Large sample prediction intervals for future geometric mean a comparative study

This paper provides simulation comparisons among the performance of 11 possible prediction intervals for the geometric.mean of a Pareto distribution with parameters (αB, ). Six different procedures were used to obtain these intervals , namely; true inter -val , pivotal interval , maximum likelihood estimation interval, centrallimit teorem interval, variance stabilizing interval and a mixture of the above intervals . Some of these intervals are valid if the observed sample size m,are large , others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of α or B, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLE's are the best. The second best intervalsare those obtained through pivotal methods or variance stabilization transformation. The third group of intervals is that which depends on the central limit theorem when λ is known. There are two intervals which proved to be unacceptable under any criterion.     

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.     

Implicitly-weighted total least squares

In a total least squares (TLS) problem, we estimate an optimal set of model parameters X, so that (A-ΔA)X=B-ΔB, where A is the model matrix, B is the observed data, and ΔA and ΔB are corresponding corrections. When B is a single vector, Rao (1997) and Paige and Strakoš (2002) suggested formulating standard least squares problems, for which ΔA=0, and data least squares problems, for which ΔB=0, as weighted and scaled TLS problems. In this work we define an implicitly-weighted TLS formulation (ITLS) that reparameterizes these formulations to make computation easier. We derive asymptotic properties of the estimates as the number of rows in the problem approaches infinity, handling the rank-deficient case as well. We discuss the role of the ratio between the variances of errors in A and B in choosing an appropriate parameter in ITLS. We also propose methods for computing the family of solutions efficiently and for choosing the appropriate solution if the ratio of variances is unknown. We provide experimental results on the usefulness of the ITLS family of solutions.     

Jackknife evaluation of uncertainty judgments aggregated by the Kullback-Leibler distance

One feasible approach to aggregating uncertainty judgments in risk assessments is to use calibration variables (or seed questions) and the Kullback-Leibler (K-L) distance to evaluate experts’ substantive or normative expertise and assign weights based on the corresponding scores. However, the reliability of this aggregation model and the effects of the number of seed questions or experts on the stability of the aggregated results are still at issue. To assess the stability of the aggregation model, this study applies the jackknife re-sampling technique to a large data set of real-world expert opinions. We also use a nonlinear regression model to analyze and interpret the resulting jackknife estimates. Our statistical model indicates that the stability of Cooke’s classical model, in which the components of the scoring rule are determined by the K-L distance, increases exponentially as the number of seed questions increases. Considering the difficulty and importance of creating and choosing appropriate seed variables, the results of this study justify the use of the K-L distance to determine and aggregate better probability interval or distribution estimates.     

Heteroscedastic normal-exponential mixture models: Bayesian and classical approaches

In this paper, we introduce a Bayesian analysis for mixture of distributions belonging to the exponential family. As a special case we consider a mixture of normal exponential distributions including joint modeling of the mean and variance. We also consider joint modeling of the mean and variance heterogeneity. Markov Chain Monte Carlo (MCMC) methods are used to obtain the posterior summaries of interest. We also introduce and apply an EM algorithm, where the maximization is obtained applying the Fisher scoring algorithm. Finally, we also include analysis of real data sets to illustrate the proposed methodology.     

Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres - except for two methods limited to narrow angle lidars - the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.     

基于BPLT模型的小麦叶片背景扣除方法的研究

为准确且无损测定小麦叶片的反射光谱,研究了不同背景对叶片表面反射光谱的影响,在400～1 000 nm波段范围测定了小麦叶片8种背景下的反射光谱以及叶绿素含量。以PLATE模型为基础,首次提出了BPLT(background plate)模型,扣除由不同背景导致的叶片反射光谱的变化。模型以背景下叶片的反射率R₀,不同背景反射率σ为输入,空气和致密叶片的界面反射比R₁₂,致密叶片和空气的界面反射比R₂₁,致密叶片的透射系数τ三参数中间变量,得到最终无背景时叶片反射率R值的2-3-1模型。采用方差分析法(analysis of variance, ANOVA)进行了BPLT模型验证,对比分析了背景扣除前后10种叶绿素指数值的变化。结果表明,当反演的确定系数DC(determination coefficients)>0.90且残差平方和SSE<1时,反演的灵敏度较高,对小麦叶片不同叶绿素浓度的背景扣除有着较好的效果;采用BPLT模型背景扣除后,背景因素所占的百分比低于5%;优选了NDI&MCARI的函数关系,NDI&MCARI的斜率和叶绿素浓度的R2由背景扣除前的0.847 4提高到背景扣除后的0.977 8。为真实测定不同背景下小麦叶片的反射光谱提供了依据。     

Estimating the intensity of a cyclic Poisson process in the presence of linear trend

We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance, and the mean-squared error of the proposed estimator are also computed. A simulation study shows that the first order asymptotic approximations to the bias and variance of the estimator are not accurate enough. Second order terms for bias and variance were derived in order to be able to predict the numerical results in the simulation. Bias reduction of our estimator is also proposed.