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稳健性、模型检验与层级模型AI 解读

Abstract Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to check assumptions on the latent parameters. Diagnostic statistics are often used to quantify the degree to which a model fit deviates from the observed data. We construct diagnostic statistics by (a) defining an alternative model…

利用变分贝叶斯与拉普拉斯近似拟合潜在非高斯模型AI 解读

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that contain inherently non-Gaussian features, such as sudden jumps or spikes, that adversely affect the inferences and predictions made using an LGM. These datasets require more general latent non-Gaussian models (LnGMs) that can handle…

惩罚高斯随机场复杂度的先验构造AI 解读

Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under in-fill asymptotics. We extend the recent penalized complexity prior framework and develop a principled joint prior for the range and the marginal variance of one-dimensional, two-dimensional, and three-dimensional Matérn GRFs with fixed…

高斯场与高斯马尔可夫随机场的显式联系：随机偏微分方程方法AI 解读

Summary Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorizing dense matrices is cubic in the dimension. Although computational power today is at an all time high, this fact seems still to be a…

利用积分嵌套拉普拉斯近似进行潜在高斯模型的近似贝叶斯推断AI 解读

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…

隐高斯马尔可夫随机场的近似AI 解读

Summary Gaussian Markov random-field (GMRF) models are frequently used in a wide variety of applications. In most cases parts of the GMRF are observed through mutually independent data; hence the full conditional of the GMRF, a hidden GMRF (HGMRF), is of interest. We are concerned with the case where the likelihood is non-Gaussian, leading to non-Gaussian HGMRF models. Several researchers have constructed block sampling Markov chain Monte Carlo schemes based on…

高斯马尔可夫随机场的快速抽样AI 解读

Summary This paper demonstrates how Gaussian Markov random fields (conditional autoregressions) can be sampled quickly by using numerical techniques for sparse matrices. The algorithm is general and efficient, and expands easily to various forms for conditional simulation and evaluation of normalization constants. We demonstrate its use by constructing efficient block updates in Markov chain Monte Carlo algorithms for disease mapping.

两条 Gibbs 采样链的对偶耦合AI 解读

Two coupled Gibbs sampler chains, both with invariant probability density $p$, are run in parallel so that the chains are negatively correlated.We define an asymptotically unbiased estimator of the $\pi$-expectation $E(f(\mathbf(X))$ which achieves significant variance reduction with respect to the usual Gibbs sampler at comparable computational cost. The variance of the estimator based on the new algorithm is always smaller than the variance of a single Gibbs sampler chain,…