Bayesian Inference Framework Research Articles

Assessing the ability of adaptive designs to capture trends in hard coral cover

Coral reefs have become one of the most vulnerable ecosystems worldwide due to rising environmental and anthropogenic pressures. Methods from experimental design can be used to furnish our ability to monitor such ecosystems efficiently. Recently, adaptive design approaches have been proposed for monitoring coral reefs; however, questions have surfaced around the ability of such approaches to capture trends over time. The aim of this study was to develop an approach to assess trends in hard coral cover and evaluate the effectiveness of adaptive designs for estimating such trends in coral reef communities within a region of the Great Barrier Reef. Our approach was couched within a Bayesian design and inference framework such that uncertainty was captured rigorously and so that information from accumulating data can be incorporated straightforwardly to inform future data collection. The designs found under this approach were compared to historical non‐adaptive designs which surveyed all locations over time. Through this comparison, we show that adaptive designs can maintain trends over time with little to no loss in information, even when sampling effort is substantially reduced. Accordingly, this research serves to further promote adaptive design methods for efficiently and effectively sampling in ecological monitoring.

Finite mixture modeling in time series: A survey of Bayesian filters and fusion approaches

From the celebrated Gaussian mixture, model averaging estimators to the cutting-edge multi-Bernoulli mixture of various forms, finite mixture models offer a fundamental and flexible means to deal with uncertainties arisen in the estimation and learning realm. In the context of recursive estimation, both the uncertainties due to model maneuvering and multi-target data association derive a need for representing the single/multiple-target probability distribution by a finite mixture described by a number of parameters that are iteratively updated over time in the framework of Bayesian inference, which we call generally the Bayesian mixture (BM) filtering. In addition, density fusion between netted agents/sensors may be addressed by linearly combining their local estimations which are often correlated with each other in a complicated means, leading to a fused mixture too. In either case, the final estimate is given by the arithmetic average (AA) of all the weighted components in the mixture, regarding either a single target or multiple targets. Along with this are versatile mixture adaption and optimization strategies which aim to use a small number of components for the best fit to the target distribution. This survey provides a comprehensive overview of representative single/multiple-target BM filters and fusion approaches with the use of either a single sensor or multiple sensors in a unified and coherent fashion. State-of-the-art, relevant adaption and optimization technologies and remaining challenges are discussed. All strive to gain more insights of the approach.

Functional principal component models for sparse and irregularly spaced data by Bayesian inference

The area of functional principal component analysis (FPCA) has seen relatively few contributions from the Bayesian inference. A Bayesian method in FPCA is developed under the cases of continuous and binary observations for sparse and irregularly spaced data. In the proposed Markov chain Monte Carlo (MCMC) method, Gibbs sampler approach is adopted to update the different variables based on their conditional posterior distributions. In FPCA, a set of eigenfunctions is suggested under Stiefel manifold, and samples are drawn from a Langevin–Bingham matrix variate distribution. Penalized splines are used to model mean trajectory and eigenfunction trajectories in generalized functional mixed models; and the proposed model is casted into a mixed-effects model framework for Bayesian inference. To determine the number of principal components, reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm is implemented. Four different simulation settings are conducted to demonstrate competitive performance against non-Bayesian approaches in FPCA. Finally, the proposed method is illustrated to the analysis of body mass index (BMI) data by gender and ethnicity.

Density-adaptive registration of pointclouds based on Dirichlet Process Gaussian Mixture Models

We propose an algorithm for rigid registration of pre- and intra-operative patient anatomy, represented as pointclouds, during minimally invasive surgery. This capability is essential for development of augmented reality systems for guiding such interventions. Key challenges in this context are differences in the point density in the pre- and intra-operative pointclouds, and potentially low spatial overlap between the two. Solutions, correspondingly, must be robust to both of these phenomena. We formulated a pointclouds registration approach which considers the pointclouds after rigid transformation to be observations of a global non-parametric probabilistic model named Dirichlet Process Gaussian Mixture Model. The registration problem is solved by minimizing the Kullback-Leibler divergence in a variational Bayesian inference framework. By this means, all unknown parameters are recursively inferred, including, importantly, the optimal number of mixture model components, which ensures the model complexity efficiently matches that of the observed data. By presenting the pointclouds as KDTrees, both the data and model are expanded in a coarse-to-fine style. The scanning weight of each point is estimated by its neighborhood, imparting the algorithm with robustness to point density variations. Experiments on several datasets with different levels of noise, outliers and pointcloud overlap show that our method has a comparable accuracy, but higher efficiency than existing Gaussian Mixture Model methods, whose performance is sensitive to the number of model components.

