In classical manpower systems analysis, control of the system usually results in a set of admissible controls. This forms the basis for the use of the concepts of optimal control to distinguish this set of admissible controls for optimality. In this paper, the concepts of classical deterministic optimal control are extended to examine the optimal controllability of manpower system modeled by stochastic differential equations in terms of the differential flow matrices for both time varying and time invariant manpower systems. Necessary and sufficient conditions for controllability are given. The Hamilton–Jacobi–Bellman (HJB) equation is used to obtain an algebraic Riccati equation for an optimal tracking linear quadratic problem in a finite time horizon. A 2-norm optimality criterion which is equivalent to a minimum effort criterion is used to obtain a 2-norm optimal control for the system. An optimal time control is also obtained.

Identifying genes differentially expressed between a treatment and a control experimental condition is a common task for gene expression data analysts. Standard existing methods are the two-sample t-test, the regularized t-test (Cyber-T) and the Bayesian t-test. In this paper, we propose a Bayesian approach to identify genes differentially expressed based on the posterior probability of the difference calculated via the Bayes factor. In order to calculate the Bayes factor, we use the predictive density that is constructed by using the previously observed gene expression levels. We perform a simulation study with small sample sizes, which is usual in gene expression data analysis, to verify the performance of the proposed method and compare it with the standard ones. The results revel a better performance of the proposed methodology in identification of difference of means and/or variance. The methodology is also illustrated on the Escherichia coli bacterium dataset.

We propose a dynamic model to analyze polychotomous data subject to temporal variation. In particular, we propose to model categorized levels of rainfall across time. Our model assumes that the observed category is related to an underlying latent continuous variable, which is modelled according to a power transformation of a Gaussian latent process, centered on a predictor that assigns dynamic effects to observable covariates. The inference procedure is based on the Bayesian paradigm and makes use of Markov chain Monte Carlo methods. We analyze artificial sets of data and daily measurements of rainfall in Rio de Janeiro, Brazil. When compared to the fitting of the actual observed volume of rainfall, our categorized model seems to recover well the structure of the data.

The Weibull distribution is characterized via the ratio of two upper record statistics. Also the uniform distribution is characterized via the ratio of two lower record statistics. As an application, an improved confidence interval for the Weibull shape parameter is presented.

This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to buy and selling the next period, with no shorting, and furthermore for weak convergence of the random walk to a Gaussian continuous-time stochastic process. The conditions are given in terms of the kernel representation with respect to ordinary Brownian motion and the discretisation chosen. Arbitrage and free lunch with vanishing risk examples are established where the continuous-time analogue is arbitrage-free under small transaction costs—including for the semimartingale modifications of fractional Brownian motion suggested in the seminal Rogers [Math. Finance 7 (1997) 95–105] article proving arbitrage in fBm models.

In a panel count data setup, repeated counts of an individual are assumed to be influenced by the individual’s random effect. Consequently, conditional on the random effect, the repeated responses of the individual are assumed to be serially correlated. Under the assumption that the random effects of the individuals follow a normal distribution, Jowaheer and Sutradhar (Statist. Probab. Letters 79 (2009) 1928–1934) have demonstrated that the generalized quasi-likelihood (GQL) estimation approach produces more efficient estimates than the so-called generalized method of moments (GMM) approach for both regression effects and the variance component of the normal random effects. For the cases where the distribution of the random effects is unknown, there exist two estimation approaches, namely the conditional maximum likelihood (CML) and instrumental variables based GMM (IVGMM) approaches, for the estimation of the regression effects. The purpose of this paper is to examine the asymptotic efficiency performances of the CML and IVGMM approaches as compared to the GQL approach for the regression estimation. When the covariates are stationary, that is, time independent, it is, however, known that the CML and IVGMM approaches are useless for the regression estimation, whereas the GQL approach does not encounter any such limitations. For the general case, that is, when the covariates are time dependent, the IVGMM approach appears to be computationally expensive and hence it is not included in efficiency comparison. Between the CML and GQL approaches, it is found through exact asymptotic variance calculations that the GQL approach is asymptotically more efficient than the CML approach in estimating the regression effects. This makes the GQL as a unified efficient approach irrespective of the cases whether the panel count data are stationary or nonstationary.

In this paper, we work under the setting of data with high dimension $d$ greater than the sample size $n$ (HDLSS). We study asymptotics of the first $p\geq2$ sample eigenvalues and their corresponding eigenvectors under a spiked covariance model for which its first $p$ largest population eigenvalues have the same asymptotic order of magnitude as $d$ tends to infinity and the rest are constant. We get the asymptotic joint distribution of the nonzero sample eigenvalues when $d\rightarrow\infty$ and the sample size $n$ is fixed. We then prove that the $p$ largest sample eigenvalues increase jointly at the same speed as their population counterpart, in the sense that the vector of ratios of the sample and population eigenvalues converges to a multivariate distribution when $d\rightarrow\infty$ and $n$ is fixed, and to the vector of ones when both $d,n\rightarrow\infty$ and $d\gg n$. We also show the subspace consistency of the corresponding sample eigenvectors when $d$ goes to infinity and $n$ is fixed. Furthermore, using the asymptotic joint distribution of the sample eigenvalues we study some inference problems for the spiked covariance model and propose hypothesis tests for a particular case of this model and confidence intervals for the $p$ largest eigenvalues. A simulation is performed to assess the behavior of the proposed statistical methodologies.

We consider parametric accelerated failure time models with random effects to predict the probability of possibly correlated failures occurring in oil wells. In this context, we first consider empirical Bayes predictors (EBP) based on a Weibull distribution for the failure times and on a Gaussian distribution for the random effects. We also obtain empirical best linear unbiased predictors (EBLUP) using a linear mixed model for which the form of the distribution of the random effects is not specified. We compare both approaches using data obtained from an oil-drilling company and suggest how the results may be employed in designing a preventive maintenance program.

In this paper, we propose a new wide class of hypergeometric heavy tailed priors that is given as the convolution of a Student-t density for the location parameter and a Scaled Beta 2 prior for the squared scale parameter. These priors may have heavier tails than Student-t priors, and the variances have a sensible behaviour both at the origin and at the tail, making it suitable for objective analysis. Since the representation of our proposal is a scale mixture, it is suitable to detect sudden changes in the model. Finally, we propose a Gibbs sampler using this new family of priors for modelling outliers and structural breaks in Bayesian dynamic linear models. We demonstrate in a published example, that our proposal is more suitable than the Inverted Gamma’s assumption for the variances, which makes very hard to detect structural changes.