Bayesian Inference Algorithm Research Articles

Shallow water transmission loss inversion for seafloor characterization

A Bayesian inference algorithm has been developed for seafloor geoacoustic parameter determination through analysis of transmission loss measurements taken in shallow water environments. It uses a parallel tempering scheme for improved parameter space sampling and bias reduction, and evaluates ray acoustic forward models in Bellhop. The algorithm is verified by application to synthetic data generated using finite element and ray acoustic propagation models for frequencies from 0.5 to 5 kHz. Verification is assessed through the ability to recover inversion parameter values prescribed within the synthetic data, and inspection of ambiguous inversion situations. Initial inversion parameters include bulk sediment density, sound speed, and attenuation, as well as ripple height and wavelength for some seafloors. The inversion yields posterior probability distributions for each inversion parameter, which inform parameter resolvability and covariance. Algorithm accuracy, efficiency, and applicability to data from different ocean environments will be discussed. [This work has been supported by the Office of Naval Research, Task Force Ocean.]

PERTURBED FACTOR ANALYSIS: ACCOUNTING FOR GROUP DIFFERENCES IN EXPOSURE PROFILES.

In this article we investigate group differences in phthalate exposure profiles using NHANES data. Phthalates are a family of industrial chemicals used in plastics and as solvents. There is increasing evidence of adverse health effects of exposure to phthalates on reproduction and neurodevelopment and concern about racial disparities in exposure. We would like to identify a single set of low-dimensional factors summarizing exposure to different chemicals, while allowing differences across groups. Improving on current multigroup additive factor models, we propose a class of Perturbed Factor Analysis (PFA) models that assume a common factor structure after perturbing the data via multiplication by a group-specific matrix. Bayesian inference algorithms are defined using a matrix normal hierarchical model for the perturbation matrices. The resulting model is just as flexible as current approaches in allowing arbitrarily large differences across groups but has substantial advantages that we illustrate in simulation studies. Applying PFA to NHANES data, we learn common factors summarizing exposures to phthalates, while showing clear differences across groups.

Identifying the Recurrence of Sleep Apnea Using A Harmonic Hidden Markov Model.

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a trans-dimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.

A Bayesian inference and model selection algorithm with an optimization scheme to infer the model noise power

ABSTRACT Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent years, Bayesian inference tools have gained traction. Usually, Markov chain Monte Carlo (MCMC) methods are applied to inference problems, but they present some disadvantages, particularly when comparing different models fitted to the same data set. Other Bayesian methods can deal with this issue in a natural and effective way. We have implemented an importance sampling (IS) algorithm adapted to Bayesian inference problems in which the power of the noise in the observations is not known a priori. The main advantage of IS is that the model evidence can be derived directly from the so-called importance weights – while MCMC methods demand considerable postprocessing. The use of our adaptive target adaptive importance sampling (ATAIS) method is shown by inferring, on the one hand, the parameters of a simulated flaring event that includes a damped oscillation and, on the other hand, real data from the Kepler mission. ATAIS includes a novel automatic adaptation of the target distribution. It automatically estimates the variance of the noise in the model. ATAIS admits parallelization, which decreases the computational run-times notably. We compare our method against a nested sampling method within a model selection problem.

Small-scale lithospheric heterogeneity characterization using Bayesian inference and energy flux models

