Clarice Garcia Borges Demétrio.

Brindar elementos teóricos y prácticos relacionados al análisis de bases de datos biotecnológicos, principalmente basadas en datos de marcadores moleculares, secuencias de nucleótidos y proteínas y microarreglos, e ilustrar la diversidad de aplicaciones de métodos bioinformáticas y modelos estadísticos contemporáneos para el análisis de este tipo de datos. Projeto aprovado pelo Centro Argentino Brasileño de Biotecnología (CNPq e Governo Argentino)

Genomic evaluations have revolutionized dairy cattle breeding, and the demand for embryos produced from very young heifers with high genetic merit has increased over time. The combination of low oocyte recovery, young age of donors, and milk production status can make the in vitro embryo production (IVP) of Holstein cattle incredibly challenging. Several factors need to be coordinated to obtain a live calf from an IVP embryo. The quality of the oocyte at the start of the process is one of the key factors. High pregnancy rates can be achieved with good quality embryos selected at optimal time and stage of development, transferred by an experienced embryo transfer technician, to well managed recipients 7 or 8 days after estrus The standard model used to analyze counts over time or space is the Poisson regression model. For this very simple model we assume that events happen independently, singly, and at random at some constant underlying rate. However, in general oocyte and embryo counts are overdispersed, and the variability of the data is larger than the variability specified by the Poisson model (Hinde and Demétrio, 1998). The response variables number of oocytes and number of embryos have two extra-variability sources, one caused by the heterogeneity of the animals and the other by the random effects of donor and sire. A mixed negative binomial model (Molenberghs et al., 2007) can be used to analyze the data taking into consideration both factors. Alternative nested models with different combinations of the covariates in the linear predictor can be compared using likelihood ratio tests. For an individual binary outcome as is the pregnancy variable (with only two possible outcomes: pregnant or not) the basic probability model is the Bernoulli distribution. Alternative nested models, with different combinations of the covariates in the linear predictor of the logistic regression model, are compared using likelihood ratio tests. Several aspects of the models need to be better explored.
References
Hinde, J. and Demétrio, C.G.B. (1998). Overdispersion: models and estimation. Computational Statistics and Data Analysis, 27, 151-170.
Molenberghs, G.; Verbeke, G.; Demétrio, C. (2007). An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Analysis, 13, 513-531.

In the early stages of a plant-breeding program, many crosses are made, and many lines are developed, but usually the genetic material allows only few seeds of each and because of this, the early-generation trials are often laid out in unreplicated designs. The first experiments used a check-plot design, e.g. a known variety, named check variety, was included each five or six plots, besides the test lines; however, they have a lower selection intensity. A commonly used design is the systematic arrangement of check-plots and the unreplicated test lines are added in the blocks, for example, without the use of randomization, this design being the most used in Brazil for several years. Many authors studied how to allocate the test lines to the plots and proposed different designs.
Some authors suggested the augmented designs using known varieties and others suggested do not include them in the trials, but evaluate only the test lines, allowing replication for part of them, characterizing the partially replicated (p-rep) designs, which has been considered an optimal design under some assumptions. In this context, the objective of this project is to investigate optimal designs for plant-breeding experiments, including Brazilian ones, evaluating them under a wide range of models, spatial and genetic, and optimality criteria, like A-optimal, average prediction error variance and realized genetic gain.

Data from insect studies may present different features. Univariate responses may be analyzed using generalized linear models (continuous and discrete data), survival models (time until event data), mixed effects models (longitudinal data), among other methods. These models may be used to analyze experiments which assess complex ecological processes, such as competition. In that sense, computational tools are useful for researchers on several fields, e.g., insect biology and physiology, applied ecology and biological control. This project aims to develop a statistical toolbox to analyze data from insect studies. These methods will be implemented as a package for statistical software R, so that they are available for researchers worldwide for free.

Dados provenientes de experimentos em entomologia podem exibir diferentes caracterí sticas. Respostas univariadas podem ser analisadas por meio de modelos lineares generalizados (dados contí nuos e discretos), modelos de an álise de sobrevivência (dados de tempo at é evento), modelos de efeitos mistos (dados longitudinais), entre outros m étodos. Esses modelos podem ser utilizados para analisar dados provenientes de experimentos que avaliam processos ecol ógicos complexos, como competi ção. Nesse contexto, ferramentas computacionais de f acil utiliza ção para an álise de dados entomol ógicos são uteis para pesquisadores da área de biologia e fi siologia de insetos, ecologia aplicada e controle biól ogico. Este projeto tem como objetivos desenvolver métodos e ferramentas estat sticas para a análise de dados provenientes de experimentos em entomologia no software R, para que estejam disponí veis gratuitamente aos pesquisadores.

