Bayesian Set Research Articles

On exact Bayesian credible sets for discrete parameters

We introduce a generalized Bayesian credible set that can achieve any preassigned credible level, addressing a limitation of the current credible sets. This is achieved by exploiting a connection between the highest posterior density set and the Neyman–Pearson lemma.

Inflation targeting and monetary policy response in India

India adopted the Flexible Inflation Targeting (FIT) regime in 2016 under the mentorship of the Monetary Policy Committee (MPC). With FIT’s introduction, the effectiveness of monetary policy transmission channels required a re-visit and this paper is a valuable contribution in this direction. Using the multivariate model with an augmented Bayesian set- up, we find that FIT-MPC has strengthened the credit and interest rate channels while their impact on output has weakened. The impact of Operation Twist – a set of unconventional measures pursued during the pandemic is visible. Overall, the findings highlight the overhauling effect of monetary policy transmission in the Indian context.

A method for quality fault diagnosis based on Bayesian network D-cut set

Abstract Quality issues are important factors restricting the development of hydrogen fuel cells. Quality problems in hydrogen fuel cells may stem from various stages, including technology, preparation processes, equipment used, usage environment, and personnel operation. Moreover, different problems are coupled with each other, resulting in the characteristics of one cause with multiple effects and multiple causes with one effect in the quality issues of hydrogen fuel cells. However, there are often similarities between these qualities in high-level information, such as mechanism, object, and behaviour, which are reflected in the similarity of network models in Bayesian diagnostic networks. Therefore, this article discusses how to reuse the Bayesian diagnosis network of previous quality problem cases to construct a Bayesian diagnosis network for hydrogen fuel cell quality problem diagnosis, thereby effectively improving the diagnosis efficiency of hydrogen fuel cell quality problems.

AI/ML driven intrusion detection framework for IoT enabled cold storage monitoring system

AbstractAn IoT‐based monitoring system remotely controls and manages intelligent environments. Due to wireless communication, deployed sensor nodes are more vulnerable to attacks. An intrusion detection system is an efficient mechanism to detect malicious traffic and prevent abnormal activities. This article suggests an intrusion detection framework for the cold storage monitoring system. The temperature is the main parameter that affects the environment and harms stored products. A malicious node injects false data that manipulates temperature and forwards manipulated data. It also floods the data to neighbor nodes. In this work, data are generated and collected for intrusion detection. Two machine learning techniques have been applied: supervised learning (Bayesian rough set) and unsupervised learning (micro‐clustering). The proposed method shows better performance than existing methods.

A Bayesian spatio-temporal level set dynamic model and application to fire front propagation

A Bayesian spatio-temporal level set dynamic model and application to fire front propagation

Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model

We develop appropriate Bayesian procedures to draw inference about the parameters under a multivariate normal model based on synthetic data. We consider two standard forms of synthetic data, generated under plug in sampling method and posterior predictive sampling method. In addition to point estimates of the mean vector and dispersion matrix, Bayesian credible sets for the mean vector and the generalized variance are also provided under both the scenarios. The analysis in the case when some (partial) features are sensitive and need to be hidden is also briey indicated.
 Vol. 23(2), November, 2023, pp 1-18

Bayesian nonparametric method for genetic dissection of brain activation region.

Biological evidence indicewates that the brain atrophy can be involved at the onset of neuropathological pathways of Alzheimer's disease. However, there is lack of formal statistical methods to perform genetic dissection of brain activation phenotypes such as shape and intensity. To this end, we propose a Bayesian hierarchical model which consists of two levels of hierarchy. At level 1, we develop a Bayesian nonparametric level set (BNLS) model for studying the brain activation region shape. At level 2, we construct a regression model to select genetic variants that are strongly associated with the brain activation intensity, where a spike-and-slab prior and a Gaussian prior are chosen for feature selection. We develop efficient posterior computation algorithms based on the Markov chain Monte Carlo (MCMC) method. We demonstrate the advantages of the proposed method via extensive simulation studies and analyses of imaging genetics data in the Alzheimer's disease neuroimaging initiative (ADNI) study.

