STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Mathematical methods to analyze and interpret calcium signals of astrocytes

Astrocytes are the most numerous glial cell type in the mammalian brain and permeate the entire CNS interacting with neurons, vasculature, and other glial cells. Astrocytes display intracellular calcium signals that encode information about local synaptic function, distributed network activity, and high-level cognitive functions. Several studies have investigated the calcium dynamics of astrocytes in sensory areas and have shown that these cells can encode sensory stimuli. Nevertheless, only recently the neuro-scientific community has focused its attention on the role and functions of astrocytes in associative areas such as the hippocampus. In our first study, we used the information theory formalism to show that astrocytes in the CA1 area of the hippocampus recorded with 2-photon fluorescence microscopy during spatial navigation encode spatial information that is complementary and synergistic to information encoded by nearby "place cell" neurons. In our second study, we investigated various computational aspects of applying the information theory formalism to astrocytic calcium data. For this reason, we generated realistic simulations of calcium signals in astrocytes to determine optimal hyperparameters and procedures of information measures and applied them to real astrocytic calcium imaging data. Calcium signals of astrocytes are characterized by complex spatiotemporal dynamics occurring in subcellular parcels of the astrocytic domain which makes studying these cells in 2-photon calcium imaging recordings difficult. However, current analytical tools which identify the astrocytic subcellular regions are time consuming and extensively rely on user-defined parameters. Here, we present Rapid Astrocytic calcium Spatio-Temporal Analysis (RASTA), a novel machine learning algorithm for spatiotemporal semantic segmentation of 2-photon calcium imaging recordings of astrocytes which operates without human intervention. We found that RASTA provided fast and accurate identification of astrocytic cell somata, processes, and cellular domains, extracting calcium signals from identified regions of interest across individual cells and populations of hundreds of astrocytes recorded in awake mice.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Effector function of human tumor-specific CD8 T cells in melanoma lesions: a state of local functional tolerance.

Although tumor-specific CD8 T-cell responses often develop in cancer patients, they rarely result in tumor eradication. We aimed at studying directly the functional efficacy of tumor-specific CD8 T cells at the site of immune attack. Tumor lesions in lymphoid and nonlymphoid tissues (metastatic lymph nodes and soft tissue/visceral metastases, respectively) were collected from stage III/IV melanoma patients and investigated for the presence and function of CD8 T cells specific for the tumor differentiation antigen Melan-A/MART-1. Comparative analysis was conducted with peripheral blood T cells. We provide evidence that in vivo-priming selects, within the available naive Melan-A/MART-1-specific CD8 T-cell repertoire, cells with high T-cell receptor avidity that can efficiently kill melanoma cells in vitro. In vivo, primed Melan-A/MART-1-specific CD8 T cells accumulate at high frequency in both lymphoid and nonlymphoid tumor lesions. Unexpectedly, however, whereas primed Melan-A/MART-1-specific CD8 T cells that circulate in the blood display robust inflammatory and cytotoxic functions, those that reside in tumor lesions (particularly in metastatic lymph nodes) are functionally tolerant. We show that both the lymph node and the tumor environments blunt T-cell effector functions and offer a rationale for the failure of tumor-specific responses to effectively counter tumor progression.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Regional coronary endothelial function is closely related to local early coronary atherosclerosis in patients with mild coronary artery disease: pilot study.

BACKGROUND: Coronary endothelial function is abnormal in patients with established coronary artery disease and was recently shown by MRI to relate to the severity of luminal stenosis. Recent advances in MRI now allow the noninvasive assessment of both anatomic and functional (endothelial function) changes that previously required invasive studies. We tested the hypothesis that abnormal coronary endothelial function is related to measures of early atherosclerosis such as increased coronary wall thickness. METHODS AND RESULTS: Seventeen arteries in 14 healthy adults and 17 arteries in 14 patients with nonobstructive coronary artery disease were studied. To measure endothelial function, coronary MRI was performed before and during isometric handgrip exercise, an endothelial-dependent stressor, and changes in coronary cross-sectional area and flow were measured. Black blood imaging was performed to quantify coronary wall thickness and indices of arterial remodeling. The mean stress-induced change in cross-sectional area was significantly higher in healthy adults (13.5%±12.8%, mean±SD, n=17) than in those with mildly diseased arteries (-2.2%±6.8%, P<0.0001, n=17). Mean coronary wall thickness was lower in healthy subjects (0.9±0.2 mm) than in patients with coronary artery disease (1.4±0.3 mm, P<0.0001). In contrast to healthy subjects, stress-induced changes in cross-sectional area, a measure of coronary endothelial function, correlated inversely with coronary wall thickness in patients with coronary artery disease (r=-0.73, P=0.0008). CONCLUSIONS: There is an inverse relationship between coronary endothelial function and local coronary wall thickness in patients with coronary artery disease but not in healthy adults. These findings demonstrate that local endothelial-dependent functional changes are related to the extent of early anatomic atherosclerosis in mildly diseased arteries. This combined MRI approach enables the anatomic and functional investigation of early coronary disease.

