增长曲线模型（一般协方差结构）的Bayes影响分析

本文讨论具有一般协方差结构的增长曲线模型中未知参数矩阵的Ｂａｙｅｓ影响分析问题．在无信息先验分布假设下,Ｋ－Ｌ距离被用来评估指定响应阵对参数矩阵的后验分布的影响程度．     

Equity Market Description under High and Low Volatility Regimes Using Maximum Entropy Pairwise Distribution

The financial market is a complex system in which the assets influence each other, causing, among other factors, price interactions and co-movement of returns. Using the Maximum Entropy Principle approach, we analyze the interactions between a selected set of stock assets and equity indices under different high and low return volatility episodes at the 2008 Subprime Crisis and the 2020 COVID-19 outbreak. We carry out an inference process to identify the interactions, in which we implement the a pairwise Ising distribution model describing the first and second moments of the distribution of the discretized returns of each asset. Our results indicate that second-order interactions explain more than 80% of the entropy in the system during the Subprime Crisis and slightly higher than 50% during the COVID-19 outbreak independently of the period of high or low volatility analyzed. The evidence shows that during these periods, slight changes in the second-order interactions are enough to induce large changes in assets correlations but the proportion of positive and negative interactions remains virtually unchanged. Although some interactions change signs, the proportion of these changes are the same period to period, which keeps the system in a ferromagnetic state. These results are similar even when analyzing triadic structures in the signed network of couplings.     

Bayesian Influence Assessment in the Growth Curve Model with Unstructured Covariance

From a Bayesian point of view, in this paper we discuss the influence of a subset of observations on the posterior distributions of parameters in a growth curve model with unstructured covariance. The measure used to assess the influence is based on a Bayesian entropy, namely Kullback-Leibler divergence (KLD). Several new properties of the Bayesian entropy are studied, and analytically closed forms of the KLD measurement both for the matrix-variate normal distribution and the Wishart distribution are established. In the growth curve model, the KLD measurements for all combinations of the parameters are also studied. For illustration, a practical data set is analyzed using the proposed approach, which shows that the diagnostics measurements are useful in practice.     

Centralized versus decentralized control—A solvable stylized model in transportation

Today’s supply networks consist of a certain amount of logistics objects that are enabled to interact with each other and to decide autonomously upon their next steps; in other words, they exhibit a certain degree of autonomous cooperation. Therefore, modern logistics research regards them as complex adaptive logistics systems. In order to analyze evolving dynamics and underlying implications for the respective systems’ behavior as well as the potential outcomes resulting from the interaction between autonomous decision-making “smart parts”, we propose in this contribution a fully solvable stylized model. We consider a population of homogeneous, autonomous interacting agents traveling on R with a given velocity that is itself corrupted by White Gaussian Noise. Based on real time observations of the positions of his neighbors, each agent is allowed to adapt his traveling velocity. These agent interactions are restricted to neighboring entities confined in finite spatial clusters (i.e. we have range-limited interactions). In the limit of a large population of neighboring agents, a mean-field dynamics can be derived and, for small interaction range, the resulting dynamics coincides with the exactly solvable Burgers’ nonlinear field equation. Explicit Burgers’ solution enables to explicitly appreciate the emergent structure due to the local and individual agent interactions. In particular, for strongly interactive regimes in the present model, the resulting spatial distribution of agents converges to a shock wave pattern. To compare performances of centralized versus decentralized organization, we assign cost functions incurred when velocity adaptations are triggered either by multi-agent interactions or by central control. The multi-agent cumulative costs are then compared with the costs that would be incurred by implementing an effective optimal central controller able, for a given time horizon, to reproduce an identical spatial probability distribution of agents. The resulting optimal control problem can be solved exactly and the corresponding costs can be expressed as the Kullback-Leibler relative entropy between the free and the controlled probability measures. This enables one to conclude that for time horizons shorter than a critical value, multi-agent interactions generate smaller cumulative costs than an optimal effective central controller.     

受控AR信号模型下基于Kullback-Leibler信息量HMM参数的估计算法

本是在对现实世界中常见的信号模型一受控AR模型的处理中引进HMM的，并且基于Kullback-Leibler(简记为K-L)信息量在此特定信号模型下蛤出了HMM参数的估计算法。     

两个一元t-分布之间的Kullback-Leibler距离

该文首次求出了两个一元t-分布之间的Ｋｕｌｌｂａｃｋ Ｌｅｉｂｌｅｒ距离的精确表达式．     

Statistical Asymptotic Theory of Active Learning

We study a parametric estimation problem. Our aim is to estimate or to identify the conditional probability which is called the system. We suppose that we can select appropriate inputs to the system when we gather the training data. This kind of estimation is called active learning in the context of the artificial neural networks. In this paper we suggest new active learning algorithms and evaluate the risk of the algorithms by using statistical asymptotic theory. The algorithms are regarded as a version of the experimental design with two-stage sampling. We verify the efficiency of the active learning by simple computer simulations.     

Possible superiority of the conditional MLE over the unconditional MLE

The possibility that the conditional maximum likelihood estimator (CMLE) is superior to the unconditional maximum likelihood estimator (UMLE) is discussed in examples where the residual likelihood is obstructive. We observe relatively smaller risks of the CMLE for a finite sample size. The models in the study include the normal, inverse Gauss, gamma, two-parameter exponential, logit, negative binomial and two-parameter geometric ones.     

Information Measure in Terms of the Hazard Function and Its Estimate

It is well-known that some information measures, including Fisher information and entropy, can be represented in terms of the hazard function. In this paper, we provide the representations of more information measures, including quantal Fisher information and quantal Kullback-leibler information, in terms of the hazard function and reverse hazard function. We provide some estimators of the quantal KL information, which include the Anderson-Darling test statistic, and compare their performances.