Inference on Survival Data with Covariate Measurement Error - An Imputation-based Approach

We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerative distribution. Simulations indicate high efficiency and robustness. We consider the special case where error-prone replicates are available on the unobserved true covariates. As expected, increasing the number of replicate for the unobserved covariates increases efficiency and reduces bias. We illustrate the practical utility of the proposed method with an Eastern Cooperative Oncology Group clinical trial where a genetic marker, c-myc expression level, is subject to measurement error.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Statistical Inference for Processes Depending on Environments and Application in Regenerative Processes

We build the Conditional Least Squares Estimator of 0 based on the observation of a single trajectory of {Zk,Ck}k, and give conditions ensuring its strong consistency. The particular case of general linear models according to 0=( 0, 0) and among them, regenerative processes, are studied more particularly. In this frame, we may also prove the consistency of the estimator of 0 although it belongs to an asymptotic negligible part of the model, and the asymptotic law of the estimator may also be calculated.

Exploring Iris Colour Prediction And Ancestry Inference In Admixed Populations Of South America.

New DNA-based predictive tests for physical characteristics and inference of ancestry are highly informative tools that are being increasingly used in forensic genetic analysis. Two eye colour prediction models: a Bayesian classifier - Snipper and a multinomial logistic regression (MLR) system for the Irisplex assay, have been described for the analysis of unadmixed European populations. Since multiple SNPs in combination contribute in varying degrees to eye colour predictability in Europeans, it is likely that these predictive tests will perform in different ways amongst admixed populations that have European co-ancestry, compared to unadmixed Europeans. In this study we examined 99 individuals from two admixed South American populations comparing eye colour versus ancestry in order to reveal a direct correlation of light eye colour phenotypes with European co-ancestry in admixed individuals. Additionally, eye colour prediction following six prediction models, using varying numbers of SNPs and based on Snipper and MLR, were applied to the study populations. Furthermore, patterns of eye colour prediction have been inferred for a set of publicly available admixed and globally distributed populations from the HGDP-CEPH panel and 1000 Genomes databases with a special emphasis on admixed American populations similar to those of the study samples.

Tori embedded in S³ with dense asymptotic lines

In this paper are given examples of tori T² embedded in S³ with all their asymptotic lines dense.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

On the asymptotic enumeration of accessible automata

We simplify the known formula for the asymptotic estimate of the number of deterministic and accessible automata with n states over a k-letter alphabet. The proof relies on the theory of Lagrange inversion applied in the context of generalized binomial series.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.

A calibration approach based on Takagi-Sugeno fuzzy inference system for digital electronic compasses

Recently, the development of industrial processes brought on the outbreak of technologically complex systems. This development generated the necessity of research relative to the mathematical techniques that have the capacity to deal with project complexities and validation. Fuzzy models have been receiving particular attention in the area of nonlinear systems identification and analysis due to it is capacity to approximate nonlinear behavior and deal with uncertainty. A fuzzy rule-based model suitable for the approximation of many systems and functions is the Takagi-Sugeno (TS) fuzzy model. IS fuzzy models are nonlinear systems described by a set of if then rules which gives local linear representations of an underlying system. Such models can approximate a wide class of nonlinear systems. In this paper a performance analysis of a system based on IS fuzzy inference system for the calibration of electronic compass devices is considered. The contribution of the evaluated IS fuzzy inference system is to reduce the error obtained in data acquisition from a digital electronic compass. For the reliable operation of the TS fuzzy inference system, adequate error measurements must be taken. The error noise must be filtered before the application of the IS fuzzy inference system. The proposed method demonstrated an effectiveness of 57% at reducing the total error based on considered tests. (C) 2011 Elsevier Ltd. All rights reserved.

The transient response of a CSTR containing porous catalyst pellets. Asymptotic solutions

Transient response of a CSTR containing porous catalyst pellets is analyzed theoretically using a matched asymptotic expansion technique. This singular perturbation technique leads directly to the conditions under which the minima of reservoir concentration occur. The existence of the minima may be used to estimate some inherent parameters of the catalyst pellet.

Asymptotic limits of a self-dual Ginzburg-Landau functional in bounded domains

In the author's joint paper [HJS] with Jest and Struwe, we discuss asymtotic limits of a self-dual Ginzburg-Landau functional involving a section of a line bundle over a closed Riemann surface and a connection on this bundle. In this paper, the author generalizes the above results [HJS] to the case of bounded domains.

Inference of phylogeny and taxonomy within the Didymozoidae (Digenea) from the second internal transcribed spacer (ITS2) of ribosomal DNA

DNA sequences of the second internal transcribed spacer (ITS2) of ribosomal DNA (rDNA) were determined for 11 species from four genera of Didymozoinae (Indodidymozoon, Helicodidymozoon, Rhopalotrema and Neometadidymozoon) and a species of the Lecithasteridae, Lecithaster stellatus. Sequences were used to test the validity of species recognised on morphological criteria and to infer phylogenetic relationships. Sequences of the 11 didymozoids differed by 0.5% to 19%. Our phylogenetic analyses: (i) indicate that species in the genera Helicodidymozoon and Rhopalotrema are a monophyletic group; (ii) support separation of the genus Helicodidymozoon from the genera Indodidymozoon and Neometadidymozoon; and (iii) support recognition of Rhopalotrema as a genus distinct from Neometadidymozoon. We found the gonochoristic species, I. pearsoni and I. suttiei, to be genetically similar to the hermaphroditic species in the genus Indodidymozoon and found no evidence to indicate that they belong in a separate genus.