SUMMARYObservations from different disciplines have shown that our planet is highly heterogeneous at multiple scale lengths. Still, many seismological Earth models tend not to include any small-scale heterogeneity or lateral velocity variations, which can affect measurements and predictions based on these homogeneous models. In this study, we describe the lithospheric small-scale isotropic heterogeneity structure in terms of the intrinsic, diffusion and scattering quality factors, as well as an autocorrelation function, associated with a characteristic scale length (a) and RMS fractional velocity fluctuations (ε). To obtain this characterization, we combined a single-layer and a multilayer energy flux models with a new Bayesian inference algorithm. Our synthetic tests show that this technique can successfully retrieve the input parameter values for 1- or 2-layer models and that our Bayesian algorithm can resolve whether the data can be fitted by a single set of parameters or a range of models is required instead, even for very complex posterior probability distributions. We applied this technique to three seismic arrays in Australia: Alice Springs array (ASAR), Warramunga Array (WRA) and Pilbara Seismic Array (PSAR). Our single-layer model results suggest intrinsic and diffusion attenuation are strongest for ASAR, while scattering and total attenuation are similarly strong for ASAR and WRA. All quality factors take higher values for PSAR than for the other two arrays, implying that the structure beneath this array is less attenuating and heterogeneous than for ASAR or WRA. The multilayer model results show the crust is more heterogeneous than the lithospheric mantle for all arrays. Crustal correlation lengths and RMS velocity fluctuations for these arrays range from ∼0.2 to 1.5 km and ∼2.3 to 3.9 per cent, respectively. Parameter values for the upper mantle are not unique, with combinations of low values of the parameters (a < 2 km and ε < ∼2.5 per cent) being as likely as those with high correlation length and velocity variations (a > 5 km and ε > ∼2.5 per cent, respectively). We attribute the similarities in the attenuation and heterogeneity structure beneath ASAR and WRA to their location on the proterozoic North Australian Craton, as opposed to PSAR, which lies on the archaean West Australian Craton. Differences in the small-scale structure beneath ASAR and WRA can be ascribed to the different tectonic histories of these two regions of the same craton. Overall, our results highlight the suitability of the combination of an energy flux model and a Bayesian inference algorithm for future scattering and small-scale heterogeneity studies, since our approach allows us to obtain and compare the different quality factors, while also giving us detailed information about the trade-offs and uncertainties in the determination of the scattering parameters.

MADLens, a python package for fast and differentiable non-Gaussian lensing simulations

We present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as possible. A MADLens simulation with only 2563 particles produces convergence maps whose power agrees with theoretical lensing power spectra up to L=10000 within the accuracy limits of HaloFit. This is made possible by a combination of a highly parallelizable particle-mesh algorithm, a sub-evolution scheme in the lensing projection, and a machine-learning inspired sharpening step. Further, MADLens is fully differentiable with respect to the initial conditions of the underlying particle-mesh simulations and a number of cosmological parameters. These properties allow MADLens to be used as a forward model in Bayesian inference algorithms that require optimization or derivative-aided sampling. Another use case for MADLens is the production of large, high resolution simulation sets as they are required for training novel deep-learning-based lensing analysis tools. We make the MADLens package publicly available under a Creative Commons License .

A Vector Processor for Mean Field Bayesian Channel Estimation

Physical layer signal processing algorithms in the wireless domain are seeing increased use of machine learning algorithms, especially Bayesian methods. This work presents the hardware architecture and implementation of a vector processor for one such application, Bayesian channel estimation (CE) (BCE). The BCE vector processor supports a generic instruction set with a supplement of specialized instructions to realize Bayesian algorithms in the signal processing context. The vector processor is designed to work as an accelerator in a system-on-chip (SoC) with an AHB/AXI bus interface or as stand-alone unit. The vector processor achieves more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times $ </tex-math></inline-formula> improvement in performance when compared with a traditional CE algorithm running on a commercial vector processor. To the best of authors knowledge, this is a first known hardware implementation of a variational Bayesian inference algorithm for a wireless communication application.

Molecular Evaluations and Genetic Divergence of Erynnis tages and Erynnis marloyi (Lepidoptera, Hesperiidae) Based on mtCOI Gene with Turkey Populations

Erynnis tages and Erynnis marloyi were known as European species until recent years. Due to their narrow distribution areas, the morphological similarities of the two species were very high, and their status was controversial. However, as the records of these species came from the new regions, their distribution areas turned out to be wide, contrary to what is known. With the mtCOI gene barcode, there was a chance to identify genetic variations hidden between inter-species and intra-species. The present study was the first time the barcode characterization of populations in Turkey and other registered population of barcodes with the genetic variation were assessed. Phylogenetic trees based on mt COI gene sequences were created using Neighbor-joining, Bayesian inference, and maximum-likelihood algorithms. Genetic divergence was confirmed by Automatic Barcode Gap Analysis using the Kimura 2 parameter. It is genetically confirmed that E.tages and E.marloyi are two distinct species independent from each other. E.tages population of Turkey was found genetically similar to that of the population belonging to southern Italy. Southern Russia was also genetically similar. However, E. marloyi Turkey's population was genetically similar to the population of Iran.

