Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

PALEOCLIMATIC CONTROLS ON STABLE OXYGEN AND CARBON ISOTOPES IN CALICHE OF THE ABO FORMATION (PERMIAN), SOUTH-CENTRAL NEW-MEXICO, USA

The stable oxygen and carbon isotopic composition of caliche in fluvial and supratidal rocks of the Abo Formation (Permian), south-central New Mexico, is controlled by palecoclimate and depositional environment. Fluvial caliche consists of low-Mg calcite nodules and vertically oriented tubules that display stage II texture. Micrite matrix support, brecciation, ooids/pisoliths, aveolar-septal texture, and peloids are common in the fluvial caliche and, along with red color and slickensides in the host shale, indicate pedogenesis in a well-oxidized vadose zone. In contrast, periodic waterlogging of the supratidal paleosols, probably due to high water table, is indicated by drab colors, carbonaceous flecks, horizontal rhizoliths, and the paucity of vadose textures in the stage II caliche nodules.Stable oxygen isotopes are similar in the fluvial and supratidal caliches and range from 21.6 to 30.5 parts per thousand (SMOW). The data exhibit a crude bimodality and delta-O-18 enrichment with a decrease in age (higher in the section). Consideration of these data in the context of delta-temperature relations suggests that 1) surface waters responsible for caliche formation increased in delta-O-18 (from roughly -8 to + 1 parts per thousand) over the 18 m.y. time interval that separated the lowest stratigraphic nodule horizon from the highest, 2) the increasing delta-O-18 values also reflect a warming trend (approximately 15-degrees to nearly 30-degrees-C) in the mean monthly temperature over this same time period, with perhaps an associated increase in Permian ocean temperatures, and 3) the significant variation in delta-O-18 from oldest to youngest caliche was probably enhanced by the amount effect, such that as the temperature increased, the amount of precipitation decreased, resulting in high delta-O-18 values.Caliches in the Abo are enriched in heavy carbon (-7.2 to -1.5 part per thousand PDB) compared to that of soil carbonate derived exclusively from C3 plants (-12 part per thousand PDB), and the supratidal caliches contain somewhat heavier carbon compared to the fluvial caliche. The delta-C-13 values for both environments increase with a decrease in caliche age. These results indicate that as the temperature increased and rainfall decreased with time, the level of C3 plant productivity apparently declined, allowing a greater influx of atmospheric CO2 into the soil. This can only occur when soil respiration rates are quite low or at very shallow depths (less than 10 cm), or both. Atmospheric CO2 seems to have invaded the supratidal soils to a somewhat greater extent than the fluvial soils.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

SOME CONSEQUENCES OF A SYMMETRY IN STRONG DISTRIBUTIONS

Some polynomials and interpolatory quadrature rules associated with strong Stieltjes distributions are considered, especially when the distributions satisfy a Certain symmetric property. (C) 1995 Academic Press, Inc.

An ultra stable glass system for optical fiber devices

In this paper a modified chalcogenide glass was studied by X-ray powder diffraction, differential thermal analysis, infrared and Raman scattering spectroscopies. The study of this new matrix opens new perspectives to fabricate Pr3+-doped fibers to operate as an optical amplifier in the 1.3 mum telecommunications window. The Pr3+-doped 70Ga(2)S(3)-30La(2)S(3) glass was modified through the substitution of La2S3 by La2O3, which improves the thermal stability of these glasses without any modification of phonon energy. The possibility to pull a fiber from this glass system without any devitrification is easily achieved.

Sn-polymetallic greisen-type deposits associated with late-stage rapakivi granites, Brazil: fluid inclusion and stable isotope characteristics