An improved hybrid structure learning strategy for Bayesian networks based on ensemble learning

In the application of Bayesian networks to solve practical problems, it is likely to encounter the situation that the data set is expensive and difficult to obtain in large quantities and the small data set is easy to cause the inaccuracy of Bayesian network (BN) scoring functions, which affects the BN optimization results. Therefore, how to better learn Bayesian network structures under a small data set is an important problem we need to pay attention to and solve. This paper introduces the idea of parallel ensemble learning and proposes a new hybrid Bayesian network structure learning algorithm. The algorithm adopts the elite-based structure learner using genetic algorithm (ESL-GA) as the base learner. Firstly, the adjacency matrices of the network structures learned by ESL-GA are weighted and averaged. Then, according to the preset threshold, the edges between variables with weak dependence are filtered to obtain a fusion matrix. Finally, the fusion matrix is modified as the adjacency matrix of the integrated Bayesian network so as to obtain the final Bayesian network structure. Comparative experiments on the standard Bayesian network data sets show that the accuracy and reliability of the proposed algorithm are significantly better than other algorithms.

A Bayesian level set method for identifying subsurface geometries and rheological properties in Stokes flow

SUMMARY We aim to simultaneously infer the shape of subsurface structures and material properties such as density or viscosity from surface observations. Modelling mantle flow using incompressible instantaneous Stokes equations, the problem is formulated as an infinite-dimensional Bayesian inverse problem. Subsurface structures are described as level sets of a smooth auxiliary function, allowing for geometric flexibility. As inverting for subsurface structures from surface observations is inherently challenging, knowledge of plate geometries from seismic images is incorporated into the prior probability distributions. The posterior distribution is approximated using a dimension-robust Markov-chain Monte Carlo sampling method, allowing quantification of uncertainties in inferred parameters and shapes. The effectiveness of the method is demonstrated in two numerical examples with synthetic data. In a model with two higher-density sinkers, their shape and location are inferred with moderate uncertainty, but a trade-off between sinker size and density is found. The uncertainty in the inferred is significantly reduced by combining horizontal surface velocities and normal traction data. For a more realistic subduction problem, we construct tailored level-set priors, representing “seismic” knowledge and infer subducting plate geometry with their uncertainty. A trade-off between thickness and viscosity of the plate in the hinge zone is found, consistent with earlier work.

Bayesian Calibration of Computational Knee Models to Estimate Subject-Specific Ligament Properties, Tibiofemoral Kinematics, and Anterior Cruciate Ligament Force With Uncertainty Quantification.

High-grade knee laxity is associated with early anterior cruciate ligament (ACL) graft failure, poor function, and compromised clinical outcome. Yet, the specific ligaments and ligament properties driving knee laxity remain poorly understood. We described a Bayesian calibration methodology for predicting unknown ligament properties in a computational knee model. Then, we applied the method to estimate unknown ligament properties with uncertainty bounds using tibiofemoral kinematics and ACL force measurements from two cadaver knees that spanned a range of laxities; these knees were tested using a robotic manipulator. The unknown ligament properties were from the Bayesian set of plausible ligament properties, as specified by their posterior distribution. Finally, we developed a calibrated predictor of tibiofemoral kinematics and ACL force with their own uncertainty bounds. The calibrated predictor was developed by first collecting the posterior draws of the kinematics and ACL force that are induced by the posterior draws of the ligament properties and model parameters. Bayesian calibration identified unique ligament slack lengths for the two knee models and produced ACL force and kinematic predictions that were closer to the corresponding in vitro measurement than those from a standard optimization technique. This Bayesian framework quantifies uncertainty in both ligament properties and model outputs; an important step towards developing subject-specific computational models to improve treatment for ACL injury.

Adaptive Bayesian inference for current status data on a grid

We study a Bayesian approach to the inference of an event time distribution in the current status model where observation times are supported on a grid of potentially unknown sparsity and multiple subjects share the same observation time. The model leads to a very simple likelihood, but statistical inferences are non-trivial due to the unknown sparsity of the grid. In particular, for an inference based on the maximum likelihood estimator, one needs to estimate the density of the event time distribution which is challenging because the event time is not directly observed. We consider Bayes procedures with a Dirichlet prior on the event time distribution. With this prior, the Bayes estimator and credible sets can be easily computed via a Gibbs sampler algorithm. Our main contribution is to provide thorough investigation of frequentist’s properties of the posterior distribution. Specifically, it is shown that the posterior convergence rate is adaptive to the unknown sparsity of the grid. If the grid is sufficiently sparse, we further prove the Bernstein–von Mises theorem which guarantees frequentist’s validity of Bayesian credible sets. A numerical study is also conducted for illustration.

