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.

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

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended

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

Making Multiple Decisions Adaptively

The asymptotic behavior of multiple decision procedures is studied when the underlying distributions depend on an unknown nuisance parameter. An adaptive procedure must be asymptotically optimal for each value of this nuisance parameter, and it should not depend on its value. A necessary and sufficient condition for the existence of such a procedure is derived. Several examples are investigated in detail, and possible lack of adaptation of the traditional overall maximum likelihood rule is discussed.

SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

[food Insecurity In Brazilian Families With Children Under Five Years Of Age].

This article analyzes food insecurity and hunger in Brazilian families with children under five years of age. This was a nationally representative cross-sectional study using data from the National Demographic and Health Survey on Women and Children (PNDS-2006), in which the outcome variable was moderate to severe food insecurity, measured by the Brazilian Food Insecurity Scale (EBIA). Prevalence estimates and prevalence ratios were generated with 95% confidence intervals. The results showed a high prevalence of moderate to severe food insecurity, concentrated in the North and Northeast regions (30.7%), in economic classes D and E (34%), and in beneficiaries of conditional cash transfer programs (36.5%). Multivariate analysis showed that the socioeconomic relative risks (beneficiaries of conditional cash transfers), regional relative risks (North and Northeast regions), and economic relative risks (classes D and E) were 1.8, 2.0 and 2.4, respectively. Aggregation of the three risks showed 48% of families with moderate to severe food insecurity, meaning that adults and children were going hungry during the three months preceding the survey.

The G209A mutation in the alpha-synuclein gene in Brazilian families with Parkinson's disease

A missense G209A mutation of the alpha-synuclein gene was recently described in a large Contursi kindred with Parkinson's disease (PD). The objective of this study is to determine if the mutation G209A of the alpha-synuclein gene was present in 10 Brazilian families with PD. PD patients were recruited from movement disorders clinics of Brazil. A family history with two or more affected in relatives was the inclusion criterion for this study. The alpha-synuclein G209A mutation assay was made using polymerase chain reaction and the restriction enzyme Tsp45I. Ten patients from 10 unrelated families were studied. The mean age of PD onset was 42.7 years old. We did not find the G209A mutation in our 10 families with PD. Our results suggest that alpha-synuclein mutation G209A is uncommon in Brazilian PD families.

Evaluating gene by sex and age interactions on cardiovascular risk factors in Brazilian families

Background: In family studies, it is important to evaluate the impact of genes and environmental factors on traits of interest. In particular, the relative influences of both genes and the environment may vary in different strata of the population of interest, such as young and old individuals, or males and females. Methods: In this paper, extensions of the variance components model are used to evaluate heterogeneity in the genetic and environmental variance components due to the effects of sex and age (the cutoff between young and old was 43 yrs). The data analyzed were from 81 Brazilian families (1,675 individuals) of the Baependi Family Heart Study. Results: The models allowing for heterogeneity of variance components by sex suggest that genetic and environmental variances are not different in males and females for diastolic blood pressure, LDL-cholesterol, and HDL-cholesterol, independent of the covariates included in the models. However, for systolic blood pressure, fasting glucose and triglycerides, the evidence for heterogeneity was dependent on the covariates in the model. For instance, in the presence of sex and age covariates, heterogeneity in the genetic variance component was suggested for fasting glucose. But, for systolic blood pressure, there was no evidence of heterogeneity in any of the two variance components. Except for the LDL-cholesterol, models allowing for heterogeneity by age provide evidence of heterogeneity in genetic variance for triglycerides and systolic and diastolic blood pressure. There was evidence of heterogeneity in environmental variance in fasting glucose and HDL-cholesterol. Conclusions: Our results suggest that heterogeneity in trait variances should not be ignored in the design and analyses of gene-finding studies involving these traits, as it may generate additional information about gene effects, and allow the investigation of more sophisticated models such as the model including sex-specific oligogenic variance components.

