A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

On the Mahalanobis Distance Classification Criterion for Multidimensional Normal Distributions

Many existing engineering works model the statistical characteristics of the entities under study as normal distributions. These models are eventually used for decision making, requiring in practice the definition of the classification region corresponding to the desired confidence level. Surprisingly enough, however, a great amount of computer vision works using multidimensional normal models leave unspecified or fail to establish correct confidence regions due to misconceptions on the features of Gaussian functions or to wrong analogies with the unidimensional case. The resulting regions incur in deviations that can be unacceptable in high-dimensional models. Here we provide a comprehensive derivation of the optimal confidence regions for multivariate normal distributions of arbitrary dimensionality. To this end, firstly we derive the condition for region optimality of general continuous multidimensional distributions, and then we apply it to the widespread case of the normal probability density function. The obtained results are used to analyze the confidence error incurred by previous works related to vision research, showing that deviations caused by wrong regions may turn into unacceptable as dimensionality increases. To support the theoretical analysis, a quantitative example in the context of moving object detection by means of background modeling is given.

MBIS: Multivariate Bayesian Image Segmentation Tool

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multi-channel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.

New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

Multivariate Appoximations to Portfolio Return Distribution

This article proposes a three-step procedure to estimate portfolio return distributions under the multivariate Gram-Charlier (MGC) distribution. The method combines quasi maximum likelihood (QML) estimation for conditional means and variances and the method of moments (MM) estimation for the rest of the density parameters, including the correlation coefficients. The procedure involves consistent estimates even under density misspecification and solves the so-called ‘curse of dimensionality’ of multivariate modelling. Furthermore, the use of a MGC distribution represents a flexible and general approximation to the true distribution of portfolio returns and accounts for all its empirical regularities. An application of such procedure is performed for a portfolio composed of three European indices as an illustration. The MM estimation of the MGC (MGC-MM) is compared with the traditional maximum likelihood of both the MGC and multivariate Student’s t (benchmark) densities. A simulation on Value-at-Risk (VaR) performance for an equally weighted portfolio at 1% and 5% confidence indicates that the MGC-MM method provides reasonable approximations to the true empirical VaR. Therefore, the procedure seems to be a useful tool for risk managers and practitioners.

Effects of a harmful algal bloom on the community ecology, movements and spatial distributions of fishes in a microtidal estuary

Harmful algal blooms can adversely affect fish communities, though their impacts are highly context-dependent and typically differ between fish species. Various approaches, comprising univariate and multivariate analyses and multimetric Fish Community Indices (FCI), were employed to characterise the perceived impacts of a Karlodinium veneficum bloom on the fish communities and ecological condition of the Swan Canning Estuary, Western Australia. The combined evidence suggests that a large proportion of the more mobile fish species in the offshore waters of the bloom-affected area relocated to other regions during the bloom. This was indicated by marked declines in mean species richness, catch rates and FCI scores in the bloom region but concomitant increases in these characteristics in more distal regions, and by pronounced and atypical shifts in the pattern of inter-regional similarities in fish community composition during the bloom. The lack of any significant changes among the nearshore fish communities revealed that bloom impacts were less severe there than in deeper, offshore waters. Nearshore habitats, which generally are in better ecological condition than adjacent offshore waters in this system, may provide refuges for fish during algal blooms and other perturbations, mirroring similar observations of fish avoidance responses to such stressors in estuaries worldwide.

Effects of a harmful algal bloom on the community ecology, movements and spatial distributions of fishes in a microtidal estuary

Harmful algal blooms can adversely affect fish communities, though their impacts are highly context-dependent and typically differ between fish species. Various approaches, comprising univariate and multivariate analyses and multimetric Fish Community Indices (FCI), were employed to characterise the perceived impacts of a Karlodinium veneficum bloom on the fish communities and ecological condition of the Swan Canning Estuary, Western Australia. The combined evidence suggests that a large proportion of the more mobile fish species in the offshore waters of the bloom-affected area relocated to other regions during the bloom. This was indicated by marked declines in mean species richness, catch rates and FCI scores in the bloom region but concomitant increases in these characteristics in more distal regions, and by pronounced and atypical shifts in the pattern of inter-regional similarities in fish community composition during the bloom. The lack of any significant changes among the nearshore fish communities revealed that bloom impacts were less severe there than in deeper, offshore waters. Nearshore habitats, which generally are in better ecological condition than adjacent offshore waters in this system, may provide refuges for fish during algal blooms and other perturbations, mirroring similar observations of fish avoidance responses to such stressors in estuaries worldwide.

