A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.

Estimation in a multiplicative mixed model involving a genetic relationship matrix.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

Prediction of breeding values for average fruit weight in mango using a multivariate individual mixed model

Mango is an important horticultural fruit crop and breeding is a key strategy to improve ongoing sustainability. Knowledge of breeding values of potential parents is important for maximising progress from breeding. This study successfully employed a mixed linear model methods incorporating a pedigree to predict breeding values for average fruit weight from highly unbalanced data for genotypes planted over three field trials and assessed over several harvest seasons. Average fruit weight was found to be under strong additive genetic control. There was high correlation between hybrids propagated as seedlings and hybrids propagated as scions grafted onto rootstocks. Estimates of additive genetic correlation among trials ranged from 0.69 to 0.88 with correlations among harvest seasons within trials greater than 0.96. These results suggest that progress from selection for broad adaptation can be achieved, particularly as no repeatable environmental factor that could be used to predict G x E could be identified. Predicted breeding values for 35 known cultivars are presented for use in ongoing breeding programs.

A Markov modulated Poisson process model for rainfall increments

The problems encountered when using traditional rectangular pulse hierarchical point processmodels for fine temporal resolution and the growing number of available tip-time records suggest that rainfall increments from tipping-bucket gauges be modelled directly. Poisson processes are used with an arrival rate modulated by a Markov chain in Continuous time. The paper shows how, by using two or three states for this chain, much of the structure of the rainfall intensity distribution and the wet/dry sequences can be represented for time-scales as small as 5 minutes.

MIXED-MODEL PRODUCTION SYSTEM DESIGN FOR AIRCRAFT ASSEMBLY

With the advancement of flexible fixture and flexible tooling, mixed production has become possible for aircraft assembly as the manufacturing processes of different aircraft/sub-assembly models are similar. However, it is a great challenge to model the problem and provide a practical solution due to the low volume and complex constraints of aircraft assemblies. To tackle this problem, this work proposes a methodology for designing the mixed production system, and a new scheduling approach is proposed by combined backward and forward scheduling methods. These methods are validated through a real-life industrial case study. Simulation results show that the number of workstations and the cycle time for making a fuselage can be reduced by 50% and 39% respectively with the newly designed mixed-model system.

Balancing and lot-sizing mixed-model lines in the footwear industry

This report describes the full research proposal for the project \Balancing and lot-sizing mixed-model lines in the footwear industry", to be developed as part of the master program in Engenharia Electrotécnica e de Computadores - Sistemas de Planeamento Industrial of the Instituto Superior de Engenharia do Porto. The Portuguese footwear industry is undergoing a period of great development and innovation. The numbers speak for themselves, Portugal footwear exported 71 million pairs of shoes to over 130 countries in 2012. It is a diverse sector, which covers different categories of women, men and children shoes, each of them with various models. New and technologically advanced mixed-model assembly lines are being projected and installed to replace traditional mass assembly lines. Obviously there is a need to manage them conveniently and to improve their operations. This work focuses on balancing and lot-sizing stitching mixed-model lines in a real world environment. For that purpose it will be fundamental to develop and evaluate adequate effective solution methods. Different objectives may be considered, which are relevant for the companies, such as minimizing the number of workstations, and minimizing the makespan, while taking into account a lot of practical restrictions. The solution approaches will be based on approximate methods, namely by resorting to metaheuristics. To show the impact of having different lots in production the initial maximum amount for each lot is changed and a Tabu Search based procedure is used to improve the solutions. The developed approaches will be evaluated and tested. A special attention will be given to the solution of real applied problems. Future work may include the study of other neighbourhood structures related to Tabu Search and the development of ways to speed up the evaluation of neighbours, as well as improving the balancing solution method.

Randomized observation periods for the compound Poisson risk model: Dividends

In the framework of the classical compound Poisson process in collective risk theory, we study a modification of the horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin can be observed. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. Numerical illustrations for several sets of parameters are given and the effect of random observation times on the performance of the dividend strategy is studied.

The two-way mixed model : A long and winding controversy

Resumen tomado de la publicación

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

Benchmark generation algorithm for stochastic mixed model assembly shop simulation and optimization

The Operations Research (OR) community have defined many deterministic manufacturing control problems mainly focused on scheduling. Well-defined benchmark problems provide a mechanism for communication of the effectiveness of different optimization algorithms. Manufacturing problems within industry are stochastic and complex. Common features of these problems include: variable demand, machine part specific breakdown patterns, part machine specific process durations, continuous production, Finished Goods Inventory (FGI) buffers, bottleneck machines and limited production capacity. Discrete Event Simulation (DES) is a commonly used tool for studying manufacturing systems of realistic complexity. There are few reports of detail-rich benchmark problems for use within the simulation optimization community that are as complex as those faced by production managers. This work details an algorithm that can be used to create single and multistage production control problems. The reported software implementation of the algorithm generates text files in eXtensible Markup Language (XML) format that are easily edited and understood as well as being cross-platform compatible. The distribution and acceptance of benchmark problems generated with the algorithm would enable researchers working on simulation and optimization of manufacturing problems to effectively communicate results to benefit the field in general.

A nonparametric Bayesian Poisson Gamma model for count data

We propose a nonparametric Bayesian, linear Poisson gamma model for count data and use it for dictionary learning. A key property of this model is that it captures the parts-based representation similar to nonnegative matrix factorization. We present an auxiliary variable Gibbs sampler, which turns the intractable inference into a tractable one. Combining this inference procedure with the slice sampler of Indian buffet process, we show that our model can learn the number of factors automatically. Using synthetic and real-world datasets, we show that the proposed model outperforms other state-of-the-art nonparametric factor models.

A mixed model QTL analysis for sugarcane multiple-harvest-location trial data

Sugarcane-breeding programs take at least 12 years to develop new commercial cultivars. Molecular markers offer a possibility to study the genetic architecture of quantitative traits in sugarcane, and they may be used in marker-assisted selection to speed up artificial selection. Although the performance of sugarcane progenies in breeding programs are commonly evaluated across a range of locations and harvest years, many of the QTL detection methods ignore two- and three-way interactions between QTL, harvest, and location. In this work, a strategy for QTL detection in multi-harvest-location trial data, based on interval mapping and mixed models, is proposed and applied to map QTL effects on a segregating progeny from a biparental cross of pre-commercial Brazilian cultivars, evaluated at two locations and three consecutive harvest years for cane yield (tonnes per hectare), sugar yield (tonnes per hectare), fiber percent, and sucrose content. In the mixed model, we have included appropriate (co)variance structures for modeling heterogeneity and correlation of genetic effects and non-genetic residual effects. Forty-six QTLs were found: 13 QTLs for cane yield, 14 for sugar yield, 11 for fiber percent, and 8 for sucrose content. In addition, QTL by harvest, QTL by location, and QTL by harvest by location interaction effects were significant for all evaluated traits (30 QTLs showed some interaction, and 16 none). Our results contribute to a better understanding of the genetic architecture of complex traits related to biomass production and sucrose content in sugarcane.