Trimmed sampling algorithm for the noisy generalized eigenvalue problem

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose entries are inner products of the basis states, and the process is unfortunately susceptible to even small errors. The problem is especially bad when matrix elements are evaluated using stochastic methods and have significant error bars. In this work, we introduce the trimmed sampling algorithm in order to solve this problem. Using the framework of Bayesian inference, we sample prior probability distributions determined by uncertainty estimates of the various matrix elements and likelihood functions composed of physics-informed constraints. The result is a probability distribution for the eigenvectors and observables which automatically comes with a reliable estimate of the error and performs far better than standard regularization methods. The method should have immediate use for a wide range of applications involving classical and quantum computing calculations of large quantum systems.Received 14 October 2022Accepted 15 March 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L022001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose gasesNuclear many-body theoryNuclear structure & decaysQuantum algorithmsAtomic, Molecular & Optical

A Framework for Reliability Analysis of Combinational Circuits Using Approximate Bayesian Inference

A commonly used approach to compute the error rate at the primary outputs (POs) of a circuit is to compare the fault-free and faulty copies of the circuit using XOR gates. This model results in poor accuracies with nonsampling-based methods for reliability estimation. An alternative is to use a single copy of the circuit with a four-valued representation for each net corresponding to the correct and incorrect signals. One problem in this formulation is the accurate propagation of associated probabilities. We use the framework of Bayesian inference (BI) to address this issue. We derive the conditional probability distribution (CPD) corresponding to the four-valued signals and find the output error rate using various approximate BI techniques. With our formulation, we demonstrate that the output error rate scales with the gate error probabilities. It is guaranteed to be zero when the gate error probability is zero, provided approximate BI algorithms based on sum-product belief propagation (BP) are used. Although inaccuracies increase at very low gate error probabilities, it is able to capture the relative reliability of outputs with respect to each other. We also propose a new method for finding the overall circuit error rate as the partition function for a fixed state of POs. This method provides a significant improvement in accuracy when compared with the existing method using OR gates.

Noise-Aware Sparse Gaussian Processes and Application to Reliable Industrial Machinery Health Monitoring

Maintenance of machinery equipment in smart manufacturing requires real-time health monitoring, strongly supported by the rapid evolution of Artificial Intelligence (AI) technologies. Most AI-based health monitoring systems are powered by advanced modeling methods and intensive high-quality monitoring data. Such monitoring systems center on high-accuracy predictive performance but cannot necessarily convey reliability, such as satisfactory resistance to strong noises, credible uncertainty analysis, and model interpretability. This article novelly proposes noise-aware sparse Gaussian processes (NASGP) within the Bayesian inference framework. NASGP are capable of consistent high-performance and credible uncertainty assessment under strong noises. Based on NASGP, we then develop an explainable generalized additive model to bridge the gap between latent inference mechanism and domain expert knowledge. The efficacy of the proposed approach is corroborated through two case studies including remaining useful life prognosis and fault diagnosis for rolling bearings.

Bayesian Inference for Stochastic Multipath Radio Channel Models

Stochastic radio channel models based on underlying point processes of multipath components (MPCs) have been studied intensively since the seminal papers of Turin and Saleh–Valenzuela (SV). Despite this, inference regarding parameters of these models has remained a major challenge. Current methods typically have a somewhat ad hoc flavor involving a multitude of steps requiring user specification of tuning parameters. In this article, we propose to instead adopt the principled framework of Bayesian inference to conduct inference for the SV model. The posterior distribution is not analytically tractable and we therefore compute approximations of the posterior using Markov chain Monte Carlo (MCMC) methods specific to point processes. To demonstrate the flexibility of our approach, we additionally propose a new multipath model and apply our inference method to it. The resulting inference methodology is computationally demanding and our successful implementation relies critically on our novel MPC updates within the MCMC sampler. We demonstrate the usefulness of our approach on simulated and real radio channel data.

A Bayesian inference approach for parametric identification through optimal control method

AbstractThe objective of the research is to obtain deterministic and probabilistic resolution of material parameters from full field measurements of kinematic data acquired from digital image correlation. The deterministic inverse problem involves formulation of an optimal control approach where the complete knowledge of the boundary conditions and the measurement data are not required. The probabilistic framework inculcates this optimal control method in a Bayesian inference framework. A Markov chain Monte Carlo sampling method is applied to obtain the posterior probability density function, along with a radial basis function network for the numerical frugality of the samplings.

Robust sparse Bayesian learning based on the Bernoulli-Gaussian model of impulsive noise

Traditional sparse reconstruction methods suffer from performance degradation in the presence of impulsive noise. In this paper, we adopt the Bernoulli-Gaussian distribution to model the impulsive noise and introduce the hidden state variables to indicate the state of the noise. Based on the new hierarchical Bayesian model, a robust sparse reconstruction algorithm called Bernoulli-Gaussian robust sparse Bayesian learning (BG-RSBL) is developed through the variational Bayesian inference framework. Different from existing robust reconstruction methods, BG-RSBL does not make sparse assumptions about the impulses and outliers. The employment of the Bernoulli-Gaussian model enables BG-RSBL to adapt to environments with a wider range of impulse densities. Comparative analysis shows that the reconstruction performance can be improved by including the outliers in posterior inference with appropriate weightings. Simulations performed under both Bernoulli-Gaussian and symmetric α-stable distributed impulsive noise demonstrate the robust and outstanding reconstruction performance of the proposed algorithm.

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli-Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

Understanding Factors Influencing Click-Through Decision in Mobile OTA Search Engine Systems

Mobile commerce has changed the decision environment for users who intend to reserve a preferred hotel. This study aims to investigate the factors that affect the dynamic click-through decision (CTD) in mobile online travel agency (OTA) search engines. We propose a dynamic Bayesian inference framework to model individual-level users’ CTDs and examine the effects of item position, price, search cost, and the use of refinement tools. The study uses real-world search log datasets from a global OTA for both mobile and desktop searches. Our results show that (1) the primacy effect is weaker and the effect of item-ranking positions is non-linear in a mobile OTA search compared to a desktop OTA search. Mobile users pay the most attention to the top-ranking results and are less likely to click through the middle or bottom results. (2) Hotel prices have a positive effect on mobile CTDs in the whole mobile searching journey. Additionally, mobile users also tend to seek out hotels with lower price rankings on the current search engine result page. (3) The search cost, measured by the cumulative time duration, has a positive impact on mobile CTDs. The use of refinement tools enhances the effect of search cost. This study extends previous research on position and price effects in an online consumer search from PC-based internet to mobile devices. It also provides managerial implications for mobile OTA search engine marketing and investment for bidding ranking positions.

A two-level copula joint model for joint analysis oflongitudinal and competing risks data.

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

Bayesian Joint Channel-and-Data Estimation for Quantized OFDM Over Doubly Selective Channels

This paper investigates the design of orthogonal frequency division multiplexing (OFDM) receiver, which operates over time-frequency doubly selective (DS) channels and uses a low-resolution analog-to-digital converter (ADC) to quantize the received signal. The time-varying multipaths in DS channel and the nonlinear quantization distortion caused by low-resolution ADC, destroy the orthogonality among OFDM subcarriers, incurring severe inter-carrier interference (ICI). Therefore, joint channel-and-data estimation is preferred, since in this way one can effectively tackle the ICI and make the best of the quantized signal in each OFDM symbol. In this paper, we elaborately develop the joint estimation scheme by casting the problem into the Bayesian inference framework. The proposed scheme not only takes into account of the nonlinear quantization in a probabilistic manner, but also exploits the channel sparsity enabled by the basis expansion model (BEM) approximation to DS channels. Furthermore, to benchmark the proposed scheme, we derive the asymptotic theoretical bounds in the large-system regime. Simulation results demonstrate that the proposed scheme can achieve the performance close to the theoretical bounds, thereby verifying the effectiveness of the proposed scheme.

Channel Estimation for RIS-Aided mmWave Massive MIMO System Using Few-Bit ADCs

Millimeter wave (mmWave) massive multiple-input multiple-output (massive MIMO) is one of the most promising technologies for the fifth generation and beyond wireless communication system. However, a large number of antennas incur high power consumption and hardware costs, and high-frequency communications place a heavy burden on the analog-to-digital converters (ADCs) at the base station (BS). Furthermore, it is too costly to equipping each antenna with a high-precision ADC in a large antenna array system. It is promising to adopt low-resolution ADCs to address this problem. In this letter, we investigate the cascaded channel estimation for a mmWave massive MIMO system aided by a reconfigurable intelligent surface (RIS) with the BS equipped with few-bit ADCs. Due to the low-rank property of the cascaded channel, the estimation of the cascaded channel can be formulated as a low-rank matrix completion problem. We introduce the Bayesian optimal inference framework to tackle with the information loss caused by quantization. To implement the estimator and achieve the matrix completion, we use efficient bilinear generalized approximate message passing (BiG-AMP) algorithm. Extensive simulation results verify that our proposed method can accurately estimate the cascaded channel for the RIS-aided mmWave massive MIMO system with low-resolution ADCs.

Bayesian selection of plane-wave decomposition models.

Plane-wave decompositions, whereby a measured sound field is described as a superposition of plane waves, are central to many applications in acoustics and audio engineering. This letter applies a Bayesian probabilistic inference framework to the plane wave decomposition problem and examines the Deviance Information Criterion (DIC) for selecting the optimum number of waves in the decomposition. The framework learns the model directly from the data and, as such, adapts to the wavefield under study. The DIC is applied to data measured in two reverberant sound fields (highly-reverberant and lightly-damped) to determine the simplest models providing the preferred fit to the data.

The DESI PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) Mock Challenge

The PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) catalog will provide measurements of galaxy properties, such as stellar mass (M *), star formation rate (SFR), stellar metallicity (Z), and stellar age (t age), for >10 million galaxies of the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey. Full posterior distributions of the galaxy properties will be inferred using state-of-the-art Bayesian spectral energy distribution (SED) modeling of DESI spectroscopy and Legacy Surveys photometry. In this work, we present the SED model, the neural emulator for the model, and the Bayesian inference framework of PROVABGS. Furthermore, we apply the PROVABGS SED modeling on realistic synthetic DESI spectra and photometry, constructed using the L-Galaxies semi-analytic model. We compare the inferred galaxy properties to the true values of the simulation using a hierarchical Bayesian framework to quantify accuracy and precision. Overall, we accurately infer the true M *, SFR, Z, and t age of the simulated galaxies. However, the priors on galaxy properties induced by the SED model have a significant impact on the posteriors, which we characterize in detail. This work also demonstrates that a joint analysis of spectra and photometry significantly improves the constraints on galaxy properties over photometry alone and is necessary to mitigate the impact of the priors. With the methodology presented and validated in this work, PROVABGS will maximize information extracted from DESI observations and extend current galaxy studies to new regimes and unlock cutting-edge probabilistic analyses. https://github.com/changhoonhahn/provabgs/

Bayesian inference of three-dimensional gas maps

The 21 cm emission from atomic hydrogen (H I ) is one of the most important tracers of the structure and dynamics of the interstellar medium. Thanks to Galactic rotation, the line is Doppler shifted and, assuming a model for the velocity field, data from gas line surveys can be deprojected along the line of sight. However, given our vantage point in the Galaxy, such a reconstruction suffers from a number of ambiguities. Here, we argue that those can be cured by exploiting the spatial coherence of the gas density that is implied by the physical processes shaping it. We have adopted a Bayesian inference framework that allows reconstructing the three-dimensional map of H I and quantifying its uncertainty. We employ data from the HI4PI compilation to produce three-dimensional maps of Galactic H I. The reconstructed density shows structure on a variety of scales. In particular, some spurs and spiral arms can be identified with ease. We discuss the morphology of the surface mass density and the radial and vertical profiles.