A multi-criteria group decision making framework for sustainability evaluation of sintering flue gas treatment technologies in the iron and steel industry

The iron and steel industry (ISI) is at a critical stage of upgrading to ultra-low emission technologies in China. It is imperative to construct a life cycle sustainability evaluation framework as a guide for the selection of ultra-low emission technologies for the ISI. This research developed a novel multi-criteria group decision making framework. Four mature treatment technologies for sintering flue gas (SFG) were selected for analysis from an environmental, economic, and technological multi-dimensional perspective. The results of the life cycle assessment and life cycle costing are incorporated into the evaluation framework. The sustainability of ultra-low emission technologies was evaluated by combining Bayesian and hesitant fuzzy set theories for the first time. The results revealed that of the four alternatives considered, the most sustainable technology consists of semi-dry flue gas desulfurization, bag filter, and selective catalytic reduction denitrification. Triple sensitivity analysis and comparative analysis verified the consistency, robustness, and superiority of the proposed methodology. The interrelationship among criteria showed that technical maturity is key to enhancing the sustainability of ultra-low emission technologies, as it has a significant impact on costs and improves the environmental impact of the system. The conclusions provide optimization suggestions for further improving the sustainability of ultra-low emission technologies for SFG of ISI.

A Discussion of “A Note on Universal Inference” by Tse and Davison

A Discussion of “A Note on Universal Inference” by Tse and Davison

Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses; 2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.

Bayesian Rule Set: A Quantitative Alternative to Qualitative Comparative Analysis

We introduce the Bayesian Rule Set (BRS) as an alternative to Qualitative Comparative Analysis (QCA) when data are large and noisy. BRS is an interpretable machine learning algorithm that classifies observations using rule sets, which are conditions connected by logical operators (e.g., IF (condition A AND condition B) OR (condition C), THEN Y = TRUE). Like QCA, BRS is highly interpretable and capable of revealing complex nonlinear relationships in data. It also has several advantages over QCA: it is compatible with probabilistically generated data, it avoids overfitting and improves interpretability by making direct trade-offs between in-sample fitness and complexity, and it remains computationally efficient with many covariates. Our contributions are threefold: we modify the BRS algorithm to facilitate its usage in the social sciences, propose methods to quantify uncertainties of rule sets, and develop graphical tools for presenting rule sets. We illustrate these methods with two empirical examples from political science.

Effect of all-but-one conditional analysis for eQTL isolation in peripheral blood.

Expression quantitative trait locus detection has become increasingly important for understanding how noncoding variants contribute to disease susceptibility and complex traits. The major challenges in expression quantitative trait locus fine-mapping and causal variant discovery relate to the impact of linkage disequilibrium on signals due to one or multiple functional variants that lie within a credible set. We perform expression quantitative trait locus fine-mapping using the all-but-one approach, conditioning each signal on all others detected in an interval, on the Consortium for the Architecture of Gene Expression cohorts of microarray-based peripheral blood gene expression in 2,138 European-ancestry human adults. We contrast these results with traditional forward stepwise conditional analysis and a Bayesian localization method. All-but-one conditioning significantly modifies effect-size estimates for 51% of 2,351 expression quantitative trait locus peaks, but only modestly affects credible set size and location. On the other hand, both conditioning approaches result in unexpectedly low overlap with Bayesian credible sets, with just 57% peak concordance and between 50% and 70% SNP sharing, leading us to caution against the assumption that any one localization method is superior to another. We also cross reference our results with ATAC-seq data, cell-type-specific expression quantitative trait locus, and activity-by-contact-enhancers, leading to the proposal of a 5-tier approach to further reduce credible set sizes and prioritize likely causal variants for all known inflammatory bowel disease risk loci active in immune cells.

471 Integrated psoriasis GWAS and eQTL analysis reveals risk-associated genetic control of TRAF3IP2-AS1 expression in activated CD8 T-cells