A Comparison of Bayesian Inference Strategies for Parameterisation of Large Amplitude AC Voltammetry Derived from Total Current and Fourier Transformed Versions

AbstractUse of carefully designed computer supported parameterisation methods in voltammetric studies can provide highly robust and accurate methods for simultaneously quantifying the large number of parameters present in complex electrochemical reactions. In this study, a computer program has been developed to parameterise large amplitude AC voltammetric data using mathematical optimisation in combination with Bayesian inference algorithms for calculating posterior distributions of parameters and hence uncertainties in parameter values. The computer program has been applied to objective functions, relevant to total AC current, frequency domain data in the form of the power spectrum derived from Fourier transformation and multivariate based methods using the resolved harmonic data. The robustness of the objective functions have been confirmed and Bayesian inference methods have been validated using “noisy” synthetic and experimental data for the [Fe(CN)6]3−/4− reduction process in aqueous 3.0 M KCl electrolyte at a gold electrode. It was found that the harmonic based Bayesian inference methods outperformed other methods in parameterisation of the thermodynamics and electrode kinetics of the close to reversible [Fe(CN)6]3−/4− process due to their ability to compensate for non‐ideality in the modelling and the superior parameter sensitivities available in the higher harmonics. The computer supported and heuristic methods were compared. Their advantages and limitations are discussed.

A matrix analytic approach for Bayesian network modeling and inference of a manufacturing system

A shared digital twin of a manufacturing system is valuable to provide maintenance services in a collaborative manner. An accurate analytical model of the Bayesian network is crucial to depict endogenous failure mechanisms in the digital twin. Nodes’ connections in Bayesian networks correspond to a range of linear, bilinear or multilinear mappings over finite-state variables. The conditional probability table (CPT) of a child node can be represented as a k-dimensional tensor if it has (k-1) parent nodes. A new matrix analytic approach is proposed for Bayesian network inference based on the theory of semi-tensor product. The matrix representation of probabilistic networks is firstly studied, and a specific parameter training algorithm is constructed based on the matrix model. Bayesian network inference algorithms, including both forward and backward reasoning, are then presented for reliability analysis and fault diagnosis. A real manufacturing system is applied to verify the proposed approach. This matrix analytic approach helps to study the Bayesian network’s mathematical properties, and it is proved to be convenient and efficient in probability network modeling and inference.

DNA Barcoding And Species Delimitation Of Pyrausta (Lepidoptera: Crambidae, Pyraustinae) With Some Populations In Turkey

Pyrausta aurata (Scopoli, 1763), P. despicata (Scopoli, 1763), P. sanguinalis (Linnaeus, 1767), P. castalis (Treitschke, 1829), P. pavidalis (Zerny in Osthelder, 1935) and P. gulpembe (Kemal &amp;amp; Koçak, 2018) from Turkey were first time barcoded in the present study. Turkish populations and new species P. tatarica (Kemal, Kızıldağ &amp;amp; Koçak, 2020) were evaluated the phylogenetic positions with other Pyrausta species and populations. In the phylogenetic tree based on the mtCOI gene region delimitation of species and populations constructed with Neighbor-joining, Bayesian inference, and maximum-likelihood algorithms. For understanding the importance of the phylogenetic species concept in species delimitation, was reviewed cladistic topology and genetic distances of Pyrausta species with new data.

Improved neuronal ensemble inference with generative model and MCMC

Neuronal ensemble inference is a significant problem in the study of biological neural networks. Various methods have been proposed for ensemble inference from experimental data of neuronal activity. Among them, Bayesian inference approach with generative model was proposed recently. However, this method requires large computational cost for appropriate inference. In this work, we give an improved Bayesian inference algorithm by modifying update rule in Markov chain Monte Carlo method and introducing the idea of simulated annealing for hyperparameter control. We compare the performance of ensemble inference between our algorithm and the original one, and discuss the advantage of our method.

Aurora: A Generalized Retrieval Framework for Exoplanetary Transmission Spectra

Abstract Atmospheric retrievals of exoplanetary transmission spectra provide important constraints on various properties, such as chemical abundances, cloud/haze properties, and characteristic temperatures, at the day–night atmospheric terminator. To date, most spectra have been observed for giant exoplanets due to which retrievals typically assume hydrogen-rich atmospheres. However, recent observations of mini Neptunes/super-Earths, and the promise of upcoming facilities including the James Webb Space Telescope (JWST), call for a new generation of retrievals that can address a wide range of atmospheric compositions and related complexities. Here we report Aurora, a next-generation atmospheric retrieval framework that builds upon state-of-the-art architectures and incorporates the following key advancements: (a) a generalized compositional retrieval allowing for H-rich and H-poor atmospheres, (b) a generalized prescription for inhomogeneous clouds/hazes, (c) multiple Bayesian inference algorithms for high-dimensional retrievals, (d) modular considerations for refraction, forward scattering, and Mie scattering, and (e) noise modeling functionalities. We demonstrate Aurora on current and/or synthetic observations of the hot Jupiter HD 209458 b, mini Neptune K2-18b, and rocky exoplanet TRAPPIST-1 d. Using current HD 209458 b spectra, we demonstrate the robustness of our framework and cloud/haze prescription against assumptions of H-rich/H-poor atmospheres, improving on previous treatments. Using real and synthetic spectra of K2-18b, we demonstrate an agnostic approach to confidently constrain its bulk atmospheric composition and obtain precise abundance estimates. For TRAPPIST-1 d, 10 JWST-NIRSpec transits can enable identification of the main atmospheric component for cloud-free, CO2-rich, and N2-rich atmospheres and abundance constraints on trace gases, including initial indications of O3 if present at enhanced levels (∼10×–100× Earth levels).

Identification of point source emission in river pollution incidents based on Bayesian inference and genetic algorithm: Inverse modeling, sensitivity, and uncertainty analysis

Identification of pollution point source in rivers is strenuous due to accidental chemical spills or unmanaged wastewater discharges. It is crucial to take physical characteristics into account in the estimation of pollution sources. In this study, an integrated inverse modeling framework is developed to identify a point source of accidental water pollution based on the contaminant concentrations observed at monitoring sites in time series. The modeling approach includes a Markov chain Monte Carlo method based on Bayesian inference (Bayesian-MCMC) inverse model and a genetic algorithm (GA) inverse model. Both inverse models can estimate the pollution sources, including the emission mass quantity, release time, and release position in an accidental river pollution event. The developed model is first tested for a hypothetical case with field river conditions. The results show that the source parameters identified by the Bayesian-MCMC inverse model are very close to the true values with relative errors of 0.02% or less; the GA inverse model also works with relative errors in the range of 2%–7%. Additionally, the uncertainties associated with model parameters are analyzed based on global sensitive analysis (GSA) in this study. It is also found that the emission mass of pollution source positively correlates with the dispersion coefficient and the river cross-sectional area, whereas the flow velocity significantly affects release position and release time. A real case study in the Fen River is further conducted to test the applicability of the developed inverse modeling approach. Results confirm that the Bayesian-MCMC model performs better than the GA model in terms of accuracy and stability for the field application. The findings of this study would support decision-making during emergency responses to river pollution incidents.

Clinical Validation of the Champagne Algorithm for Epilepsy Spike Localization.

Magnetoencephalography (MEG) is increasingly used for presurgical planning in people with medically refractory focal epilepsy. Localization of interictal epileptiform activity, a surrogate for the seizure onset zone whose removal may prevent seizures, is challenging and depends on the use of multiple complementary techniques. Accurate and reliable localization of epileptiform activity from spontaneous MEG data has been an elusive goal. One approach toward this goal is to use a novel Bayesian inference algorithm—the Champagne algorithm with noise learning—which has shown tremendous success in source reconstruction, especially for focal brain sources. In this study, we localized sources of manually identified MEG spikes using the Champagne algorithm in a cohort of 16 patients with medically refractory epilepsy collected in two consecutive series. To evaluate the reliability of this approach, we compared the performance to equivalent current dipole (ECD) modeling, a conventional source localization technique that is commonly used in clinical practice. Results suggest that Champagne may be a robust, automated, alternative to manual parametric dipole fitting methods for localization of interictal MEG spikes, in addition to its previously described clinical and research applications.

