Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual evaluation of such $p$-values is by simulations, and such simulations do verify that the global distribution of the $p$-values is uniform(0, 1), to high accuracy in repeated sampling. The derivation of the $p$-values, however, asserts a stronger statement, that they have a uniform(0, 1) distribution conditionally, given identified precision information provided by the data. We take a simple regression example that involves exact precision information and use large sample techniques to extract highly accurate information as to the statistical position of the data point with respect to the parameter: specifically, we examine various $p$-values and Bayesian posterior survivor $s$-values for validity. With observed data we numerically evaluate the various $p$-values and $s$-values, and we also record the related general formulas. We then assess the numerical values for accuracy using Markov chain Monte Carlo (McMC) methods. We also propose some third-order likelihood-based procedures for obtaining means and variances of Bayesian posterior distributions, again followed by McMC assessment. Finally we propose some adaptive McMC methods to improve the simulation acceptance rates. All these methods are based on asymptotic analysis that derives from the effect of additional data. And the methods use simple calculations based on familiar maximizing values and related informations. The example illustrates the general formulas and the ease of calculations, while the McMC assessments demonstrate the numerical validity of the $p$-values as percentage position of a data point. The example, however, is very simple and transparent, and thus gives little indication that in a wide generality of models the formulas do accurately separate information for almost any parameter of interest, and then do give accurate $p$-value determinations from that information. As illustration an enigmatic problem in the literature is discussed and simulations are recorded; various examples in the literature are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Spectral Evolution of Hot White Dwarf Stars. IV. The Diffusion and Mixing of Residual Hydrogen in Helium-rich White Dwarfs

In the framework of our extensive modeling study of the spectral evolution of white dwarfs, we present here a new set of detailed calculations of the transport of residual hydrogen in helium-rich white dwarfs. First, we investigate the so-called float-up process at high effective temperature, whereby the upward diffusion of trace hydrogen leads to the formation of a hydrogen atmosphere. We examine the dependence of this phenomenon on the initial hydrogen abundance and on the strength of the radiative wind that opposes gravitational settling. Combined with our empirical knowledge of spectral evolution, our simulations provide new quantitative constraints on the hydrogen content of the hot helium-dominated white dwarf population. Then, we study the outcome of the so-called convective dilution process at low effective temperature, whereby the superficial hydrogen layer is mixed within the underlying helium-rich envelope. In stark contrast with previous works on convective dilution, we demonstrate that, under reasonable assumptions, our models successfully reproduce the observed atmospheric composition of cool DBA stars, thereby solving one of the most important problems of spectral evolution theory. This major improvement is due to our self-consistent modeling of the earlier float-up process, which predicts the existence of a massive hydrogen reservoir underneath the thin superficial layer. We argue that the trace hydrogen detected at the surface of DBA white dwarfs is, in most cases, of primordial origin rather than the result of external accretion.Comment: 21 pages, 9 figures, accepted for publication in The Astrophysical Journa

Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances ($\approx$10~$\mu m$) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig

Maternal iron status during pregnancy and respiratory and atopic outcomes in the offspring: a Mendelian randomisation study.

INTRODUCTION: Limited evidence from birth cohort studies suggests that lower prenatal iron status may be a risk factor for childhood respiratory and atopic outcomes, but these observational findings may be confounded. Mendelian randomisation (MR) can potentially provide unconfounded estimates of causal effects by using common genetic variants as instrumental variables. We aimed to study the relationship between prenatal iron status and respiratory and atopic outcomes in the offspring using MR. METHODS: In the Avon Longitudinal Study of Parents and Children birth cohort, we constructed four maternal genotypic risk scores by summing the total number of risk alleles (associated with lower iron status) across single nucleotide polymorphisms known to be associated with at least one of four iron biomarkers (serum iron, ferritin, transferrin and transferrin saturation). We used MR to study their associations with respiratory and atopic outcomes in children aged 7-9 years (n=6002). RESULTS: When analyses were restricted to mothers without iron supplementation during late pregnancy, negative associations were found between the maternal transferrin saturation score and childhood forced expiratory volume in 1 s and forced vital capacity (difference in age, height and gender-adjusted SD units per SD increase in genotypic score: -0.05 (-0.09, -0.01) p=0.03, and -0.04 (-0.08, 0.00) p=0.04, respectively). CONCLUSION: Using MR we have found weak evidence suggesting that low maternal iron status during pregnancy may cause impaired childhood lung function

On the Nature of Ultracool White Dwarfs: Not so Cool Afterall

A recent analysis of the 100 pc white dwarf sample in the SDSS footprint demonstrated for the first time the existence of a well defined ultracool -- or IR-faint -- white dwarf sequence in the Hertzsprung-Russell diagram. Here we take advantage of this discovery to enlarge the IR-faint white dwarf sample threefold. We expand our selection to the entire Pan-STARRS survey footprint as well as the Montreal White Dwarf Database 100 pc sample, and identify 37 candidates with strong flux deficits in the optical. We present follow-up Gemini optical spectroscopy of 30 of these systems, and confirm all of them as IR-faint white dwarfs. We identify an additional set of 33 objects as candidates based on their colors and magnitudes. We present a detailed model atmosphere analysis of all 70 newly identified IR-faint white dwarfs together with 35 previously known objects reported in the literature. We discuss the physics of model atmospheres and show that the key physical ingredient missing in our previous generation of model atmospheres was the high-density correction to the He-minus free-free absorption coefficient. With new model atmospheres calculated for the purpose of this analysis, we now obtain significantly higher effective temperatures and larger stellar masses for these IR-faint white dwarfs than the Teff and M values reported in previous analyses, thus solving a two decade old problem. In particular, we identify in our sample a group of ultramassive white dwarfs in the Debye cooling phase with stellar parameters never measured before.Comment: Accepted for publication in The Astrophysical Journal (33 pages, 21 figures

Does the 1/f frequency-scaling of brain signals reflect self-organized critical states?

Many complex systems display self-organized critical states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of self-organized critical states in neuronal activity. By analyzing simultaneous recordings of global and neuronal activities, we confirm the 1/f scaling of global variables for selected frequency bands, but show that neuronal activity is not consistent with critical states. We propose a model of 1/f scaling which does not rely on critical states, and which is testable experimentally.Comment: 3 figures, 6 page