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.

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)

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Real-time Sampling of Particulate Matter Smaller than 2.5 µm from Amazon Forest Biomass Combustion

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

Matrix-Assisted Laser Desorption/Ionization Time-of-Flight Mass Spectrometry Characterization of Primary Amine End-Functionalized Polystyrene and Poly(methyl methacrylate) Synthesized by Living Anionic Polymerization Techniques

The reaction of living anionic polymers with 2,2,5,5-tetramethyl-1-(3-bromopropyl)-1-aza-2,5- disilacyclopentane (1) was investigated using coupled thin layer chromatography and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. Structures of byproducts as well as the major product were determined. The anionic initiator having a protected primary amine functional group, 2,2,5,5-tetramethyl- 1-(3-lithiopropyl)-1-aza-2,5-disilacyclopentane (2), was synthesized using all-glass high-vacuum techniques, which allows the long-term stability of this initiator to be maintained. The use of 2 in the preparation of well-defined aliphatic primary amine R-end-functionalized polystyrene and poly(methyl methacrylate) was investigated. Primary amino R-end-functionalized poly(methyl methacrylate) can be obtained near-quantitatively by reacting 2 with 1,1-diphenylethylene in tetrahydrofuran at room temperature prior to polymerizing methyl methacrylate at -78 °C. When 2 is used to initiate styrene at room temperature in benzene, an additive such as N,N,N',N'- tetramethylethylenediamine is necessary to activate the polymerization. However, although the resulting polymers have narrow molecular weight distributions and well-controlled molecular weights, our mass spectra data suggest that the yield of primary amine α-end-functionalized polystyrene from these syntheses is very low. The majority of the products are methyl α-end-functionalized polystyrene.

Few-cycle attosecond pulse chirp effects on asymmetries in ionized electron momentum distributions

The momentum distributions of electrons ionized from H atoms by chirped few-cycle attosecond pulses are investigated by numerically solving the time-dependent Schrödinger equation. The central carrier frequency of the pulse is chosen to be 25 eV, which is well above the ionization threshold. The asymmetry (or difference) in the yield of electrons ionized along and opposite to the direction of linear laser polarization is found to be very sensitive to the pulse chirp (for pulses with fixed carrier-envelope phase), both for a fixed electron energy and for the energy-integrated yield. In particular, the larger the pulse chirp, the larger the number of times the asymmetry changes sign as a function of ionized electron energy. For a fixed chirp, the ionized electron asymmetry is found to be sensitive also to the carrier-envelope phase of the few-cycle pulse.

Subcritical crack growth and in vitro lifetime prediction of resin composites with different filler distributions

Objectives. Verify the influence of different filler distributions on the subcritical crack growth (SCG) susceptibility, Weibull parameters (m and sigma(0)) and longevity estimated by the strength-probability-time (SPT) diagram of experimental resin composites. Methods. Four composites were prepared, each one containing 59 vol% of glass powder with different filler sizes (d(50) = 0.5; 0.9; 1.2 and 1.9 mu m) and distributions. Granulometric analyses of glass powders were done by a laser diffraction particle size analyzer (Sald-7001, Shimadzu, USA). SCG parameters (n and sigma(f0)) were determined by dynamic fatigue (10(-2) to 10(2) MPa/s) using a biaxial flexural device (12 x 1.2 mm; n = 10). Twenty extra specimens of each composite were tested at 10(0) MPa/s to determine m and sigma(0). Specimens were stored in water at 37 degrees C for 24 h. Fracture surfaces were analyzed under SEM. Results. In general, the composites with broader filler distribution (C0.5 and C1.9) presented better results in terms of SCG susceptibility and longevity. C0.5 and C1.9 presented higher n values (respectively, 31.2 +/- 6.2(a) and 34.7 +/- 7.4(a)). C1.2 (166.42 +/- 0.01(a)) showed the highest and C0.5 (158.40 +/- 0.02(d)) the lowest sigma(f0) value (in MPa). Weibull parameters did not vary significantly (m: 6.6 to 10.6 and sigma(0): 170.6 to 176.4 MPa). Predicted reductions in failure stress (P-f = 5%) for a lifetime of 10 years were approximately 45% for C0.5 and C1.9 and 65% for C0.9 and C1.2. Crack propagation occurred through the polymeric matrix around the fillers and all the fracture surfaces showed brittle fracture features. Significance. Composites with broader granulometric distribution showed higher resistance to SCG and, consequently, higher longevity in vitro. (C) 2012 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

On scale-mixture Birnbaum-Saunders distributions

We present for the first time a justification on the basis of central limit theorems for the family of life distributions generated from scale-mixture of normals. This family was proposed by Balakrishnan et al. (2009) and can be used to accommodate unexpected observations for the usual Birnbaum-Saunders distribution generated from the normal one. The class of scale-mixture of normals includes normal, slash, Student-t, logistic, double-exponential, exponential power and many other distributions. We present a model for the crack extensions where the limiting distribution of total crack extensions is in the class of scale-mixture of normals. (C) 2012 Elsevier B.V. All rights reserved.

