Template-based Gravitational-Wave Echoes Search Using Bayesian Model Selection

The ringdown of the gravitational-wave signal from a merger of two black holes has been suggested as a probe of the structure of the remnant compact object, which may be more exotic than a black hole. It has been pointed out that there will be a train of echoes in the late-time ringdown stage for different types of exotic compact objects. In this paper, we present a template-based search methodology using Bayesian statistics to search for echoes of gravitational waves. Evidence for the presence or absence of echoes in gravitational-wave events can be established by performing Bayesian model selection. The Occam factor in Bayesian model selection will automatically penalize the more complicated model that echoes are present in gravitational-wave strain data because of its higher degree of freedom to fit the data. We find that the search methodology was able to identify gravitational-wave echoes with Abedi et al.'s echoes waveform model about 82.3% of the time in simulated Gaussian noise in the Advanced LIGO and Virgo network and about 61.1% of the time in real noise in the first observing run of Advanced LIGO with $\geq 5\sigma$ significance. Analyses using this method are performed on the data of Advanced LIGO's first observing run, and we find no statistical significant evidence for the detection of gravitational-wave echoes. In particular, we find $<1\sigma$ combined evidence of the three events in Advanced LIGO's first observing run. The analysis technique developed in this paper is independent of the waveform model used, and can be used with different parametrized echoes waveform models to provide more realistic evidence of the existence of echoes from exotic compact objects.Comment: 16 pages, 6 figure

Speaker Identification by BYY Automatic Local Factor Analysis based Three-Level Voting Combination

Local Factor Analysis (LFA) is known as more general and powerful than Gaussian Mixture Model (GMM) in unsupervised learning with local subspace structure analysis. In the literature of text-independent speaker identification, GMM has been widely used and investigated, with some preprocessing or postprocessing approaches, while there still lacks efforts on LFA for this task. In pursuit of fast implementation for LFA modeling, this paper focuses on the Bayesian Ying-Yang automatic learning with data smoothing based regularization (BYY-A), which makes automatic model selection during parameter learning. Furthermore for sequence classification, based on trained LFA models, we design and analyze a three-level combination, namely sequence, classifier and committee, respectively. Different combination approaches are designed with variant sequential topologies and voting schemes. Experimental results on the KING speech corpus demonstrate the proposed approaches' effectiveness and potentials

Three-step Bayesian factor analysis applied to QTL detection in crosses between outbred pig populations

AbstractMarker assisted selection (MAS) can be used to improve the efficiency of genetic selection of traits for which phenotypic measurements are expensive or cannot be obtained on selection candidates, such as carcass traits. Marker information required for MAS may be acquired through the identification of QTLs. Generally, univariate models are used for QTL detection, although multiple-trait models (MTM) may enhance QTL detection and breeding value estimation. In MTM, however, the number of parameters can be large and, if traits are highly correlated, such as carcass traits, estimates of (co)variance matrices may be close to singular. Because of this, dimension reduction techniques such as Factor Analysis (FA) may be useful. The aim of our project is to evaluate the use of FA for structuring (co)variance matrices in the context of Bayesian models for QTL detection in crosses between outbred populations. In our method, QTL effects are postulated at the level of common factors (CF) rather than the original traits, using a three-step approach. In a first step, a MTM is fitted to arrive at estimates of systematic effects and prediction of breeding values (procedure A) and only systematic effect (procedure B). These estimates/predictions are then used to generate an adjusted phenotype that is further analyzed with a Bayesian FA model. This step yields estimates of factor scores for each animal and CF. In the last step, the scores relative to each CF are analyzed independently using probabilities for the line of origin combination. To illustrate the methodology, data on 416 F2 pigs (Brazilian Piau X commercial) with ten traits (5 fat-related, 2 loin measurements, and 3 carcass classification systems) were analyzed. For each of the three resulting CFs, an independent QTL scan was performed on chromosome 7 considering three models: I) null (i.e., absence of QTL); II) additive effect QTL, and III) additive and dominance effect QTL. The posterior probability (PP) of each model was calculated from Bayes factor for each considered procedures (A and B). A Three-step Bayesian factor analysis allowed us to calculate the probability of QTLs that simultaneously affect a group of carcass traits for each position of SSC 7. The removal of systematic effects in the first step of the evaluation (procedure B) allowed that the factor analysis, which was performed in the second step, identify three distinct factors that explained 85% of the total traits variation. For the common factor that represented fat-related traits (bacon depth, midline lower backfat thickness, higher backfat thickness on the shoulder; midline backfat thickness after the last rib; midline backfat thickness on the last lumbar vertebrae) the third step of the analysis showed that the highest probability of an additive QTL effect at the 65cM position was 86%

Bayesian Model Selection in terms of Kullback-Leibler discrepancy

In this article we investigate and develop the practical model assessment and selection methods for Bayesian models, when we anticipate that a promising approach should be objective enough to accept, easy enough to understand, general enough to apply, simple enough to compute and coherent enough to interpret. We mainly restrict attention to the Kullback-Leibler divergence, a widely applied model evaluation measurement to quantify the similarity between the proposed candidate model and the underlying true model, where the true model is only referred to a probability distribution as the best projection onto the statistical modeling space once we try to understand the real but unknown dynamics/mechanism of interest. In addition to review and discussion on the advantages and disadvantages of the historically and currently prevailing practical model selection methods in literature, a series of convenient and useful tools, each designed and applied for different purposes, are proposed to asymptotically unbiasedly assess how the candidate Bayesian models are favored in terms of predicting a future independent observation. What's more, we also explore the connection of the Kullback-Leibler based information criterion to the Bayes factors, another most popular Bayesian model comparison approaches, after seeing the motivation through the developments of the Bayes factor variants. In general, we expect to provide a useful guidance for researchers who are interested in conducting Bayesian data analysis

Bayesian Model Selection in Complex Linear Systems, as Illustrated in Genetic Association Studies

Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent {\it a priori} information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems