A note on model uncertainty in linear regression

We consider model selection uncertainty in linear regression. We study theoretically and by simulation the approach of Buckland and co-workers, who proposed estimating a parameter common to all models under study by taking a weighted average over the models, using weights obtained from information criteria or the bootstrap. This approach is compared with the usual approach in which the 'best' model is used, and with Bayesian model averaging. The weighted predictor behaves similarly to model averaging, with generally more realistic mean-squared errors than the usual model-selection-based estimator.

On the optical flow model selection through metaheuristics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reactive power planning under conditional-value-at-risk assessment using chance-constrained optimisation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Model selection for discriminative restricted boltzmann machines through meta-heuristic techniques

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An animal movement model incorporating home range and habitat selection

Wildlife biologists are often interested in how an animal uses space and the habitat resources within that space. We propose a single model that estimates an animal’s home range and habitat selection parameters within that range while accounting for the inherent autocorrelation in frequently sampled telemetry data. The model is applied to brown bear telemetry data in southeast Alaska.

A general threshold stress hybrid hazard model for lifetime data

In this paper we propose a hybrid hazard regression model with threshold stress which includes the proportional hazards and the accelerated failure time models as particular cases. To express the behavior of lifetimes the generalized-gamma distribution is assumed and an inverse power law model with a threshold stress is considered. For parameter estimation we develop a sampling-based posterior inference procedure based on Markov Chain Monte Carlo techniques. We assume proper but vague priors for the parameters of interest. A simulation study investigates the frequentist properties of the proposed estimators obtained under the assumption of vague priors. Further, some discussions on model selection criteria are given. The methodology is illustrated on simulated and real lifetime data set.

Study of using marker assisted selection on a beef cattle breeding program by model comparison

A data set of a commercial Nellore beef cattle selection program was used to compare breeding models that assumed or not markers effects to estimate the breeding values, when a reduced number of animals have phenotypic, genotypic and pedigree information available. This herd complete data set was composed of 83,404 animals measured for weaning weight (WW), post-weaning gain (PWG), scrotal circumference (SC) and muscle score (MS), corresponding to 116,652 animals in the relationship matrix. Single trait analyses were performed by MTDFREML software to estimate fixed and random effects solutions using this complete data. The additive effects estimated were assumed as the reference breeding values for those animals. The individual observed phenotype of each trait was adjusted for fixed and random effects solutions, except for direct additive effects. The adjusted phenotype composed of the additive and residual parts of observed phenotype was used as dependent variable for models' comparison. Among all measured animals of this herd, only 3160 animals were genotyped for 106 SNP markers. Three models were compared in terms of changes on animals' rank, global fit and predictive ability. Model 1 included only polygenic effects, model 2 included only markers effects and model 3 included both polygenic and markers effects. Bayesian inference via Markov chain Monte Carlo methods performed by TM software was used to analyze the data for model comparison. Two different priors were adopted for markers effects in models 2 and 3, the first prior assumed was a uniform distribution (U) and, as a second prior, was assumed that markers effects were distributed as normal (N). Higher rank correlation coefficients were observed for models 3_U and 3_N, indicating a greater similarity of these models animals' rank and the rank based on the reference breeding values. Model 3_N presented a better global fit, as demonstrated by its low DIC. The best models in terms of predictive ability were models 1 and 3_N. Differences due prior assumed to markers effects in models 2 and 3 could be attributed to the better ability of normal prior in handle with collinear effects. The models 2_U and 2_N presented the worst performance, indicating that this small set of markers should not be used to genetically evaluate animals with no data, since its predictive ability is restricted. In conclusion, model 3_N presented a slight superiority when a reduce number of animals have phenotypic, genotypic and pedigree information. It could be attributed to the variation retained by markers and polygenic effects assumed together and the normal prior assumed to markers effects, that deals better with the collinearity between markers. (C) 2012 Elsevier B.V. All rights reserved.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

Experimental model of tooth movement in mice: A standardized protocol for studying bone remodeling under compression and tensile strains

During orthodontic tooth movement (OTM), alveolar bone is resorbed by osteoclasts in compression sites (CS) and is deposited by osteoblasts in tension sites (TS). The aim of this study was to develop a standardized OTM protocol in mice and to investigate the expression of bone resorption and deposition markers in CS and TS. An orthodontic appliance was placed in C57BL6/J mice. To define the ideal orthodontic force, the molars of the mice were subjected to forces of 0.1 N, 0.25 N, 0.35 N and 0.5 N. The expression of mediators that are involved in bone remodeling at CS and TS was analyzed using a Real-Time PCR. The data revealed that a force of 0.35 N promoted optimal OTM and osteoclast recruitment without root resorption. The levels of TNF-alpha, RANKL, MMP13 and OPG were all altered in CS and TS. Whereas TNF-a and Cathepsin K exhibited elevated levels in CS. RUNX2 and OCN levels were higher in TS. Our results suggest that 0.35 N is the ideal force for OTM in mice and has no side effects. Moreover, the expression of bone remodeling markers differed between the compression and the tension areas, potentially explaining the distinct cellular migration and differentiation patterns in each of these sites. (C) 2012 Elsevier Ltd. All rights reserved.

The importance of plant life form on spatial associations along a subtropical coastal dune gradient

Questions Does the spatial association between isolated adult trees and understorey plants change along a gradient of sand dunes? Does this association depend on the life form of the understorey plant? Location Coastal sand dunes, southeast Brazil. Methods We recorded the occurrence of understorey plant species in 100 paired 0.25 m2 plots under adult trees and in adjacent treeless sites along an environmental gradient from beach to inland. Occurrence probabilities were modelled as a function of the fixed variables of the presence of a neighbour, distance from the seashore and life form, and a random variable, the block (i.e. the pair of plots). Generalized linear mixed models (GLMM) were fitted in a backward step-wise procedure using Akaike's information criterion (AIC) for model selection. Results The occurrence of understorey plants was affected by the presence of an adult tree neighbour, but the effect varied with the life form of the understorey species. Positive spatial association was found between isolated adult neighbour and young trees, whereas a negative association was found for shrubs. Moreover, a neutral association was found for lianas, whereas for herbs the effect of the presence of an adult neighbour ranged from neutral to negative, depended on the subgroup considered. The strength of the negative association with forbs increased with distance from the seashore. However, for the other life forms, the associational pattern with adult trees did not change along the gradient. Conclusions For most of the understorey life forms there is no evidence that the spatial association between isolated adult trees and understorey plants changes with the distance from the seashore, as predicted by the stress gradient hypothesis, a common hypothesis in the literature about facilitation in plant communities. Furthermore, the positive spatial association between isolated adult trees and young trees identified along the entire gradient studied indicates a positive feedback that explains the transition from open vegetation to forest in subtropical coastal dune environments.

The use of parthenotegenetic and IVF bovine blastocysts as a model for the creation of human embryonic stem cells under defined conditions

Clinical application of human embryonic stem cells will be possible, when cell lines are created under xeno-free and defined conditions. We aimed to establish methodologies for parthenogenetic activation, culture to blastocyst and mechanical isolation of the inner cell mass (ICM) using bovine oocytes, as a model for derivation and proliferation of human embryonic stem cells under defined xeno-free culture conditions. Cumulus-oocyte-complexes were in vitro matured and activated using Ca(2+)Ionophore and 6-DMAP or in vitro fertilized (IVF). Parthenotes and biparental embryos were cultured to blastocysts, when their ICM was mechanically isolated and placed onto a substrate of fibronectin in StemProA (R) medium. After attachment, primary colonies were left to proliferate and stained for pluripotency markers, alkaline phosphatase and Oct-4. Parthenogenesis and fertilization presented significantly different success rates (91 and 79 %, respectively) and blastocyst formation (40 and 43 %, respectively). ICMs from parthenogenetic and IVF embryos formed primary and expanded colonies at similar rates (39 % and 33 %, respectively). Six out of eight parthenogenetic colonies tested positive for alkaline phosphatase. Three colonies were analyzed for Oct-4 and they all tested positive for this pluripotency marker. Our data show that Ca2+ Ionophore, and 6-DMAP are efficient in creating large numbers of blastocysts to be employed as a model for human oocyte activation and embryo development. After mechanical isolation, parthenogetic derived ICMs showed a good rate of derivation in fibronectin and Stem-Pro forming primary and expanded colonies of putative embryonic stem cells. This methodology may be a good strategy for parthenogenetic activation of discarded human oocytes and derivation in defined conditions for future therapeutic interventions.

Influence diagnostics for elliptical semiparametric mixed models

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.

A feature selection approach for identification of signature genes from SAGE data

Abstract Background One goal of gene expression profiling is to identify signature genes that robustly distinguish different types or grades of tumors. Several tumor classifiers based on expression profiling have been proposed using microarray technique. Due to important differences in the probabilistic models of microarray and SAGE technologies, it is important to develop suitable techniques to select specific genes from SAGE measurements. Results A new framework to select specific genes that distinguish different biological states based on the analysis of SAGE data is proposed. The new framework applies the bolstered error for the identification of strong genes that separate the biological states in a feature space defined by the gene expression of a training set. Credibility intervals defined from a probabilistic model of SAGE measurements are used to identify the genes that distinguish the different states with more reliability among all gene groups selected by the strong genes method. A score taking into account the credibility and the bolstered error values in order to rank the groups of considered genes is proposed. Results obtained using SAGE data from gliomas are presented, thus corroborating the introduced methodology. Conclusion The model representing counting data, such as SAGE, provides additional statistical information that allows a more robust analysis. The additional statistical information provided by the probabilistic model is incorporated in the methodology described in the paper. The introduced method is suitable to identify signature genes that lead to a good separation of the biological states using SAGE and may be adapted for other counting methods such as Massive Parallel Signature Sequencing (MPSS) or the recent Sequencing-By-Synthesis (SBS) technique. Some of such genes identified by the proposed method may be useful to generate classifiers.

A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma

Abstract Background The criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes. Methods We propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500. Results With 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria. Conclusion We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.

Solvable model for template coexistence in protocells

Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steadystate probability density of protocell compositions.