Tin-polymetallic greisen-type deposits in the Itu Rapakivi Province and Rondonia Tin Province, Brazil are associated with late-stage rapakivi fluorine-rich peraluminous alkali-feldspar granites. These granites contain topaz and/or muscovite or zinnwaldite and have geochemical characteristics comparable to the low-P sub-type topaz-bearing granites. Stockworks and veins are common in Oriente Novo (Rondonia Tin Province) and Correas (Itu Rapakivi Province) deposits, but in the Santa Barbara deposit (Rondonia Tin Province) a preserved cupola with associated bed-like greisen is predominant. The contrasting mineralization styles reflect different depths of formation, spatial relationship to tin granites, and different wall rock/fluid proportions. The deposits contain a similar rare-metal suite that includes Sri (+/-W, +/-Ta, +/-Nb), and base-metal suite (Zn-Cu-Pb) is present only in Correas deposit. The early fluid inclusions of the Correas and Oriente Novo deposits are (1) low to moderate-salinity (0-19 wt.% NaCl eq.) CO2-bearing aqueous fluids homogenizing at 245-450 degreesC, and (2) aqueous solutions with low CO2, low to moderate salinity (0-14 wt.% NaCl eq.), which homogenize between 100 and 340 T. In the Santa Barbara deposit, the early inclusions are represented by (1) low-salinity (5-12 wt.% NaCl eq.) aqueous fluids with variable CO2 contents, homogenizing at 340 to 390 T, and (2) low-salinity (0-3 wt.% NaCl eq.) aqueous fluid inclusions, which homogenize at 320380 degreesC. Cassiterite, wolframite, columbite-tantalite, scheelite, and sulfide assemblages accompany these fluids. The late fluid in the Oriente Novo and Correas deposit was a low-salinity (0-6 wt.% NaCl eq.) CO2-free aqueous solution, which homogenizes at (100-260 degreesC) and characterizes the sulfide fluorite-sericite association in the Correas deposit. The late fluid in the Santa Barbara deposit has lower salinity (0-3 wt.% NaCl eq.) and characterizes the late-barren-quartz, muscovite and kaolinite veins. Oxygen isotope thermometry coupled with fluid inclusion data suggest hydrothermal activity at 240-450 degreesC, and 1,0-2.6 kbar fluid pressure at Correas and Oriente Novo. The hydrogen isotope composition of breccia-greisen, stockwork, and vein fluids (delta(18)O quartz from 9.9parts per thousand to 10.9parts per thousand, deltaDH(2)O from 4.13parts per thousand to 6.95parts per thousand) is consistent with a fluid that was in equilibrium with granite at temperatures from 450 to 240 degreesC. In the Santa Barbara deposit, the inferred temperatures for quartz-pods and bed-like greisens are much higher (570 and 500 degreesC, respectively), and that for the cassiterite-quartz-veins is 415 degreesC. The oxygen and hydrogen isotope composition of greisen and quartz-pods fluids (delta(18)O(qtz-H2O)=5.5-6.1parts per thousand) indicate that the fluid equilibrated with the albite granite, consistent with a magmatic origin. The values for mica (delta(18)O(mica-H2O)=33-9.8parts per thousand) suggest mixing with meteoric water. Late muscovite veins (delta(18)O(qtz-H2O)=-6.4parts per thousand) and late quartz (delta(18)O(mica-H2O)=-3.8parts per thousand) indicate involvement of a meteoric fluid. Overall, the stable isotope and fluid inclusion data imply three fluid types: (1) an early orthomagmatic fluid, which equilibrated with granite; (2) a mixed orthomagmatic-meteoric fluid; and (3) a late hydrothermal meteoric fluid. The first two were responsible for cassiterite, wolframite, and minor coluChange in the redox conditions related to mixing-of magmatic and meteoric fluids favored important sulfide mineralization in the Correas deposit. (C) 2004 Elsevier B.V. All rights reserved.

Multifractal characterization of saprolite particle-size distributions after topsoil removal