We performed an international meta-GWAS of psoriasis, increasing effective sample size by 3.4-fold. Using COJO, we identified 191 independent psoriasis loci at genome-wide (GW) significance (179 outside the MHC). We conducted eQTL analysis of 1,195 strand-specific RNA-seq libraries passing QC (MQ30, ∼25M reads/sample) from 9 FACS-purified immune cell types (CD4/CD8, CLA-/CLA+, and 0h/24 h CD3-CD28-activated T-cells; also resting mDC) from 153 genotyped individuals, yielding 9,091 significant (p<5x10-3) cis-eQTLs mapping to the 179 non-MHC 95% Bayesian credible sets. Here we focus on TRAF3IP2 encoding Act1, an adaptor that transduces signals through IL-17R. COJO found 14 independent risk signals for this region (2 potentially protein-altering and 12 potentially regulatory). The lead protein-coding variant, rs33980500 C/T encoding Act1 D10N, is the top GWAS hit with a posterior probability of 1.00 on unconditional analysis. We have shown that rs33980500-T increases psoriasis risk and promotes Th17 expansion. We identified cis-eQTLs for the lncRNA TRAF3IP2-AS1 in activated CD8 T-cells, but not in activated CD4 or resting T-cells. In contrast, cis-eQTL signals for TRAF3IP2 itself were markedly reduced after CD8 T-cell activation. Moreover, the best cis-eQTL signal for TRAF3IP2-AS1 in activated CD8 T-cells (rs11153301, p=2.9x10-6) is a GW-significant psoriasis hit (p=3.7x10-8) after conditioning on Act1 D10N. The risk allele rs11153301-T results in reduced expression of TRAF3IP2-AS1 in activated CD8 T-cells, and a recent study (J Immunol 206:2353) describes an inhibitory effect of TRAF3IP2-AS1 on Act1 protein level and IL-17 signaling. Notably, the expanded GWAS also implicates a cluster of noncoding variants near IL17RA (p=3.9x10-9), which encodes a key subunit of IL-17R targeted by brodalumab, a highly effective psoriasis treatment. These results suggest that TRAF3IP2-AS1 acts as a brake on psoriasis via its effects on IL-17 signaling in activated CD8 T-cells.

A probability estimation-based feature reduction and Bayesian rough set approach for intrusion detection in mobile ad-hoc network

A probability estimation-based feature reduction and Bayesian rough set approach for intrusion detection in mobile ad-hoc network

Analysis of Wilson‐Hilferty distribution under progressive Type‐II censoring

AbstractA new re‐parameterize form of the Wilson‐Hilferty distribution for data modelling with increasing, decreasing and bathtub shape hazard rates has been considered. This paper takes into account the estimation for the unknown model parameters, reliability function and hazard function based on two frequentist methods and Bayesian method of estimation using Type‐II progressively censored data. In frequentist method, besides conventional likelihood based estimation, another competitive method, known as maximum product of spacing (MPS) method is proposed to estimate the model parameters, reliability function and hazard function as an alternative approach to the common likelihood method. In Bayesian paradigm, we have also considered the MPS function as an alternative to the traditional likelihood function and both are also discussed under the Bayesian set up for unknown parameters, reliability function and hazard function. Moreover, for all considered unknown quantities, the approximate confidence intervals under the proposed frequentist approaches as well as the Bayes credible intervals are constructed. Extensive Monte‐Carlo simulation studies are conducted to evaluate the performance of the proposed estimates with respect to various criteria quantities. Furthermore, we discuss an optimal progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, to show the applicability of the proposed methodologies in a real‐life scenario, an engineering dataset is analysed.

GM-PHD Filter for Searching and Tracking an Unknown Number of Targets With a Mobile Sensor With Limited FOV

We study the problem of searching for and tracking a collection of moving targets using a robot with a limited field-of-view (FOV) sensor. The actual number of targets present in the environment is not known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . We propose a search and tracking framework based on the concept of Bayesian random finite sets (RFSs). Specifically, we generalize the Gaussian mixture probability hypothesis density (GM-PHD) filter which was previously applied for tracking problems to allow for simultaneous search and tracking with a limited FOV sensor. The proposed framework can extract individual target tracks as well as estimate the number and the spatial density of targets. We also show how to use the Gaussian process (GP) regression to extract and predict unknown target trajectories in this framework. We demonstrate the efficacy of our techniques through representative simulations and a real data collected from an aerial robot. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by search-and-rescue operations where a robot with limited field-of-view (FOV) is used to search and track lost targets. This article presents an estimation and planning framework to estimate the position of targets and track them over time. The key feature of the proposed algorithm is that it can deal with an unknown and varying number of targets. The framework can also deal with an unknown motion model for targets which itself can be complex. The algorithm is shown to be robust to a poor initialization and can handle an initial belief which overestimates or underestimates the actual number of targets. The proposed scheme includes various user-defined parameters. It is recommended to tune these parameters <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> using simulations for a better performance. Incorporating a multirobot approach into the proposed algorithm and finding a better planning strategy that minimizes the time are potential future works.