Generalized linear models were first introduced by Nelder and Wedderburn (1972) as an extension to the standard normal theory linear model. They have been the main statistical tool for regression modelling of normal and non-normal data over the past four decades. However, in general, the data are overdispersed, (underdispersed) characterised by a larger (smaller) variance than assumed by these simple standard models. It is important to adapt models to take account of overdispersion (underdispersion) in order to avoid incorrect and misleading inferences. Hinde and Demétrio (1998) present some commonly used models for count data and discuss general ideas of estimation. We can broadly categorise the approaches into the following two groups: (i) Assume some more general form for the variance function, possibly including additional parameters. (ii) Assume a two-stage model for the response, that is, assume that the basic response model parameter itself has some distribution. Type (ii) models lead to a compound probability model for the response and, in principle, all of the parameters can be estimated using full maximum likelihood. A standard example is the use of the negative binomial distribution for overdispersed count data. This can be extended using a more general distribution as a mixing distribution, for example, Tweedie. Other extensions for count data models that can explicitly accommodate underdispersion, equidispersion and overdispersion include COM-Poisson models and many other specific and modified Poisson distributions, such as weighted Poisson models. 
There has been a large body of work on the occurrence and modelling of overdispersion in count data, based on some possible generating mechanisms. The topic of underdispersion, where the variability is smaller than the mean, is less widely studied, although of growing interest in recent years. So one aim is to study possible mechanisms than can lead to underdispersed counts. These include specific forms of dependence in the data, such as a count data process with particular types of non-exponential inter-event times, aggregated dependent data, other features of the data collection process such as recording maxima, or minima, of independently observed counts, and situations where competition is present. The most useful families are those that can accommodate both under- and over-dispersion, particularly when used with joint models for the mean and dispersion.
Important questions of model selection and validation in the presence of under/overdispersion still require further work. Moral, Hinde and Demétrio (2014) present one potentially useful diagnostic technique and we plan to extend this to provide a toolbox of methods for checking all aspects of overdispersed models.
Another aspect of this type of data is that it can be measured repeatedly over time, inducing correlation between the repeated observations, bringing together overdispersion and longitudinal and/or multivariate data. Hence, it makes sense to consider longitudinal or multivariate versions of some overdispersion methods. In particular, random effects can account for longitudinal, clustered and/or hierarchical aspects of the design, but they also correct, to some extent, for overdispersion (Molenberghs, Verbeke and Demétrio 2007; Molenberghs et al 2010). 
While we have studied many aspects of the modelling outlined above, there are still a number of strands that we need to continue to work on, while at the same time starting out on new avenues of associated work.
References:
Demétrio, C.G.B.: Hinde, J.; Moral, R.A. Models for overdispersed data in entomology. In: Ferreira, C.P.; Godoy, W.A.(Eds.). Ecological Modeling Applied to Entomology. Springer, 2014, p. 219-259
Hinde, J. and Demétrio, C.G.B. (1998). Overdispersion: models and estimation. Computational Statistics and Data Analysis, 27, 151-170.

Diversos estudos têm sido feitos para verificar quais as relações entre a lagarta do cartucho-do-milho, Spodoptera frugiperda e potenciais agentes de controle biológico, visto que é uma importante praga de diversas culturas. Os parasitóides têm sido muito estudados para esse propósito, assim como predadores de diversas ordens. A tesourinha (Doru luteipes) apresenta grande potencial para controlar S. frugiperda, assim como insetos da família Reduviidae (Hemiptera). O parasitóide Campoletis flavicincta é também considerado um potencial agente controlador de S. frugiperda no campo. Este projeto apresenta como objetivo estudar as relações ecológicas entre as espécies citadas, utilizando a teoria de modelagem estatística e matemática, para tentar ilustrar o que pode, possivelmente, ocorrer em campo em caso de liberação de um ou mais inimigos naturais.