Comparing non-stationary and irregularly spaced time series

In this paper, we present approximate distributions for the ratio of the cumulative wavelet periodograms considering stationary and non-stationary time series generated from independent Gaussian processes. We also adapt an existing procedure to use this statistic and its approximate distribution in order to test if two regularly or irregularly spaced time series are realizations of the same generating process. Simulation studies show good size and power properties for the test statistic. An application with financial microdata illustrates the test usefulness. We conclude advocating the use of these approximate distributions instead of the ones obtained through randomizations, mainly in the case of irregular time series. (C) 2012 Elsevier B.V. All rights reserved.

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.

Investigation of the nuclear matter density distributions of the exotic 12 Be, 14 Be and 8 B nuclei by elastic proton scattering in inverse kinematics

The proton-nucleus elastic scattering at intermediate energies is a well-established method for the investigation of the nuclear matter distribution in stable nuclei and was recently applied also for the investigation of radioactive nuclei using the method of inverse kinematics. In the current experiment, the differential cross sections for proton elastic scattering on the isotopes $^{7,9,10,11,12,14}$Be and $^8$B were measured. The experiment was performed using the fragment separator at GSI, Darmstadt to produce the radioactive beams. The main part of the experimental setup was the time projection ionization chamber IKAR which was simultaneously used as hydrogen target and a detector for the recoil protons. Auxiliary detectors for projectile tracking and isotope identification were also installed. As results from the experiment, the absolute differential cross sections d$sigma$/d$t$ as a function of the four momentum transfer $t$ were obtained. In this work the differential cross sections for elastic p-$^{12}$Be, p-$^{14}$Be and p-$^{8}$B scattering at low $t$ ($t leq$~0.05~(GeV/c)$^2$) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The analysis of the differential cross section for the isotope $^{14}$Be shows that a good description of the experimental data is obtained when density distributions consisting of separate core and halo components are used. The determined {it rms} matter radius is $3.11 pm 0.04 pm 0.13$~fm. In the case of the $^{12}$Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of $2.82 pm 0.03 pm 0.12$~fm was determined. An interesting result is that the free $^{12}$Be nucleus behaves differently from the core of $^{14}$Be and is much more extended than it. The data were also compared with theoretical densities calculated within the FMD and the few-body models. In the case of $^{14}$Be, the calculated cross sections describe the experimental data well while, in the case of $^{12}$Be there are discrepancies in the region of high momentum transfer. Preliminary experimental results for the isotope $^8$B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is $2.60pm 0.02pm 0.26$~fm. The data were compared with microscopic calculations in the frame of the FMD model and reasonable agreement was observed. The results obtained in the present analysis are in most cases consistent with the previous experimental studies of the same isotopes with different experimental methods (total interaction and reaction cross section measurements, momentum distribution measurements). For future investigation of the structure of exotic nuclei a universal detector system EXL is being developed. It will be installed at the NESR at the future FAIR facility where higher intensity beams of radioactive ions are expected. The usage of storage ring techniques provides high luminosity and low background experimental conditions. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented.

Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons

Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1-4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron's firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (<10 ms, PYR neurons only), to fast adaptation (<300 ms), early facilitation (0.5-1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

Brain connectivity at different time-scales measured with EEG

We present an overview of different methods for decomposing a multichannel spontaneous electroencephalogram (EEG) into sets of temporal patterns and topographic distributions. All of the methods presented here consider the scalp electric field as the basic analysis entity in space. In time, the resolution of the methods is between milliseconds (time-domain analysis), subseconds (time- and frequency-domain analysis) and seconds (frequency-domain analysis). For any of these methods, we show that large parts of the data can be explained by a small number of topographic distributions. Physically, this implies that the brain regions that generated one of those topographies must have been active with a common phase. If several brain regions are producing EEG signals at the same time and frequency, they have a strong tendency to do this in a synchronized mode. This view is illustrated by several examples (including combined EEG and functional magnetic resonance imaging (fMRI)) and a selective review of the literature. The findings are discussed in terms of short-lasting binding between different brain regions through synchronized oscillations, which could constitute a mechanism to form transient, functional neurocognitive networks.