Multi-Emitter Localization via Concurrent Variational Bayesian Inference in UAV-Based WSN

Applying Compressive Sensing (CS) to Received Signal Strength (RSS) based multi-emitter localization using Unmanned Arial Vehicles (UAVs) attracts much attention for its simplicity and efficiency. However, the RSS-based CS approach is vulnerable to the noise in a practical scenario. To mitigate this, we propose a robust localization framework for multiple emitters in UAV-based Wireless Sensor Network (WSN). We first approximate the lognormal noise’s influence on the dictionary by a two-layer hierarchical prior model. Then, by exploiting multi-frequency measurements, the multi-emitter localization is transformed into the joint estimation for multiple sparse vectors and noise level. Finally, the joint estimation problem is solved by a Concurrent Variational Bayesian Inference (CVBI) algorithm, where an adaptive grid pruning mechanism is designed. The merits of the proposed framework are testified by numerical simulations.

Sequential Bayesian inference of transition rates in the hidden Markov model for multi-state system degradation

The more easily available system performance data and advances in data analytics have provided us with opportunities to optimize maintenance programs for engineered systems, for example nuclear power plants. One key task in maintenance optimization is to obtain an accurate model for system degradation. In this research, we propose a Bayesian method to address this problem. Noting that systems usually exhibit multiple states and that the actual state of a system usually is not directly observable, in the method we first model the system degradation process and the observation process based on a hidden Markov model. Then we develop a sequential Bayesian inference algorithm based on importance sampling and the forward algorithm to infer the posterior distributions of the transition rates in the hidden Markov model based on available observations. The proposed Bayesian method allows us to take advantage of evidence from multiple sources, and also allows us to perform Bayesian inference sequentially, without the need to use the entire history of observations every time new observations are collected. We demonstrate the proposed method using both synthetic data for a nuclear power plant feedwater pump and realistic data for a nuclear power plant chemistry analytical device.

Variational Bayesian Compressive Multipolarization Indoor Radar Imaging

This article introduces a probabilistic Bayesian model for addressing the problem of compressive multipolarization through-wall radar imaging (TWRI). The proposed approach formulates the task of wall-clutter mitigation and multipolarization image reconstruction as a Bayesian inference problem for a joint distribution between observed radar measurements and latent wall-clutter matrix and indoor target images. The joint probability distribution incorporates three prior beliefs: low-dimensional structure of the wall reflections, group sparsity structure of the target images, and joint sparsity among the polarization images. These signal attributes are modeled through hierarchical priors, whose parameters and hyperparameters are treated with a full Bayesian formulation. Furthermore, this article presents a variational Bayesian inference algorithm that estimates wall-clutter and multipolarization images as posterior distributions and optimizes the model parameters and hyperparameters simultaneously. Experimental results on simulated and real radar data show that the proposed model is very effective at removing wall clutter and enhancing target localization even when the radar measurements are significantly reduced.

Shadow Simulated Annealing: A new algorithm for approximate Bayesian inference of Gibbs point processes

This paper presents a new algorithm for statistical inference and analysis of spatial patterns assumed to be realisations of Gibbs point processes. This approach has a general character and it contributes to the existing methods based on Approximate Bayesian Computation, by providing control properties of the proposed solution. Results on simulated data and real data are presented. The real data application fits an inhomogeneous area interaction point process to cosmological data. The obtained results validate two important aspects of the galaxies distribution in our Universe: proximity of the galaxies from the cosmic filament network together with territorial clustering at given range of interactions. Finally, conclusions and perspectives are depicted.

Bayesian Analysis of Intraday Stochastic Volatility Models of High-Frequency Stock Returns with Skew Heavy-Tailed Errors

Intraday high-frequency data of stock returns exhibit not only typical characteristics (e.g., volatility clustering and the leverage effect) but also a cyclical pattern of return volatility that is known as intraday seasonality. In this paper, we extend the stochastic volatility (SV) model for application with such intraday high-frequency data and develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for Bayesian inference of the proposed model. Our modeling strategy is two-fold. First, we model the intraday seasonality of return volatility as a Bernstein polynomial and estimate it along with the stochastic volatility simultaneously. Second, we incorporate skewness and excess kurtosis of stock returns into the SV model by assuming that the error term follows a family of generalized hyperbolic distributions, including variance-gamma and Student’s t distributions. To improve efficiency of MCMC implementation, we apply an ancillarity-sufficiency interweaving strategy (ASIS) and generalized Gibbs sampling. As a demonstration of our new method, we estimate intraday SV models with 1 min return data of a stock price index (TOPIX) and conduct model selection among various specifications with the widely applicable information criterion (WAIC). The result shows that the SV model with the skew variance-gamma error is the best among the candidates.