DesG: uma nova metodologia para intervenção e coleta de dados magnetotelúricos

Esta tese apresenta duas contribuições para a interpretação geofísica, voltadas ao Método Magnetotelúrico. A primeira trata de uma nova abordagem para a interpretação MT, denominada MÉTODO DESCRITIVO-GEOLÓGICO (DesG), em alusão à incorporação explícita de informação a priori de correlação fácil com a descrição geológica tradicional. O intérprete define por meio de elementos geométricos (pontos e linhas) o arcabouço de feições geológicas bem como fornece valores de resistividade aos corpos geológicos presumidos. O método estima a distribuição de resistividade subsuperficial em termos de fontes anômalas próximas aos elementos geométricos, ajustando as respostas produzidas por estes corpos às medidas de campo. A solução obtida fornece então informações que podem auxiliar na modificação de algumas informações a priori imprecisas, permitindo que sucessivas inversões sejam realizadas até que a solução ajuste os dados e faça sentido geológico. Entre as características relevantes do método destacam-se: (i) os corpos podem apresentar resistividade maior ou menor do que a resistividade do meio encaixante, (ii) vários meios encaixantes contendo ou não corpos anômalos podem ser cortados pelo perfil e (iii) o contraste de resistividade entre corpo e encaixante pode ser abrupto ou gradativo. A aplicação do método a dados sintéticos evidencia, entre outras vantagens, a sua potencialidade para estimar o mergulho de falhas com inclinação variável, que merece especial interesse em Tectônica, e delinear soleiras de diabásio em bacias sedimentares, um sério problema para a prospecção de petróleo. O método permite ainda a interpretação conjunta das causas do efeito estático e das fontes de interesse. A aplicação a dados reais é ilustrada tomando-se como exemplo dados do COPROD2, cuja inversão produziu soluções compatíveis com o conhecimento geológico sobre a área. A segunda contribuição refere-se a desenho de experimento geofísico. Por meio de indicadores diversos, em especial a matriz densidade de informação, é mostrado que a resolução teórica dos dados pode ser estudada, que guia o planejamento da prospecção. A otimização do levantamento permite determinar os períodos e as posições das estações de medida mais adequados ao delineamento mais preciso de corpos cujas localizações são conhecidas aproximadamente.

Multiple-trait genomic evaluation for milk yield and milk quality traits using genomic and phenotypic data in buffalo in Brazil

The use of markers distributed all long the genome may increase the accuracy of the predicted additive genetic value of young animals that are candidates to be selected as reproducers. In commercial herds, due to the cost of genotyping, only some animals are genotyped and procedures, divided in two or three steps, are done in order to include these genomic data in genetic evaluation. However, genomic evaluation may be calculated using one unified step that combines phenotypic data, pedigree and genomics. The aim of the study was to compare a multiple-trait model using only pedigree information with another using pedigree and genomic data. In this study, 9,318 lactations from 3061 buffaloes were used, 384 buffaloes were genotyped using a Illumina bovine chip (Illumina Infinium (R) bovineHD BeadChip). Seven traits were analyzed milk yield (MY), fat yield (FY), protein yield (PY), lactose yield (LY), fat percentage (F%), protein percentage (P%) and somatic cell score (SCSt). Two analyses were done: one using phenotypic and pedigree information (matrix A) and in the other using a matrix based in pedigree and genomic information (one step, matrix H). The (co) variance components were estimated using multiple-trait analysis by Bayesian inference method, applying an animal model, through Gibbs sampling. The model included the fixed effects of contemporary groups (herd-year-calving season), number of milking (2 levels), and age of buffalo at calving as (co) variable (quadratic and linear effect). The additive genetic, permanent environmental, and residual effects were included as random effects in the model. The heritability estimates using matrix A were 0.25, 0.22, 0.26, 0.17, 0.37, 0.42 and 0.26 and using matrix H were 0.25, 0.24, 0.26, 0.18, 0.38, 0.46 and 0.26 for MY, FY, PY, LY, % F, % P and SCCt, respectively. The estimates of the additive genetic effect for the traits were similar in both analyses, but the accuracy were bigger using matrix H (superior to 15% for traits studied). The heritability estimates were moderated indicating genetic gain under selection. The use of genomic information in the analyses increases the accuracy. It permits a better estimation of the additive genetic value of the animals.

