theoretical investigation, we obtain strong consistency and asymptotic normality when the dimension p of predictors is of convergence rate O { n 1/2 / log ( n )} and o ( n 1/3 ) respectively where n is the sample size. When there are no other constraints on the covariance of predictors, the rates n 1/2 and n 1/3 are optimal. We also propose a Bayesian information criterion type of criterion to estimate the dimension of the Krylov space in the partial least squares procedure. Illustrative examples with a real data set and comprehensive simulations demonstrate that the method is robust to non-ellipticity and works well even in 'small n –large p ' problems. 相似文献
204.
Hiep Duc Bin Jalaludin Geoff Morgan 《Australian & New Zealand Journal of Statistics》2009,51(3):289-303
Using generalized linear models (GLMs), Jalaludin et al. (2006; J. Exposure Analysis and Epidemiology 16 , 225–237) studied the association between the daily number of visits to emergency departments for cardiovascular disease by the elderly (65+) and five measures of ambient air pollution. Bayesian methods provide an alternative approach to classical time series modelling and are starting to be more widely used. This paper considers Bayesian methods using the dataset used by Jalaludin et al. (2006) , and compares the results from Bayesian methods with those obtained by Jalaludin et al. (2006) using GLM methods. 相似文献
205.
This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector
is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed
to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally
adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided
that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard
PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates
via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to
the well known primary biliary cirrhosis clinical data. 相似文献
206.
207.
随着中国城镇化进程的推进,越来越多的农村户籍人口实现了身份转换,成为制度认可的新市民。本文利用中国综合社会调查(CGSS)数据发现,即使户口状况相同,"新市民"与"老市民"之间依然存在一定的收入差距。分位数回归及其分解的结果显示,"农转非"人群在劳动力市场上仍受到制度性或非制度性歧视,且歧视程度随着分位数的变化呈现倒U型趋势。同时,"农转非"人群内部也存在较大的差异,歧视降低了自致型"农转非"人群相较于城市原居民的禀赋优势,而外致型"农转非"人群则面临人力资本劣势与就业市场歧视的双重压力。 相似文献
208.
209.
Fabrizio Leisen Luca Rossini Cristiano Villa 《Journal of Statistical Computation and Simulation》2017,87(6):1179-1188
The Yule–Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is illustrated with simulation studies, including count data regression, and a real data application to text analysis. We compare our proposal to the frequentist counterparts showing better performance of our algorithm when a small sample size is considered. 相似文献
210.