Local transient myocardial liposomal gene transfer of inducible nitric oxide synthase does not aggravate myocardial function and fibrosis and leads to moderate neovascularization in chronic myocardial ischemia in pigs.

Microcirculation (2010) 17, 69-78. doi: 10.1111/j.1549-8719.2010.00002.x Abstract Background: This study was designed to explore the effect of transient inducible nitric oxide synthase (iNOS) overexpression via cationic liposome-mediated gene transfer on cardiac function, fibrosis, and microvascular perfusion in a porcine model of chronic ischemia. Methods and Results: Chronic myocardial ischemia was induced using a minimally invasive model in 23 landrace pigs. Upon demonstration of heart failure, 10 animals were treated with liposome-mediated iNOS-gene-transfer by local intramyocardial injection and 13 animals received a sham procedure to serve as control. The efficacy of this iNOS-gene-transfer was demonstrated for up to 7 days by reverse transcriptase-polymerase chain reaction in preliminary studies. Four weeks after iNOS transfer, magnetic resonance imaging showed no effect of iNOS overexpression on cardiac contractility at rest and during dobutamine stress (resting ejection fraction: control 27%, iNOS 26%; P = ns). Late enhancement, infarct size, and the amount of fibrosis were similar between groups. Although perfusion and perfusion reserve in response to adenosine and dobutamine were not significantly modified by iNOS-transfer, both vessel number and diameter were significantly increased in the ischemic area in the iNOS-treated group versus control (point score: control 15.3, iNOS 34.7; P < 0.05). Conclusions: Our findings demonstrate that transient iNOS overexpression does not aggravate cardiac dysfunction or postischemic fibrosis, while potentially contributing to neovascularization in the chronically ischemic heart.

TSLP promotes influenza-specific CD8+ T-cell responses by augmenting local inflammatory dendritic cell function.

Thymic stromal lymphopoietin (TSLP) is a mucosal tissue-associated cytokine that has been widely studied in the context of T helper type 2 (Th2)-driven inflammatory disorders. Although TSLP is also produced upon viral infection in vitro, the role of TSLP in antiviral immunity is unknown. In this study we report a novel role for TSLP in promoting viral clearance and virus-specific CD8+ T-cell responses during influenza A infection. Comparing the immune responses of wild-type and TSLP receptor (TSLPR)-deficient mice, we show that TSLP was required for the expansion and activation of virus-specific effector CD8+ T cells in the lung, but not the lymph node. The mechanism involved TSLPR signaling on newly recruited CD11b+ inflammatory dendritic cells (DCs) that acted to enhance interleukin-15 production and expression of the costimulatory molecule CD70. Taken together, these data highlight the pleiotropic activities of TSLP and provide evidence for its beneficial role in antiviral immunity.

Small but powerful: Top predator local extinction affects ecosystem structure and function in an intermittent stream.

Top predator loss is a major global problem, with a current trend in biodiversity loss towards high trophic levels that modifies most ecosystems worldwide. Most research in this area is focused on large-bodied predators, despite the high extinction risk of small-bodied freshwater fish that often act as apex consumers. Consequently, it remains unknown if intermittent streams are affected by the consequences of top-predators' extirpations. The aim of our research was to determine how this global problem affects intermittent streams and, in particular, if the loss of a small-bodied top predator (1) leads to a 'mesopredator release', affects primary consumers and changes whole community structures, and (2) triggers a cascade effect modifying the ecosystem function. To address these questions, we studied the topdown effects of a small endangered fish species, Barbus meridionalis (the Mediterranean barbel), conducting an enclosure/exclosure mesocosm experiment in an intermittent stream where B. meridionalis became locally extinct following a wildfire.We found that top predator absence led to 'mesopredator release', and also to 'prey release' despite intraguild predation, which contrasts with traditional food web theory. In addition, B. meridionalis extirpation changed whole macroinvertebrate community composition and increased total macroinvertebrate density. Regarding ecosystem function, periphyton primary production decreased in apex consumer absence. In this study, the apex consumer was functionally irreplaceable; its local extinction led to the loss of an important functional role that resulted in major changes to the ecosystem's structure and function. This study evidences that intermittent streams can be affected by the consequences of apex consumers' extinctions, and that the loss of small-bodied top predators can lead to large ecosystem changes. We recommend the reintroduction of small-bodied apex consumers to systems where they have been extirpated, to restore ecosystem structure and function.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].

Local Influence Under Parameter Constraints

Calculations of local influence curvatures and leverage have been well developed when the parameters are unrestricted. In this article, we discuss the assessment of local influence and leverage under linear equality parameter constraints with extensions to inequality constraints. Using a penalized quadratic function we express the normal curvature of local influence for arbitrary perturbation schemes and the generalized leverage matrix in interpretable forms, which depend on restricted and unrestricted components. The results are quite general and can be applied in various statistical models. In particular, we derive the normal curvature under three useful perturbation schemes for generalized linear models. Four illustrative examples are analyzed by the methodology developed in the article.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.