Penalized Pseudolikelihood Inference in Spatial Interaction Models with Covariates

Given spatially located observed random variables ( x , z = {( x _i , z _i )} _i , we propose a new method for non-parametric estimation of the potential functions of a Markov random field p ( x | z ), based on a roughness penalty approach. The new estimator maximizes the penalized log-pseudolikelihood function and is a natural cubic spline. The calculations involved do not rely on Monte Carlo simulation. We suggest the use of B-splines to stabilize the numerical procedure. An application in Bayesian image reconstruction is described.     

Machine learning and design of experiments with an application to product innovation in the chemical industry

Industrial statistics plays a major role in the areas of both quality management and innovation. However, existing methodologies must be integrated with the latest tools from the field of Artificial Intelligence. To this end, a background on the joint application of Design of Experiments (DOE) and Machine Learning (ML) methodologies in industrial settings is presented here, along with a case study from the chemical industry. A DOE study is used to collect data, and two ML models are applied to predict responses which performance show an advantage over the traditional modeling approach. Emphasis is placed on causal investigation and quantification of prediction uncertainty, as these are crucial for an assessment of the goodness and robustness of the models developed. Within the scope of the case study, the models learned can be implemented in a semi-automatic system that can assist practitioners who are inexperienced in data analysis in the process of new product development.     

A strong law of large numbers for independent random variables under non-additive probabilities

Abstract

Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.     

年轻夫妇“两头走”——乡村家庭权力结构变迁的新现象

近年来,年轻夫妇“两头走”这一新型家庭居住模式逐渐在鄂西农村变得普遍起来。通过实地调查着重分析了这种物理空间意义上的居住模式重塑的微观家庭权力结构,进而探讨家庭成员间的权利义务关系的变迁。不同于传统从父居模式下的以男方父代家庭与年轻夫妇为主、女方父代家庭较为次要的主次型家庭权力结构,两头走的婚居模式形塑的家庭权力结构为男女双方父代家庭与年轻夫妇的三角平等结构。这对我们认识当下的代际关系与养老、年轻人的独立等问题有着现实意义。     

Throughput and delay analysis of an opportunistic tree algorithm

Tree algorithms are a well-known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this article, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are allowed to use the channel only if there is no primary user activity. The tree algorithm designed in this article can be used by the secondary users to share the channel capacity left by the primary users.

We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.

Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.     

A combinatorial study of two-periodic random walks

Two-periodic random walks have up-steps and down-steps of one unit as usual, but the probability of an up-step is α after an even number of steps and β = 1 ? α after an odd number of steps, and reversed for down-steps. This concept was studied by Böhm and Hornik^{[2 Böhm, W.; Hornik, K. On two-periodic random walks with boundaries. Stoch. Models 2010, 26, 165–194.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]}. We complement this analysis by using methods from (analytic) combinatorics. By using two steps at once, we can reduce the analysis to the study of Motzkin paths, with up-steps, down-steps, and level-steps. Using a proper substitution, we get the generating functions of interest in an explicit and neat form. The parameters that are discussed here are the (one-sided) maximum (already studied by Böhm and Hornik^{[2 Böhm, W.; Hornik, K. On two-periodic random walks with boundaries. Stoch. Models 2010, 26, 165–194.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]}) and the two-sided maximum. For the asymptotic evaluation of the average value of the two-sided maximum after n random steps, more sophisticated methods from complex analysis (Mellin transform, singularity analysis) are required. The approach to transfer the analysis to Motzkin paths is, of course, not restricted to the two parameters under consideration.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

Linear Increments with Non‐monotone Missing Data and Measurement Error

Linear increments (LI) are used to analyse repeated outcome data with missing values. Previously, two LI methods have been proposed, one allowing non‐monotone missingness but not independent measurement error and one allowing independent measurement error but only monotone missingness. In both, it was suggested that the expected increment could depend on current outcome. We show that LI can allow non‐monotone missingness and either independent measurement error of unknown variance or dependence of expected increment on current outcome but not both. A popular alternative to LI is a multivariate normal model ignoring the missingness pattern. This gives consistent estimation when data are normally distributed and missing at random (MAR). We clarify the relation between MAR and the assumptions of LI and show that for continuous outcomes multivariate normal estimators are also consistent under (non‐MAR and non‐normal) assumptions not much stronger than those of LI. Moreover, when missingness is non‐monotone, they are typically more efficient.