The Kumaraswamy Gumbel distribution

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

The McDonald inverted beta distribution

We introduce a five-parameter continuous model, called the McDonald inverted beta distribution, to extend the two-parameter inverted beta distribution and provide new four- and three-parameter sub-models. We give a mathematical treatment of the new distribution including expansions for the density function, moments, generating and quantile functions, mean deviations, entropy and reliability. The model parameters are estimated by maximum likelihood and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The Truncated Inflated Beta Distribution

The study of proportions is a common topic in many fields of study. The standard beta distribution or the inflated beta distribution may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0, c), 0 < c < 1. For these variables, the authors introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c, 1) and the trinomial distribution. The authors present the moments of the distribution, its scoring vector, and Fisher information matrix, and discuss estimation of its parameters. The properties of the suggested estimators are studied using Monte Carlo simulation. In addition, the authors present an application of the TBEINF distribution for unemployment insurance data.

Prospective evaluation of a D-optimal designed population pharmacokinetic study

Recently, methods for computing D-optimal designs for population pharmacokinetic studies have become available. However there are few publications that have prospectively evaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design with three sampling windows (0-30 min, 1.5-5 hr and 11 - 12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectively represented the entire dose interval. Each patient was assigned to have one blood sample taken from three different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, while the optimal design supported a two compartment linear model with additive residual error as did the model derived from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the optimal'' design derived model was superior to the empirical design model in terms of precision and was similar to the model developed from the full dataset. This study suggests optimal design techniques may be useful, even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deviated from the nominal design.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.

Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

Sublimation of new matrix candidates for high spatial resolution imaging mass spectrometry of lipids: enhanced information in both positive and negative polarities after 1,5-diaminonapthalene deposition.

Matrix sublimation has demonstrated to be a powerful approach for high-resolution matrix-assisted laser desorption ionization (MALDI) imaging of lipids, providing very homogeneous solvent-free deposition. This work presents a comprehensive study aiming to evaluate current and novel matrix candidates for high spatial resolution MALDI imaging mass spectrometry of lipids from tissue section after deposition by sublimation. For this purpose, 12 matrices including 2,5-dihydroxybenzoic acid (DHB), sinapinic acid (SA), α-cyano-4-hydroxycinnamic acid (CHCA), 2,6-dihydroxyacetphenone (DHA), 2',4',6'-trihydroxyacetophenone (THAP), 3-hydroxypicolinic acid (3-HPA), 1,8-bis(dimethylamino)naphthalene (DMAN), 1,8,9-anthracentriol (DIT), 1,5-diaminonapthalene (DAN), p-nitroaniline (NIT), 9-aminoacridine (9-AA), and 2-mercaptobenzothiazole (MBT) were investigated for lipid detection efficiency in both positive and negative ionization modes, matrix interferences, and stability under vacuum. For the most relevant matrices, ion maps of the different lipid species were obtained from tissue sections at high spatial resolution and the detected peaks were characterized by matrix-assisted laser desorption ionization time-of-flight/time-of-flight (MALDI-TOF/TOF) mass spectrometry. First proposed for imaging mass spectrometry (IMS) after sublimation, DAN has demonstrated to be of high efficiency providing rich lipid signatures in both positive and negative polarities with high vacuum stability and sub-20 μm resolution capacity. Ion images from adult mouse brain were generated with a 10 μm scanning resolution. Furthermore, ion images from adult mouse brain and whole-body fish tissue sections were also acquired in both polarity modes from the same tissue section at 100 μm spatial resolution. Sublimation of DAN represents an interesting approach to improve information with respect to currently employed matrices providing a deeper analysis of the lipidome by IMS.

Information source evaluation matrix

An information source evaluation matrix, produced by the Library at De Montfort University