DYNAMICS OF THE SHORT TERM AND LONG TERM AVIAN DISTRIBUTIONS IN NORTH AMERICA - THE ROLES OF VEGETATION HEIGHT HETEROGENEITY AND CLIMATIC FACTORS

Understanding how biodiversity spatially distribute over both the short term and long term, and what factors are affecting the distribution, are critical for modeling the spatial pattern of biodiversity as well as for promoting effective conservation planning and practices. This dissertation aims to examine factors that influence short-term and long-term avian distribution from the geographical sciences perspective. The research develops landscape level habitat metrics to characterize forest height heterogeneity and examines their efficacies in modelling avian richness at the continental scale. Two types of novel vegetation-height-structured habitat metrics are created based on second order texture algorithms and the concepts of patch-based habitat metrics. I correlate the height-structured metrics with the richness of different forest guilds, and also examine their efficacies in multivariate richness models. The results suggest that height heterogeneity, beyond canopy height alone, supplements habitat characterization and richness models of two forest bird guilds. The metrics and models derived in this study demonstrate practical examples of utilizing three-dimensional vegetation data for improved characterization of spatial patterns in species richness. The second and the third projects focus on analyzing centroids of avian distributions, and testing hypotheses regarding the direction and speed of these shifts. I first showcase the usefulness of centroids analysis for characterizing the distribution changes of a few case study species. Applying the centroid method on 57 permanent resident bird species, I show that multi-directional distribution shifts occurred in large number of studied species. I also demonstrate, plain birds are not shifting their distribution faster than mountain birds, contrary to the prediction based on climate change velocity hypothesis. By modelling the abundance change rate at regional level, I show that extreme climate events and precipitation measures associate closely with some of the long-term distribution shifts. This dissertation improves our understanding on bird habitat characterization for species richness modelling, and expands our knowledge on how avian populations shifted their ranges in North America responding to changing environments in the past four decades. The results provide an important scientific foundation for more accurate predictive species distribution modeling in future.

Modelling and classification with quantile-based distributions

In this work, we explore and demonstrate the potential for modeling and classification using quantile-based distributions, which are random variables defined by their quantile function. In the first part we formalize a least squares estimation framework for the class of linear quantile functions, leading to unbiased and asymptotically normal estimators. Among the distributions with a linear quantile function, we focus on the flattened generalized logistic distribution (fgld), which offers a wide range of distributional shapes. A novel naïve-Bayes classifier is proposed that utilizes the fgld estimated via least squares, and through simulations and applications, we demonstrate its competitiveness against state-of-the-art alternatives. In the second part we consider the Bayesian estimation of quantile-based distributions. We introduce a factor model with independent latent variables, which are distributed according to the fgld. Similar to the independent factor analysis model, this approach accommodates flexible factor distributions while using fewer parameters. The model is presented within a Bayesian framework, an MCMC algorithm for its estimation is developed, and its effectiveness is illustrated with data coming from the European Social Survey. The third part focuses on depth functions, which extend the concept of quantiles to multivariate data by imposing a center-outward ordering in the multivariate space. We investigate the recently introduced integrated rank-weighted (IRW) depth function, which is based on the distribution of random spherical projections of the multivariate data. This depth function proves to be computationally efficient and to increase its flexibility we propose different methods to explicitly model the projected univariate distributions. Its usefulness is shown in classification tasks: the maximum depth classifier based on the IRW depth is proven to be asymptotically optimal under certain conditions, and classifiers based on the IRW depth are shown to perform well in simulated and real data experiments.

Data-driven multivariate flood hazard modeling

The present Dissertation shows how recent statistical analysis tools and open datasets can be exploited to improve modelling accuracy in two distinct yet interconnected domains of flood hazard (FH) assessment. In the first Part, unsupervised artificial neural networks are employed as regional models for sub-daily rainfall extremes. The models aim to learn a robust relation to estimate locally the parameters of Gumbel distributions of extreme rainfall depths for any sub-daily duration (1-24h). The predictions depend on twenty morphoclimatic descriptors. A large study area in north-central Italy is adopted, where 2238 annual maximum series are available. Validation is performed over an independent set of 100 gauges. Our results show that multivariate ANNs may remarkably improve the estimation of percentiles relative to the benchmark approach from the literature, where Gumbel parameters depend on mean annual precipitation. Finally, we show that the very nature of the proposed ANN models makes them suitable for interpolating predicted sub-daily rainfall quantiles across space and time-aggregation intervals. In the second Part, decision trees are used to combine a selected blend of input geomorphic descriptors for predicting FH. Relative to existing DEM-based approaches, this method is innovative, as it relies on the combination of three characteristics: (1) simple multivariate models, (2) a set of exclusively DEM-based descriptors as input, and (3) an existing FH map as reference information. First, the methods are applied to northern Italy, represented with the MERIT DEM (∼90m resolution), and second, to the whole of Italy, represented with the EU-DEM (25m resolution). The results show that multivariate approaches may (a) significantly enhance flood-prone areas delineation relative to a selected univariate one, (b) provide accurate predictions of expected inundation depths, (c) produce encouraging results in extrapolation, (d) complete the information of imperfect reference maps, and (e) conveniently convert binary maps into continuous representation of FH.