Multifractal analysis is now increasingly used to characterize soil properties as it may provide more information than a single fractal model. During the building of a large reservoir on the Parana River (Brazil), a highly weathered soil profile was excavated to a depth between 5 and 8 m. Excavation resulted in an abandoned area with saprolite materials and, in this area, an experimental field was established to assess the effectiveness of different soil rehabilitation treatments. The experimental design consisted of randomized blocks. The aim of this work was to characterize particle-size distributions of the saprolite material and use the information obtained to assess between-block variability. Particle-size distributions of the experimental plots were characterized by multifractal techniques. Ninety-six soil samples were analyzed routinely for particle-size distribution by laser diffractometry in a range of scales, varying from 0.390 to 2000 mu m. Six different textural classes (USDA) were identified with a clay content ranging from 16.9% to 58.4%. Multifractal models described reasonably well the scaling properties of particle-size distributions of the saprolite material. This material exhibits a high entropy dimension, D-1. Parameters derived from the left side (q > 0) of the f(alpha) spectra, D-1, the correlation dimension (D-2) and the range (alpha(0)-alpha(q+)), as well as the total width of the spectra (alpha(max) - alpha(min)) all showed dependence on the clay content. Sand, silt and clay contents were significantly different among treatments as a consequence of soil intrinsic variability. The D, and the Holder exponent of order zero, alpha(0), were not significantly different between treatments; in contrast, D-2 and several fractal attributes describing the width of the f(alpha) spectra were significantly different between treatments. The only parameter showing significant differences between sampling depths was (alpha(0) - alpha(q+)). Scale independent fractal attributes may be useful for characterizing intrinsic particle-size distribution variability. (c) 2006 Elsevier B.V. All rights reserved.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Particle Competition and Cooperation in Networks for Semi-Supervised Learning with Concept Drift

Concept drift is a problem of increasing importance in machine learning and data mining. Data sets under analysis are no longer only static databases, but also data streams in which concepts and data distributions may not be stable over time. However, most learning algorithms produced so far are based on the assumption that data comes from a fixed distribution, so they are not suitable to handle concept drifts. Moreover, some concept drifts applications requires fast response, which means an algorithm must always be (re) trained with the latest available data. But the process of labeling data is usually expensive and/or time consuming when compared to unlabeled data acquisition, thus only a small fraction of the incoming data may be effectively labeled. Semi-supervised learning methods may help in this scenario, as they use both labeled and unlabeled data in the training process. However, most of them are also based on the assumption that the data is static. Therefore, semi-supervised learning with concept drifts is still an open challenge in machine learning. Recently, a particle competition and cooperation approach was used to realize graph-based semi-supervised learning from static data. In this paper, we extend that approach to handle data streams and concept drift. The result is a passive algorithm using a single classifier, which naturally adapts to concept changes, without any explicit drift detection mechanism. Its built-in mechanisms provide a natural way of learning from new data, gradually forgetting older knowledge as older labeled data items became less influent on the classification of newer data items. Some computer simulation are presented, showing the effectiveness of the proposed method.

Stable colloidal suspensions of nanostructured zirconium oxide synthesized by hydrothermal process

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

The frog Dermatonotus muelleri (Boettger 1885) (Anura Microhylidae) shifts its search tactics in response to two different prey distributions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Elicitation of multivariate prior distributions: A nonparametric Bayesian approach

In the context of Bayesian statistical analysis, elicitation is the process of formulating a prior density f(.) about one or more uncertain quantities to represent a person's knowledge and beliefs. Several different methods of eliciting prior distributions for one unknown parameter have been proposed. However, there are relatively few methods for specifying a multivariate prior distribution and most are just applicable to specific classes of problems and/or based on restrictive conditions, such as independence of variables. Besides, many of these procedures require the elicitation of variances and correlations, and sometimes elicitation of hyperparameters which are difficult for experts to specify in practice. Garthwaite et al. (2005) discuss the different methods proposed in the literature and the difficulties of eliciting multivariate prior distributions. We describe a flexible method of eliciting multivariate prior distributions applicable to a wide class of practical problems. Our approach does not assume a parametric form for the unknown prior density f(.), instead we use nonparametric Bayesian inference, modelling f(.) by a Gaussian process prior distribution. The expert is then asked to specify certain summaries of his/her distribution, such as the mean, mode, marginal quantiles and a small number of joint probabilities. The analyst receives that information, treating it as a data set D with which to update his/her prior beliefs to obtain the posterior distribution for f(.). Theoretical properties of joint and marginal priors are derived and numerical illustrations to demonstrate our approach are given. (C) 2010 Elsevier B.V. All rights reserved.

Collision and Stable Regions around Bodies with Simple Geometric Shape

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)