Nutritional status of pre-school children from low income families

Background: We evaluated growth and nutritional status of preschool children between 2 and 6 years old from low income families from 14 daycare centers. Methods: Cross-sectional study with 1544 children from daycare centers of Santo Andre, Brazil. Body weight (W), height (H) and body mass index (BMI) were classified according to the 2000 National Center for Health Statistics (CDC/NCHS). Cutoff points for nutritional disorders: -2 z scores and 2.5 and 10 percentiles for malnutrition risk, 85 to 95 percentile for overweight and above BMI 95 percentile for obesity. Stepwise Forward Regression method was used including age, gender, birth weight, breastfeeding duration, age of mother at birth and period of time they attended the daycare center. Results: Children presented mean z scores of H, W and BMI above the median of the CDC/NCHS reference. Girls were taller and heavier than boys, while we observed similar BMI between both genders. The z scores tended to rise with age. A Pearson Coefficient of Correlation of 0.89 for W, 0.93 for H and 0.95 for BMI was documented indicating positive association of age with weight, height and BMI. The frequency of children below -2 z scores was lower than expected: 1.5% for W, 1.75% for H and 0% for BMI, which suggests that there were no malnourished children. The other extremity of the distribution evidenced prevalence of overweight and obesity of 16.8% and 10.8%, respectively. Conclusion: Low income preschool children are in an advanced stage of nutritional transition with a high prevalence of overweight.

A frequency approach to identifying asteroid families II. Families interacting with nonlinear secular resonances and low-order mean-motion resonances

Aims. In an earlier paper we introduced a new method for determining asteroid families where families were identified in the proper frequency domain (n, g, g + s) ( where n is the mean-motion, and g and s are the secular frequencies of the longitude of pericenter and nodes, respectively), rather than in the proper element domain (a, e, sin(i)) (semi-major axis, eccentricity, and inclination). Here we improve our techniques for reliably identifying members of families that interact with nonlinear secular resonances of argument other than g or g + s and for asteroids near or in mean-motion resonant configurations. Methods. We introduce several new distance metrics in the frequency space optimal for determining the diffusion in secular resonances of argument 2g - s, 3g - s, g - s, s, and 2s. We also regularize the dependence of the g frequency as a function of the n frequency (Vesta family) or of the eccentricity e (Hansa family). Results. Our new approaches allow us to recognize as family members objects that were lost with previous methods, while keeping the advantages of the Carruba & Michtchenko (2007, A& A, 475, 1145) approach. More important, an analysis in the frequency domain permits a deeper understanding of the dynamical evolution of asteroid families not always obtainable with an analysis in the proper element domain.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

Roles assessment in families of children with chronic renal failure on peritoneal dialysis

Families with a child on chronic peritoneal dialysis have to assume a significant burden of care, intensifying the demands and the reorganization of roles in the families of children. The purpose of this study is to describe the implications of role changes in families of children with chronic renal disease on peritoneal dialysis. This is a case study of four families of children with chronic renal disease on peritoneal dialysis. Fourteen family members participate in the study. After the child`s chronic kidney failure and the start of treatment, each relative`s ways, acts and functions are changed, maintained or adapted to the new family dynamics, imposed by the child`s treatment conditions. Appropriate role assessment provides the nurse and the families of children with chronic renal failure on peritoneal dialysis with insight regarding current and potential health problems and aids in identifying the needs of the families.

Starting treatment: caring for patients and their families

The standards presented in this section focus on providing physical, social and psychological care for the patient at the point he or she is diagnosed with tuberculosis (TB) and starts treatment. Detailed guidance is included with regard to organising directly observed treatment (DOT) safely and acceptably for both the patient and the management unit. The aim is to give the patient the best possible chance of successfully completing treatment according to a regimen recommended by the World Health Organization. If the health service where the patient is diagnosed cannot offer ongoing treatment and care due to a lack of facilities, overcrowding or inaccessibility, the patient needs to be referred to a designated TB management unit (BMU) elsewhere. The patient may also receive treatment from a facility outside a BMU. However care is organised, it is essential for all patients who are diagnosed with TB to be registered at an appropriate BMU so that their progress can be routinely monitored and programme performance can be assessed. To avoid the risk of losing contact with the patient at any stage of their care, good communication is essential between all parties involved, from the patient him/herself to the person supervising their DOT to the BMU.