Beam Energy Dependence Of Moments Of The Net-charge Multiplicity Distributions In Au+au Collisions At Rhic.

We report the first measurements of the moments--mean (M), variance (σ(2)), skewness (S), and kurtosis (κ)--of the net-charge multiplicity distributions at midrapidity in Au+Au collisions at seven energies, ranging from sqrt[sNN]=7.7 to 200 GeV, as a part of the Beam Energy Scan program at RHIC. The moments are related to the thermodynamic susceptibilities of net charge, and are sensitive to the location of the QCD critical point. We compare the products of the moments, σ(2)/M, Sσ, and κσ(2), with the expectations from Poisson and negative binomial distributions (NBDs). The Sσ values deviate from the Poisson baseline and are close to the NBD baseline, while the κσ(2) values tend to lie between the two. Within the present uncertainties, our data do not show nonmonotonic behavior as a function of collision energy. These measurements provide a valuable tool to extract the freeze-out parameters in heavy-ion collisions by comparing with theoretical models.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

Comparing Near-infrared Conventional Diffuse Reflectance Spectroscopy And Hyperspectral Imaging For Determination Of The Bulk Properties Of Solid Samples By Multivariate Regression: Determination Of Mooney Viscosity And Plasticity Indices Of Natural Rubber.

Conventional reflectance spectroscopy (NIRS) and hyperspectral imaging (HI) in the near-infrared region (1000-2500 nm) are evaluated and compared, using, as the case study, the determination of relevant properties related to the quality of natural rubber. Mooney viscosity (MV) and plasticity indices (PI) (PI0 - original plasticity, PI30 - plasticity after accelerated aging, and PRI - the plasticity retention index after accelerated aging) of rubber were determined using multivariate regression models. Two hundred and eighty six samples of rubber were measured using conventional and hyperspectral near-infrared imaging reflectance instruments in the range of 1000-2500 nm. The sample set was split into regression (n = 191) and external validation (n = 95) sub-sets. Three instruments were employed for data acquisition: a line scanning hyperspectral camera and two conventional FT-NIR spectrometers. Sample heterogeneity was evaluated using hyperspectral images obtained with a resolution of 150 × 150 μm and principal component analysis. The probed sample area (5 cm(2); 24,000 pixels) to achieve representativeness was found to be equivalent to the average of 6 spectra for a 1 cm diameter probing circular window of one FT-NIR instrument. The other spectrophotometer can probe the whole sample in only one measurement. The results show that the rubber properties can be determined with very similar accuracy and precision by Partial Least Square (PLS) regression models regardless of whether HI-NIR or conventional FT-NIR produce the spectral datasets. The best Root Mean Square Errors of Prediction (RMSEPs) of external validation for MV, PI0, PI30, and PRI were 4.3, 1.8, 3.4, and 5.3%, respectively. Though the quantitative results provided by the three instruments can be considered equivalent, the hyperspectral imaging instrument presents a number of advantages, being about 6 times faster than conventional bulk spectrometers, producing robust spectral data by ensuring sample representativeness, and minimizing the effect of the presence of contaminants.

Multivariate analysis of the effects of soil parameters and environmental factors on the flavonoid content of leaves of Passiflora incarnata L., Passifloraceae

The aim of the present study was to evaluate the effect of soil characteristics (pH, macro- and micro-nutrients), environmental factors (temperature, humidity, period of the year and time of day of collection) and meteorological conditions (rain, sun, cloud and cloud/rain) on the flavonoid content of leaves of Passiflora incarnata L., Passifloraceae. The total flavonoid contents of leaf samples harvested from plants cultivated or collected under different conditions were quantified by high-performance liquid chromatography with ultraviolet detection (HPLC-UV/PAD). Chemometric treatment of the data by principal component (PCA) and hierarchic cluster analyses (HCA) showed that the samples did not present a specific classification in relation to the environmental and soil variables studied, and that the environmental variables were not significant in describing the data set. However, the levels of the elements Fe, B and Cu present in the soil showed an inverse correlation with the total flavonoid contents of the leaves of P. incarnata.