Hierarchical Bayesian Scheme Research Articles

Hierarchical Bayesian calibration of deck deflection models using distributed fiber optic strain data

A naval hovercraft was outfitted with a distributed fiber optic sensing system (FOSS) on its cargo deck in which two fibers were placed along orthogonal axes. A series of trucks were loaded onto the cargo deck to simulate operational loading conditions and the resulting strain profiles were measured by the distributed FOSS. The aim of this study is to quantify the deck deflections that correspond to the measured strains under different vehicular loads. This is accomplished by idealizing the cargo deck as a rectangular plate and using the data to estimate the associated plate model parameters. In order to account for measurement noise and model prediction error, as well as the inherent variability of inferences made with different data sets, a hierarchical Bayesian scheme that considers both the model parameter uncertainty and the prediction error variance is utilized to derive the posterior distributions of the model hyper-parameters, i.e., their mean and variance. Given the volume of FOSS strain data available, different approaches were taken for incorporating the data into the hierarchical approach in order to determine whether the inclusion of all available strain data meaningfully reduced the uncertainty compared to using only time-averaged strain. Comparisons between the different approaches are explored in the context of 95% confidence intervals for strain profiles, deck deflection envelopes, and reliability indices based on allowable deflections.

On the importance of source population models for gravitational-wave cosmology

Knowledge of the shape of the mass spectrum of compact objects can be used to help break the degeneracy between the mass and redshift of the gravitational wave (GW) sources, and thus can be used to infer cosmological parameters in the absence of redshift measurements obtained from electromagnetic observations. In this paper, we study extensively different aspects of this approach, including its computational limits and achievable accuracy. We focus on ground-based detectors with current and future sensitivities, we first perform the analysis of an extensive set of simulated data with a hierarchical Bayesian scheme inferring population and cosmological parameters. We consider a population model (power-law plus Gaussian) which exhibits characteristic scales (extremes of the mass spectrum, presence of an accumulation point) that allows an indirect estimate of the source redshift. Our analysis of this catalog highlights and quantifies the tight interplay between source population and cosmological parameters, as well as the influence of initial assumptions (whether formulated on the source or cosmological parameters). We then validate our results by an "end-to-end" analysis using simulated GW data and posterior samples generated from Bayesian samplers used for GW parameter estimation, thus mirroring the analysis chain used for observational data for the first time in literature. Our results then lead us to re-examine the estimation of $H_0$ obtained with GWTC-1, and we show explicitly how population assumptions impact the final $H_0$ result. Our results underline the importance of inferring population and cosmological parameters jointly (and not separately as is often assumed). The only exception, as we discuss, is if an electromagnetic counterpart was to be observed for all the BBH events: then the population assumptions have less impact on the estimation of cosmological parameters.

Galactic googly: the rotation–metallicity bias in the inner stellar halo of the Milky Way

The first and second moments of stellar velocities encode important information about the formation history of the Galactic halo. However, due to the lack of tangential motion and inaccurate distances of the halo stars, the velocity moments in the Galactic halo have largely remained "known unknowns". Fortunately, our off-centric position within the Galaxy allows us to estimate these moments in the galacto-centric frame using the observed radial velocities of the stars alone. We use these velocities coupled with the Hierarchical Bayesian scheme, which allows easy marginalisation over the missing data (the proper-motion, and uncertainty-free distance and line-of-sight velocity), to measure the velocity dispersions, orbital anisotropy ($\beta$) and streaming motion ($v_{\rm rot}$) of the halo main-sequence turn-off (MSTO) and K-giant (KG) stars in the inner stellar halo (r $\lesssim 15$ kpc). We study the metallicity bias in kinematics of the halo stars and observe that the comparatively metal-rich ([Fe/H]$>-1.4$) and the metal-poor ([Fe/H]$\leq - 1.4$) MSTO samples show a clear systematic difference in $v_{\rm rot} \sim 20-40$ km s$^{-1}$, depending on how restrictive the spatial cuts to cull the disk contamination are. The bias is also detected in KG samples but with less certainty. Both MSTO and KG populations suggest that the inner stellar halo of the Galaxy is radially biased i.e. $\sigma_r>\sigma_\theta$ or $\sigma_\phi$ and $\beta \simeq 0.5$. The apparent metallicity contrariety in the rotation velocity among the halo sub-populations supports the co-existence of multiple populations in the galactic halo that may have formed through distinct formation scenarios, i.e. in-situ versus accretion.

