Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

Nonparametric Reconstruction of the Dark Energy Equation of State from Diverse Data Sets

The cause of the accelerated expansion of the Universe poses one of the most fundamental questions in physics today. In the absence of a compelling theory to explain the observations, a first task is to develop a robust phenomenology. If the acceleration is driven by some form of dark energy, then, the phenomenology is determined by the dark energy equation of state w. A major aim of ongoing and upcoming cosmological surveys is to measure w and its time dependence at high accuracy. Since w(z) is not directly accessible to measurement, powerful reconstruction methods are needed to extract it reliably from observations. We have recently introduced a new reconstruction method for w(z) based on Gaussian process modeling. This method can capture nontrivial time-dependences in w(z) and, most importantly, it yields controlled and unbaised error estimates. In this paper we extend the method to include a diverse set of measurements: baryon acoustic oscillations, cosmic microwave background measurements, and supernova data. We analyze currently available data sets and present the resulting constraints on w(z), finding that current observations are in very good agreement with a cosmological constant. In addition we explore how well our method captures nontrivial behavior of w(z) by analyzing simulated data assuming high-quality observations from future surveys. We find that the baryon acoustic oscillation measurements by themselves already lead to remarkably good reconstruction results and that the combination of different high-quality probes allows us to reconstruct w(z) very reliably with small error bounds.Comment: 14 pages, 9 figures, 3 table

Current Migration Trends in Northeast Asia and the Russian Far East

The purpose of this work is to analyse migration trends currently observed in the countries of Northeast Asia. In the context of the pandemic, and then the beginning of a tough phase of confrontation between Russia and Western countries, certain migration trends have changed. Comparative and historical approaches were used in the study to examine the features of the migration agenda in the region, as well as the recent transformation of migration flows in different countries. It was concluded that nowadays all countries of the region need migrants, create conditions to attract them and compete for labour resources.Цель данной работы является анализ современных миграционных тенденций, присущих странам Северо-Восточной Азии на современном этапе. В условиях пандемии, а затем и начала жесткой фазы конфронтации между Россией и западными странами отдельные миграционные тренды претерпели изменения. В рамках данного исследования были использованы компаративистский и исторический подходы, которые дали возможность проанализировать особенности формирования миграционной повестки в регионе, а также того, как трансформировались в последние годы миграционные потоки в разных странах. В рамках данной работы автор приходит к выводу, что абсолютно все страны региона на сегодняшний день остро нуждаются в мигрантах, создают для их привлечения условия и включаются в международную борьбу за трудовые ресурсы

PROBLEMS OF NATIONAL SECURITY AND EASTERN REgIONS OF RUSSIA IN THE CONTEXT OF RUSSIA’S PIVOT TO THE EAST

В рамках данной работы автор анализирует проблемы национальной безопасности России на современном этапе, сквозь призму их преломления на азиатских регионах нашей страны. Сибирь, и, в особенности, Дальний Восток, значительно отстают от западных регионов России в своем экономическом развитии, в развитии человеческого капитала и в иных сферах. В последние годы принят целый ряд программ, предпринимается комплекс мер, которые должны способствовать развитию регионов, преодолению их отставания. Автор стремится проанализировать эти меры, насколько они являются своевременными и эффективными.Within the framework of this work, the author analyzes the problems of Russia’s national security at the present stage, through the prism of their refraction in the Asian regions of our country. Siberia, and, in particular, the Far East, lag significantly behind the western regions of Russia in its economic development, in the development of human capital and in other areas. In recent years, a number of programs have been adopted, a set of measures is being taken that should contribute to the development of regions and overcome their lag. The author seeks to analyze these measures, to what extent they are timely and effectiv

A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment

Nonparametric Reconstruction of the Dark Energy Equation of State

A basic aim of ongoing and upcoming cosmological surveys is to unravel the mystery of dark energy. In the absence of a compelling theory to test, a natural approach is to better characterize the properties of dark energy in search of clues that can lead to a more fundamental understanding. One way to view this characterization is the improved determination of the redshift-dependence of the dark energy equation of state parameter, w(z). To do this requires a robust and bias-free method for reconstructing w(z) from data that does not rely on restrictive expansion schemes or assumed functional forms for w(z). We present a new nonparametric reconstruction method that solves for w(z) as a statistical inverse problem, based on a Gaussian Process representation. This method reliably captures nontrivial behavior of w(z) and provides controlled error bounds. We demonstrate the power of the method on different sets of simulated supernova data; the approach can be easily extended to include diverse cosmological probes.Comment: 16 pages, 11 figures, accepted for publication in Physical Review

Extracting galactic binary signals from the first round of Mock LISA Data Challenges

We report on the performance of an end-to-end Bayesian analysis pipeline for detecting and characterizing galactic binary signals in simulated LISA data. Our principal analysis tool is the Blocked-Annealed Metropolis Hasting (BAM) algorithm, which has been optimized to search for tens of thousands of overlapping signals across the LISA band. The BAM algorithm employs Bayesian model selection to determine the number of resolvable sources, and provides posterior distribution functions for all the model parameters. The BAM algorithm performed almost flawlessly on all the Round 1 Mock LISA Data Challenge data sets, including those with many highly overlapping sources. The only misses were later traced to a coding error that affected high frequency sources. In addition to the BAM algorithm we also successfully tested a Genetic Algorithm (GA), but only on data sets with isolated signals as the GA has yet to be optimized to handle large numbers of overlapping signals.Comment: 13 pages, 4 figures, submitted to Proceedings of GWDAW-11 (Berlin, Dec. '06

From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB

We use type Ia supernovae (SN Ia) data in combination with recent baryonic acoustic oscillations (BAO) and cosmic microwave background (CMB) observations to constrain a kink-like parametrization of the deceleration parameter ($q$). This $q$-parametrization can be written in terms of the initial ($q_i$) and present ($q_0$) values of the deceleration parameter, the redshift of the cosmic transition from deceleration to acceleration ($z_t$) and the redshift width of such transition ($\tau$). By assuming a flat space geometry, $q_i=1/2$ and adopting a likelihood approach to deal with the SN Ia data we obtain, at the 68% confidence level (C.L.), that: $z_t=0.56^{+0.13}_{-0.10}$, $\tau=0.47^{+0.16}_{-0.20}$ and $q_0=-0.31^{+0.11}_{-0.11}$ when we combine BAO/CMB observations with SN Ia data processed with the MLCS2k2 light-curve fitter. When in this combination we use the SALT2 fitter we get instead, at the same C.L.: $z_t=0.64^{+0.13}_{-0.07}$, $\tau=0.36^{+0.11}_{-0.17}$ and $q_0=-0.53^{+0.17}_{-0.13}$. Our results indicate, with a quite general and model independent approach, that MLCS2k2 favors Dvali-Gabadadze-Porrati-like cosmological models, while SALT2 favors $\Lambda$CDM-like ones. Progress in determining the transition redshift and/or the present value of the deceleration parameter depends crucially on solving the issue of the difference obtained when using these two light-curve fitters.Comment: 25 pages, 9 figure

Bayesian estimation of incomplete data using conditionally specified priors

In this paper, a class of conjugate prior for estimating incomplete count data based on a broad class of conjugate prior distributions is presented. The new class of prior distributions arises from a conditional perspective, making use of the conditional specification methodology and can be considered as the generalisation of the form of prior distributions that have been used previously in the estimation of in- complete count data well. Finally, some examples of simulated and real data are given

Automated classification of periodic variable stars{Improved methodology for the automated classification of periodic variable stars}

We present a novel automated methodology to detect and classify periodic variable stars in a large database of photometric time series. The methods are based on multivariate Bayesian statistics and use a multi-stage approach. We applied our method to the ground-based data of the TrES Lyr1 field, which is also observed by the Kepler satellite, covering ~26000 stars. We found many eclipsing binaries as well as classical non-radial pulsators, such as slowly pulsating B stars, Gamma Doradus, Beta Cephei and Delta Scuti stars. Also a few classical radial pulsators were found.Comment: 11 pages, 6 figures Accepted for publication in MNRA