Statistical self-similarity is encountered, when a system has the same statistical properties regardless of scale. Many such systems satisfy Taylor?s power law, which has been observed in a large variety of biological, physical and social systems. But what is the explanation?
Shall we measure in nanometers or light-years? Normally such a questions does not lead into any major considerations, for an astrophysicist would not want to work in atomic units, any more than a nano researcher wants to use light-years. Many physical laws are tied to a certain scale, e.g. atomic, nano or micro scale. But as we know from Mandelbrot?s fractals, there are in nature many so-called self-similar systems, that are characterized by having the same form regardless of the scale in which they are considered. Such fractals exhibit at the same time chaos and regularity. 
Turning now to statistical self-similarity, where a system has the same statistical properties independently of scale, it is harder to combine practical observations with a suitable definition. But a possible explanation may be found in recent statistical convergence results.

Comparative experiments involve the allocation of treatments to units, ideally by randomization. This necessarily results in the confounding of treatment information with unit information, which can be distinguished from the other forms of information blending, in particular aliasing and marginality. One of the aims of this project is to develop a methodology to evaluate the properties of a proposed design by displaying its confounding and to formulate linear mixed models to analyse the data.
The purpose of a breeding program is to select the best test or new lines. To maximize the precision of an experiment, and hence the response to selection, requires the correct identification of the spatial and genetic effects present in the experiment. This, in turn, depends on the design used in the experiment and the models that are fitted in the analysis. Hence, the other aim in this project is to find which was the best model to select the most productive test lines of sugarcane from sugarcane experiments.

2.1 Estender métodos de inferência de segunda-ordem disponíveis para os
MLG para classes mais amplas de modelos com o auxílio da computação
simbólica. As pesquisas conjuntas que os professores do Departamento de
Estatística e Informática da UFRPE e do Departamento de Ciências Exatas da
ESALQ planejam desenvolver dizem respeito às duas linhas de pesquisas:
1. Generalizar métodos estatísticos que foram desenvolvidos para os MLG
para as seguintes classes de modelos citadas anteriormente: MNLFE, MLGD,
MLGSD e MLGH;
2. Utilizar conjuntamente métodos tradicionais de teoria assintótica
acoplados aos software de computação simbólica como Mathematica e Maple
para desenvolver uma inferência mais precisa para os modelos citados em 1.
Acreditamos que no contexto dessas linhas vários trabalhos de pesquisa
poderão ser desenvolvidos.

2.2 Desenvolver modelos bayesianos para interpretação e análise de dados
biológicos, agrários e sociais.
1.Utilizar Inferência Bayesiana para a interpretação de probabilidades que
envolvem fenômenos biológicos, agrários e sociais, explicitando assim,
resoluções de problemas práticos e teóricos.
2.Estudar dados biológicos, agrários e sociais utilizando inferência
Bayesiana, estabelecendo uma comparação entre a probabilidade à ?priori? e
a probabilidade a ?posteriori?.
3.Analisar os resultados obtidos nesta abordagem levando em consideração
as probabilidades à priori e a posteriori, resultantes das aplicações
vivenciadas, fazendo comparações entre estas e as probabilidades baseadas
somente com o conhecimento das leis clássicas de probabilidade.

2.3 Desenvolvimento e aplicação de diversas técnicas, computacionalmente
intensivas, para modelagem, análise e simulação computacional de vários
fenômenos, objeto de Biometria. Mais especificamente, aplicação de
técnicas como Monte Carlo, Autômatas Celulares e Data Envelopment
Analysis.
1. Segmentação de imagens, reconhecimento de padrões, agrupamento e
classificação de dados.

We have already completed a comparison of many of the different approaches to overdispersion modelling (Hinde and Demétrio, 1996, 1998a,b) and considered some extensions of these models. However, work remains to be done on the use of more complex forms of variance function, which are closely related to more general random effect models. Some of this will be developed for inclusion in an extended version of Hinde and Demétrio (1998b) and a proposal of Hinde and Demétrio (2009) has been accepted for publication by Chapman & Hall.
We would also like to investigate further the use of non-parametric maximum likelihood techniques (see Aitkin, 1996) and the possibility of including some form of smoothness constraint. Finally, it would be interesting to make some comparisons with Bayesian approaches and we plan to do this using Markov chain Monte Carlo techniques with the BUGS software of Spiegelhalter et al. (1996).
Important questions of model selection and validation in the presence of overdispersion still require further work. Demétrio and Hinde (1997) presents one potentially useful diagnostic technique and we plan to extend this to provide a toolbox of methods for checking all aspects of overdispersed models. A paper by Fitzmaurice (1997) considers model selection for overdispersed data using Efron's double exponential family model. We will explore these ideas and their relation to the approaches that we have adopted for model selection. Other aspect of this type of data is that it can be measured repeatedly over time, inducing correlation between the observations that bring together overdispersion and longitudinal and/or multivariate data. It might make sense to consider longitudinal or multivariate versions of some overdispersion methods. In particular, random effects account for longitudinal/clustered/hierarchical aspects of the design, but they also correct, to some extent, for overdispersion (Molenberghs, Verbeke and Demétrio 2007).

The proposed work entails the analysis of a specific data set for abundance (counts) of several fish species, such as the yellow perch, Perca flavescens, that are common in lakes across eastern Canada. Fish counts and habitat data were collected along the north and south shorelines of Lake St. Pierre in Quebec, Canada. The data have a hierarchical spatial structure; the basic sampling units are 80 stations that are nested within 20 transects, with 4 adjacent stations to each transect. The 20 transects (10 in each shore) were sampled daily in random order and were distributed approximately equidistanly along the north and south shorelines. The distribution of counts is over-dispersed (Hinde and Demétrio, 1998a, b) and zeros are over-represented in the counts for several species. Additionally, the spatial relationship among sampling units is highly structured because stations are adjacent. As well, intra-group correlations will likely arise at the transect level because all stations within a transect were sampled on the same day. The relationship between fish counts and habitat features will be examined by using the habitat variables as covariates in spatial regression models. Correlations among sampling units will be dealt with by including in the models both spatially-structured and unstructured random effects reflecting the spatial and temporal structures of the sampling scheme.

Estudos em Agricultura e sobre Meio Ambiente dão origem a uma grande variedade de dados, qualitativos e quantitativos, contínuos e discretos. Os modelos clássicos, tais como normal, Poisson e binomial, não permitem o tratamento de todos os tipos de dados. Vários procedimentos têm sido usados para analisar dados de uma forma geral, levando ao uso da família de distribuições tais como os modelos exponenciais de dispersão. Diversos conjuntos de dados resultantes de experimentos serão usados para ilustrar a teoria proposta e para mostrar a melhor análise para cada tipo de observação, além de servirem de motivação para o desenvolvimento de novas teorias.

A superdispersão (variância observada maior do que a esperada) pode ocorrer devido a uma variabilidade da média ou devido a um excesso de zeros. Ela pode ser estudada inicialmente por procedimentos que se enquadram, de uma forma geral, em dois grupos: (i) assumir uma forma mais geral para a função de variância, possivelmente incluindo parâmetros adicionais que podem ser estimados por quase-verossimilhança (modelos de média-variância); (ii) assumir um modelo de dois estágios para a resposta, isto é, assumir que o parâmetro do modelo para a resposta tem alguma distribuição, levando a modelos de probabilidade compostos, como o binomial negativo, o beta-binomial, Poisson-normal, logístico-normal e Probit-normal, utilizando-se para estimação dos parâmetros os métodos dos momentos, de máxima verossimilhança, quase-verossimilhança e pseudo-verossimilhança. Esse tipo de problema pode ocorrer nas mais diversas áreas e soluções específicas têm sido procuradas.

We have already completed a comparison of many of the different approaches to overdispersion modelling (Hinde and Demétrio, 1996, 1998a,b) and considered some extensions of these models. However, work remains to be done on the use of more complex forms of variance function, which are closely related to more general random effect models. Some of this will be developed for inclusion in an extended version of Hinde and Demétrio (1998b) and a proposal of Hinde and Demétrio (2009) has been accepted for publication by Chapman & Hall.
We would also like to investigate further the use of non-parametric maximum likelihood techniques (see Aitkin, 1996) and the possibility of including some form of smoothness constraint. Finally, it would be interesting to make some comparisons with Bayesian approaches and we plan to do this using Markov chain Monte Carlo techniques with the BUGS software of Spiegelhalter et al. (1996).
Important questions of model selection and validation in the presence of overdispersion still require further work. Demétrio and Hinde (1997) presents one potentially useful diagnostic technique and we plan to extend this to provide a toolbox of methods for checking all aspects of overdispersed models. A paper by Fitzmaurice (1997) considers model selection for overdispersed data using Efron's double exponential family model. We will explore these ideas and their relation to the approaches that we have adopted for model selection. Other aspect of this type of data is that it can be measured repeatedly over time, inducing correlation between the observations that bring together overdispersion and longitudinal and/or multivariate data. It might make sense to consider longitudinal or multivariate versions of some overdispersion methods. In particular, random effects account for longitudinal/clustered/hierarchical aspects of the design, but they also correct, to some extent, for overdispersion (Molenberghs, Verbeke and Demétrio 2007).