Online sparse and low-rank subspace learning from incomplete data: A Bayesian view

Extracting the underlying low-dimensional space where high-dimensional signals often reside has been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. Moreover, working with incomplete large scale datasets has recently been commonplace for diverse reasons. This so called big data era we are currently living calls for devising online subspace learning algorithms that can suitably handle incomplete data. Their anticipated goal is to recursively estimate the unknown subspace by processing streaming data sequentially, thus reducing computational complexity. In this paper, an online variational Bayes subspace learning algorithm from partial observations is presented. To account for the unawareness of the true rank of the subspace, commonly met in practice, low-rankness is explicitly imposed on the sought subspace data matrix by exploiting sparse Bayesian learning principles. Sparsity, simultaneously to low-rankness, is favored on the subspace matrix by the sophisticated hierarchical Bayesian scheme that is adopted. The proposed algorithm is thus adept in dealing with applications whereby the underlying subspace may be also sparse. The new subspace tracking scheme outperforms its state-of-the-art counterparts in terms of estimation accuracy, in a variety of experiments conducted on both simulated and real data.

Individual efficiency for the use of feed resources in rabbits1

A Bayesian procedure, which allows consideration of the individual variation in the feed resource allocation pattern, is described and implemented in 2 sire lines of rabbit (Caldes and R). The procedure is based on a hierarchical Bayesian scheme, where the first stage of the model consists of a multiple regression model of feed intake on metabolic BW and BW gain. In a second stage, an animal model was assumed including batch, parity order, litter size, and common environmental litter effects. Animals were reared during the fattening period (from weaning at 32 d of age to 60 d of age) in individual cages on an experimental farm, and were fed ad libitum with a commercial diet. Body weight (g) and cumulative feed intake (g) were recorded weekly. Individual BW gain (g) and average BW (ABW, g) were calculated from these data for each 7-d period. Metabolic BW (g(0.75)) was estimated as ABW(0.75). The number of animals actually measured was 444 and 445 in the Caldes and R lines, respectively. Marginal posterior distributions of the genetic parameters were obtained by Gibbs sampling. Posterior means (posterior SD) for heritabilities for partial coefficients of regression of feed intake on metabolic BW and feed intake on BW gain were estimated to be 0.35 (0.17) and 0.40 (0.17), respectively, in the Caldes line and 0.26 (0.19) and 0.27 (0.14), respectively, in line R. The estimated posterior means (posterior SD) for the proportion of the phenotypic variance due to common litter environmental effects of the same coefficients of regression were respectively, 0.39 (0.14) and 0.28 (0.13) in the Caldes line and 0.44 (0.22) and 0.49 (0.14) in line R. These results suggest that efficiency of use of feed resources could be improved by including these coefficients in an index of selection.

The value of prior information for detection of QTL affecting longitudinal traits: an example using Von Bertalanffy growth function

A Bayesian procedure is presented for detecting quantitative trait loci (QTL) affecting longitudinal traits. The statistical model assumes a QTL affecting the prior distribution of the parameters of a given production function, under a hierarchical Bayesian scheme. Marginal posterior distributions for the effects associated with the QTL are calculated using Markov chain Monte Carlo methods. Furthermore, the Bayesian analysis allows the use of some available relevant information that can improve the detection of the QTL substantially. To illustrate the procedure, an example of QTL detection using the Von Bertalanffy growth function is presented with a F2 pig population bred from Iberian boars and Landrace sows. Animals of the F2 population were genotyped for seven markers in chromosome 2 (SSC2). Two prior distributions for the mean effect of the parameters related with birth and adult weight were compared. On the one hand, vague prior distributions were used, and, on the other, there were assumed univariate Gaussian distributions that ensure biologically meaningful adult and birth weights on the posterior growth curves. Results from the second prior distribution supported the presence of QTL, by showing that individuals with both alleles of Iberian origin had lower rates of maturation. On the contrary, when vague priors were used, the procedure was not able to detect QTL.

Bayesian reconstructions and predictions of nonlinear dynamical systems via the hybrid Monte Carlo scheme

Time series prediction is a rather difficult problem when the dynamics behind the data originates from a nonlinear system and its functional form is unknown. The hierarchical Bayesian scheme previously proposed by the authors has been shown to be reasonably sound for nontrivial real world applications. A great difficulty implementing the Hierarchical Bayesian scheme lies in the computation of posterior distributions as well as predictive distributions for which Quadratic Approximations have been used so far. This paper attempts to compute predictive mean and error bar for nonlinear time series prediction problems via the Hybrid Monte Carlo scheme, a particular class of Markov Chain Monte Carlo without the Quadratic Approximations. The scheme is tested against two concrete problems; Chaotic time series prediction, and Building air-conditioning Load Prediction. The prediction results are compared with those using the Quadratic Approximations which have been used in the previous works of the authors’ group. The proposed scheme outperforms the Quadratic Approximations.