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混合图模型的选择与估计AI 解读

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different exponential family form. We identify restrictions on the parameter space required for the existence of a well-defined joint density, and establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our…

连续状态空间中马尔可夫链拟蒙特卡洛的一致性AI 解读

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than…

两阶段标记重捕实验分析的非参数方法AI 解读

We present a new approach to the analysis of two-stage mark-recapture experiments where individual covariates are available which describe the detectability of individuals in the population. Central to the theory is a single quantity α, which we call the heterogeneity index and which measures the variability in the detectability of individuals. This theory also has implications for the analysis of independent observer line transect surveys. An estimator of α is provided by…

非参数密度估计的经验似然置信区间AI 解读

We suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x. This suggestion arises from a simulation study which shows that confidence intervals produced by the kernel-based percentle-t bootstrap do not have the coverage claimed by the theory. This coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by…