Quasi-2-D Bayesian inversion of central loop transient electromagnetic data using an adaptive Voronoi parametrization

SUMMARYCentral loop transient electromagnetic (TEM) data are often interpreted by conventional 1-D or quasi-2-D inversion techniques. For example, the lateral constrained inversion (LCI) is a powerful technique for quick interpretation of central loop TEM data, and can produce spatially consistent resistivity images for profile data by assuming spatial correlation between adjacent model parameters. Such quasi-2-D techniques are very powerful in cases multidimensional effects are small or negligible. However, the inverse solution of conventional LCI methods strongly depends on subjective interpreter choices such as the model regularization and the imposed lateral constraints. Due to inherent non-linearity and nonuniqueness of the TEM inverse problems, this can result in biased model parameters and their estimated model uncertainties. We present a transdimensional Markov chain Monte Carlo method for the quasi-2-D inversion of TEM data using a Bayesian inference framework. We term the approach quasi-2-D, since the model is parametrized in 2-D with unstructured Voronoi cells, whereas the TEM response at each station is predicted using a 1-D forward solution to make the problem computationally affordable. During the inversion, the number of Voronoi cells as well as their positions and resistivities are variable. Accordingly, the level of model complexity is automatically determined by the framework and adapted to the spatial resolution of the data, thus avoiding the need for subjective model regularization or spatial constraints. The approach is validated using synthetic data and compared to 1-D Bayesian and conventional Gauss Newton inversion techniques. The application to dense field data from a floating TEM survey leads to a consistent subsurface image with unbiased uncertainty estimates and a plausible depth of investigation. The quantitative uncertainty information provided by the Bayesian framework is beneficial in identifying resolution.

The Roasting Marshmallows Program with IGRINS on Gemini South I: Composition and Climate of the Ultrahot Jupiter WASP-18 b

We present high-resolution dayside thermal emission observations of the exoplanet WASP-18 b using IGRINS on Gemini South. We remove stellar and telluric signatures using standard algorithms, and we extract the planet signal via cross-correlation with model spectra. We detect the atmosphere of WASP-18 b at a signal-to-noise ratio (S/N) of 5.9 using a full chemistry model, measure H2O (S/N = 3.3), CO (S/N = 4.0), and OH (S/N = 4.8) individually, and confirm previous claims of a thermal inversion layer. The three species are confidently detected (>4σ) with a Bayesian inference framework, which we also use to retrieve abundance, temperature, and velocity information. For this ultrahot Jupiter (UHJ), thermal dissociation processes likely play an important role. Retrieving abundances constant with altitude and allowing the temperature–pressure profile to adjust freely results in a moderately super-stellar carbon-to-oxygen ratio (C/O = ) and metallicity ([M/H] = ). Accounting for undetectable oxygen produced by thermal dissociation leads to C/O = and [M/H] = . A retrieval that assumes radiative–convective–thermochemical equilibrium and naturally accounts for thermal dissociation constrains C/O < 0.34 (2σ) and [M/H] = , in line with the chemistry of the parent star. Looking at the velocity information, we see a tantalizing signature of different Doppler shifts at the level of a few kilometers per second for different molecules, which might probe dynamics as a function of altitude and/or location on the planet disk. Our results demonstrate that ground-based, high-resolution spectroscopy at infrared wavelengths can provide meaningful constraints on the compositions and climate of highly irradiated planets. This work also elucidates potential pitfalls with commonly employed retrieval assumptions when applied to the spectra of UHJs.