Development of record-breaking statistics for climatological time-series analysis

The number of record-breaking events expected to occur in a strictly stationary time-series depends only on the number of values in the time-series, regardless of distribution. This holds whether the events are record-breaking highs or lows and whether we count from past to present or present to past. However, these symmetries are broken in distinct ways by trends in the mean and variance. We define indices that capture this information and use them to detect weak trends from multiple time-series. Here, we use these methods to answer the following questions: (1) Is there a variability trend among globally distributed surface temperature time-series? We find a significant decreasing variability over the past century for the Global Historical Climatology Network (GHCN). This corresponds to about a 10% change in the standard deviation of inter-annual monthly mean temperature distributions. (2) How are record-breaking high and low surface temperatures in the United States affected by time period? We investigate the United States Historical Climatology Network (USHCN) and find that the ratio of record-breaking highs to lows in 2006 increases as the time-series extend further into the past. When we consider the ratio as it evolves with respect to a fixed start year, we find it is strongly correlated with the ensemble mean. We also compare the ratios for USHCN and GHCN (minus USHCN stations). We find the ratios grow monotonically in the GHCN data set, but not in the USHCN data set. (3) Do we detect either mean or variance trends in annual precipitation within the United States? We find that the total annual and monthly precipitation in the United States (USHCN) has increased over the past century. Evidence for a trend in variance is inconclusive.

EXPLORATION OF THE MTSAT2 SATELLITE CAPABILITIES FOR REAL TIME DETECTION AND CHARACTERIZATION OF VOLCANIC EMISSIONS

In this report, we attempt to define the capabilities of the infrared satellite remote sensor, Multifunctional Transport Satellite-2 (MTSAT-2) (i.e. a geosynchronous instrument), in characterizing volcanic eruptive behavior in the highly active region of Indonesia. Sulfur dioxide data from NASA's Ozone Monitoring Instrument (OMI) (i.e. a polar orbiting instrument) are presented here for validation of the processes interpreted using the thermal infrared datasets. Data provided from two case studies are analyzed specifically for eruptive products producing large thermal anomalies (i.e. lava flows, lava domes, etc.), volcanic ash and SO2 clouds; three distinctly characteristic and abundant volcanic emissions. Two primary methods used for detection of heat signatures are used and compared in this report including, single-channel thermal radiance (4-µm) and the normalized thermal index (NTI) algorithm. For automated purposes, fixed thresholds must be determined for these methods. A base minimum detection limit (MDL) for single-channel thermal radiance of 2.30E+05 Wm- 2sr-1m-1 and -0.925 for NTI generate false alarm rates of 35.78% and 34.16%, respectively. A spatial comparison method, developed here specifically for use in Indonesia and used as a second parameter for detection, is implemented to address the high false alarm rate. For the single-channel thermal radiance method, the utilization of the spatial comparison method eliminated 100% of the false alarms while maintaining every true anomaly. The NTI algorithm showed similar results with only 2 false alarms remaining. No definitive difference is observed between the two thermal detection methods for automated use; however, the single-channel thermal radiance method coupled with the SO2 mass abundance data can be used to interpret volcanic processes including the identification of lava dome activity at Sinabung as well as the mechanism for the dome emplacement (i.e. endogenous or exogenous). Only one technique, the brightness temperature difference (BTD) method, is used for the detection of ash. Trends of ash area, water/ice area, and their respective concentrations yield interpretations of increased ice formation, aggregation, and sedimentation processes that only a high-temporal resolution instrument like the MTSAT-2 can analyze. A conceptual model of a secondary zone of aggregation occurring in the migrating Kelut ash cloud, which decreases the distal fine-ash component and hazards to flight paths, is presented in this report. Unfortunately, SO2 data was unable to definitively reinforce the concept of a secondary zone of aggregation due to the lack of a sufficient temporal resolution. However, a detailed study of the Kelut SO2 cloud is used to determine that there was no climatic impacts generated from this eruption due to the atmospheric residence times and e-folding rate of ~14 days for the SO2. This report applies the complementary assets offered by utilizing a high-temporal and a high-spatial resolution satellite, and it demonstrates that these two instruments can provide unparalleled observations of dynamic volcanic processes.