A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

团簇Aun+1-1、AunCr-1 (n=1-10)吸附CO的密度泛函理论研究

采用密度泛函理论对CO在阴离子团簇Aun+1-1、AunCr-1(n=1-10))表面的吸附做了系统研究.结果表明,团簇Aun+1CO-1、AunCrCO-1的基态结构是在团簇Aun+1-1、AunCr-1最低能量结构的基础上吸附CO形成; 吸附后的CO键长变长,振动频率减小,表明CO分子被活化;取值相同时,AunCrCO-1的平均结合能高,表明团簇Aun+1CO-1掺杂Cr后稳定性升高.HOMO-LOMO能隙结果表明Aun+1CO-1替代掺杂Cr原子后团簇的化学活性得到了提升,AunCrCO-1、Aun+1CO-1团簇能隙具有奇偶振荡的现象;轨道电荷分析表明CO与团簇相互作用实质是C原子与成键Au原子或Cr原子间转移电荷,CO在与团簇相互作用过程中O原子轨道电荷分布几乎没有发生变化.     

A queueing system with linear repeated attempts,bernoulli schedule and feedback

We analyse a single-server retrial queueing system with infinite buffer, Poisson arrivals, general distribution of service time and linear retrial policy. If an arriving customer finds the server occupied, he joins with probabilityp a retrial group (called orbit) and with complementary probabilityq a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority queue for another service with probability ϑ or to leave the system forever with probability =1−ϑ, where 0≤ϑ<1. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating function of system size distribution, which generalizes the well-knownPollaczek-Khinchin formula. Also we obtain a stochastic decomposition law for our queueing system and as an application we study the asymptotic behaviour under high rate of retrials. The results agree with known special cases. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.     

Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.     

Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Making Use of Incomplete Observations for Regression in Bivariate Normal Model

Two estimates of the regression coefficient in bivariate normal distribution are considered: the usual one based on a sample and a new one making use of additional observations of one of the variables. They are compared with respect to variance. The same is done for two regression lines. The conclusion is that the additional observations are worth using only when the sample is very small.     

Theorems of Large Deviations in the Approximation by the Compound Poisson Distribution

The paper is devoted to the research of large deviation probabilities in the approximation by compound Poisson law.     

Stationary Distributions of GI/M/c Queue with PH Type Vacations

We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies.     

The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.