Tuning parameter selection for a penalized estimator of species richness

Our goal is to estimate the true number of classes in a population, called the species richness. We consider the case where multiple frequency count tables have been collected from a homogeneous population and investigate a penalized maximum likelihood estimator under a negative binomial model. Because high probabilities of unobserved classes increase the variance of species richness estimates, our method penalizes the probability of a class being unobserved. Tuning the penalization parameter is challenging because the true species richness is never known, and so we propose and validate four novel methods for tuning the penalization parameter. We illustrate and contrast the performance of the proposed methods by estimating the strain-level microbial diversity of Lake Champlain over three consecutive years, and global human host-associated species-level microbial richness.     

基于主成分分析和贝叶斯正则化BP神经网络的GDP预测

选用财政收入、财政支出、消费品零售总额、实际利用外资、进出口总额以及全社会固定资产投资等对GDP有显著影响的6个因子,用1985～2008年中国的宏观经济数据建立了一个基于主成分分析和贝叶斯正则化BP神经网络的预测模型,并把它应用于我国GDP的预测。实证结果表明:通过主成分分析法和贝叶斯正则化方法对BP神经网络进行改进,可简化网络结构,增强泛化能力。与其它常用的预测方法相比,该方法数据输入简便,收敛速度快,拟合曲线光滑,且在预测精度上有明显的优势。     

耗损体系运动方程的正则形式及可积情况

给出了耗损系的运动方程以及运动方程的正则形式,讨论了由哈密顿函数的类型决定的可化为正则型运动方程的可积情况.     

由桥梁动力响应识别过桥汽车参数的灵敏度方法

为了识别通过桥梁汽车的参数，提出了在灵敏度分析的基础上由简支梁桥动力响应识别过桥汽车参数的方法。将汽车抽象为两自由度五参数模型，用有限元方法计算桥梁的动力响应。从对未知参数的猜测值开始，由测试或模拟计算的动力响应用最小二乘法和规则化技巧识别过桥汽车参数，用邻近两次识别参数的百分相对误差（RPE）控制迭代过程的终止。由数值模拟结果可知，识别得到的汽车参数是令人满意的，其中质量的识别精度最高，表明该方法识别过桥汽车参数可行。     

一维非标准热传导方程热源识别的Fourier正则化方法

探讨了热源项形式为的热传导方程的反问题。根据热传导方程的正问题理论,建立了一个联系测量数据和未知源项的积分恒等式。利用Fourier正则化方法,给出了误差估计。     

The Adaptive Gril Estimator with a Diverging Number of Parameters

We consider the problem of variables selection and estimation in linear regression model in situations where the number of parameters diverges with the sample size. We propose the adaptive Generalized Ridge-Lasso (\mboxAdaGril) which is an extension of the the adaptive Elastic Net. AdaGril incorporates information redundancy among correlated variables for model selection and estimation. It combines the strengths of the quadratic regularization and the adaptively weighted Lasso shrinkage. In this article, we highlight the grouped selection property for AdaCnet method (one type of AdaGril) in the equal correlation case. Under weak conditions, we establish the oracle property of AdaGril which ensures the optimal large performance when the dimension is high. Consequently, it achieves both goals of handling the problem of collinearity in high dimension and enjoys the oracle property. Moreover, we show that AdaGril estimator achieves a Sparsity Inequality, i.e., a bound in terms of the number of non-zero components of the “true” regression coefficient. This bound is obtained under a similar weak Restricted Eigenvalue (RE) condition used for Lasso. Simulations studies show that some particular cases of AdaGril outperform its competitors.     

A Method for Estimating Time Dependent Intervention Benefits under Arbitrarily Varying Age and Exogenous Components of Hazard

A method for estimating the dependence of intrinsic intervention benefits on time elapsed since the intervention took place is proposed. The method is aimed at intervention programs against diseases where one or all of the following components of hazard intensity may undergo important and unknown variations: 1) the intervention benefits to a subject are a function of the time elapsed since the intervention took place, or since inception for a continuing treatment, 2) the subjects vulnerability is an unknown function of their age, 3) the exogenous or environmental baseline intensity, to which all are assumed subjected, fluctuates arbitrarily with calendar time. During the time span of a study, these variables interact in a complex way, possibly masking the real contribution of the intervention. However, with very general assumptions about how hazard components interact, the cumulative hazards of subpopulations treated at different times in the past are shown to be described mathematically by a convolution of the time elapsed dependent intervention benefit function with the age and calendar time dependent baseline intensity. Starting from the cumulative hazards of untreated and treated subpopulations that had the intervention at different times in the past, a method of deconvolution through regularization is proposed to reconstruct the time elapsed dependence of the intervention benefit function. The regularization technique used is of the penalized least square smoothing type, it is applied to the solution of Volterra integral equations of the first kind under noisy inputs. Simulations, to test for the reconstruction of different modes of time elapsed variation of the intervention benefits, are carried out on realistically noisy data sets taken to be available at a limited number of time points. The stability of the estimated reconstructions, to measurement errors, is examined through repeated simulations with random noise added to inputs. The method is applied to a Brazilian data set where BCG vaccination resulted in a small reduction in the cumulated risk of leprosy infection.     

Hybrid Samplers for Ill-Posed Inverse Problems

Abstract.  In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distributions in ill-posed inverse problems. We provide an accessible set of sufficient conditions, in terms of the observational model and the prior, to ensure geometric ergodicity of RSM samplers of the posterior distribution. We illustrate how these conditions can be checked in an application to the inversion of oceanographic tracer data.