Investigating the sensitivity function's monotony of a health-related index

In this work it is investigated theoretically whether the support's length of a continuous variable, which represents a simple health-related index, affects the index's diagnostic ability of a binary health outcome. The aforementioned is attempted by studying the monotony of the index's sensitivity function, which is a measure of its diagnostic ability, in the cases that the index's distribution was either unknown or the uniform. The case of a composite health-related index which is formed by the sum of m component variables is also presented when the distribution of its component variables was either unknown or the uniform. It is proved that a health-related index's sensitivity is a non-decreasing function as to the finite length of its components' support, under certain condition. In addition, similar propositions are presented in the case that a health-related index is distributed normally according to its distribution parameters.     

矩阵方幂之和

At，Bt为m阶矩阵，rt，dt，ft，vt等为正整数（t＝1，2，…，s）．给出下列矩阵方幂和计算公式。     

Effect on probabilities and quantiles of adding a quantity with small variance

This paper gives simple approximations for the distribution function and quantiles of the sum X + Y when X is a continuous variable and Y is an independent variable with variance small compared to that of X . The approximations are based around the distribution function or quantiles of X and require only the first two or three moments of Y to be known. Example evaluations with X having a normal, Student's t or chi-squared distribution suggest that the approximations are good in unbounded tail regions when the ratio of variances is less than 0.2.     

An Efficient Algorithm for the Least-Squares Cross-Validation with Symmetric and Polynomial Kernels

The least-squares cross-validation is a completely automatic method for choosing the smoothing parameter in probability density estimation but this method consume large amounts of computer time. This article concerns an efficient computational algorithm for this method when the kernel is symmetric and polynomial functions.     

Autoregressive moving-average convolution processes on the unit circle

ARMA convolution models for processes in continuous space (in this case the unit circle) and discrete time are derived as a natural extension of the usual Box-Jenkins models. Both weakly time-stationary and nonstationary processes are considered. Sufficient conditions for the existence of weakly time-stationary AR_cMA_c processes are derived, and the covariance functions for some processes are computed. It is demonstrated that the usual scalar and multivariate ARMA processes can be embedded within the larger class of AR_CMA_c models. A possible application of these models to sea-surface temperature prediction is discussed.     

A non-stationary spatial generalized linear mixed model approach for studying plant diversity

We analyze the multivariate spatial distribution of plant species diversity, distributed across three ecologically distinct land uses, the urban residential, urban non-residential, and desert. We model these data using a spatial generalized linear mixed model. Here plant species counts are assumed to be correlated within and among the spatial locations. We implement this model across the Phoenix metropolis and surrounding desert. Using a Bayesian approach, we utilized the Langevin–Hastings hybrid algorithm. Under a generalization of a spatial log-Gaussian Cox model, the log-intensities of the species count processes follow Gaussian distributions. The purely spatial component corresponding to these log-intensities are jointly modeled using a cross-convolution approach, in order to depict a valid cross-correlation structure. We observe that this approach yields non-stationarity of the model ensuing from different land use types. We obtain predictions of various measures of plant diversity including plant richness and the Shannon–Weiner diversity at observed locations. We also obtain a prediction framework for plant preferences in urban and desert plots.     

An optimal age-replacement policy for a simple repairable system with delayed repair

In this article, a simple repairable system (i.e., a repairable system consisting of one component and one repairman) with delayed repair is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, using the geometric process repair model, we consider a replacement policy T based on system age under which the system is replaced when the system age reaches T. Our problem is to determine an optimal replacement policy T*, such that the average cost rate (i.e., the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy T* can be determined by minimizing the average cost rate of the system. Finally, a numerical example is given to illustrate some theoretical results and the model's applicability.     

Convolution of Binomial and Negative Binomial Variables

This paper considers a distribution formed by convolution of binomial and negative binomial variables. The distribution has the flexibility to adapt to the model under, equi, and over dispersion. Some properties of the proposed distribution are discussed, including characterization. Three stochastic processes leading to the distribution are also considered: (1) a three-dimensional random walk; (2) a birth, death, and immigration process; and (3) a thinned stochastic process.     

Computing exact clustering posteriors with subset convolution

ABSTRACT

An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters and pairwise co-occurrence. The method is based on subset convolution and yields the posterior distribution for the number of clusters in O(n3ⁿ) operations or O(n³2ⁿ) using fast subset convolution. Pairwise co-occurrence probabilities are then obtained in O(n³2ⁿ) operations. This is considerably faster than exhaustive enumeration of all partitions.