Gibbs Sampling Research Articles

Sampling-based Spotlight SAR Image Reconstruction from Phase History Data for Speckle Reduction and Uncertainty Quantification

Spotlight mode airborne synthetic aperture radar (SAR) is a coherent imaging modality that is an important tool in remote sensing. Existing methods for spotlight SAR image reconstruction from phase history data typically produce a single image estimate which approximates the reflectivity of an unknown ground scene, and therefore provide no quantification of the certainty with which the estimate can be trusted. In addition, speckle affects all coherent imaging modalities causing a degradation of image quality. Many point estimate image reconstruction methods incorrectly treat speckle as additive noise resulting in an unnatural smoothing of the speckle that also reduces image contrast. The purpose of this paper is to address the issues of speckle and uncertainty quantification by introducing a sampling-based approach to SAR image reconstruction directly from phase history data. In particular, a statistical model for speckle as well as a corresponding sparsity technique to reduce it are directly incorporated into the model. Rather than a single point estimate, samples of the resulting joint posterior density are efficiently obtained using a Gibbs sampler, which are in turn used to derive estimates and other statistics which aid in uncertainty quantification. The latter information is particularly important in SAR, where ground truth images even for synthetically created examples are typically unknown. While similar methods have been deployed to process formed images, this paper focuses on the integration of these techniques into image reconstruction from phase history data. An example result using real-world data shows that, when compared with existing methods, the sampling-based approach introduced provides parameter-free estimates with improved contrast and significantly reduced speckle, as well as uncertainty quantification information.

Volatility analysis for the GARCH–Itô–Jumps model based on high-frequency and low-frequency financial data

This paper introduces a model that can accommodate both the continuous-time-diffusion and discrete-time mixed-GARCH–Jump models by embedding the discrete mixed-GARCH-Jump structure in the continuous volatility process. The key feature of the proposed model is that the corresponding conditional integrated volatility adopts the mixed-GARCH-Jump structure that accounts for the effect of jumps on future volatility. A Griddy–Gibbs sampler approach is proposed to estimate parameters, and volatility forecasting and value-at-risk forecasting based on the peaks-over-threshold method are developed. Simulations are carried out to check the finite sample performance of the proposed methodology, and empirical studies show that, in general, volatility is heavily influenced by the continuous innovations, rather than the extreme reactions. We find that both the simulation and empirical results in most cases support the proposed model.

Estimation of genetic parameters for important traits using a multi-trait model in late-feathering Qingyuan partridge hens in China.

Qingyuan partridge chicken is one of the most well-known Chinese indigenous yellow broilers. In breeding programmes, five traits are usually selected when the chickens are 105 days old, namely body weight (BW), comb height (CH), shank length (SL), shank girth (SG) and feather maturity (FM). The objective of this study was to estimate the genetic parameters of these five traits, especially direct additive genetic correlations, to lay the foundation for balanced selection of Qingyuan partridge chickens. Approximately 9600 records were used for estimation. Variance components for these five traits were estimated using three multi-trait models incorporating different effects via Gibbs sampling. Based on model 1 in which the random effects included direct additive genetic effects and residuals, the estimated direct heritabilities for BW, CH, SL, SG and FM were 0.29 ± 0.04, 0.53 ± 0.04, 0.47 ± 0.04, 0.43 ± 0.05 and 0.18 ± 0.03, respectively. The direct genetic correlations ranged from -0.08 to 0.46. When additionally considering maternal additive genetic effects (model 2), the estimates of direct heritabilities and absolute values of direct additive genetic correlations were smaller. The heritabilities were 0.14 ± 0.04, 0.40 ± 0.02, 0.34 ± 0.05, 0.27 ± 0.05 and 0.12 ± 0.03 for BW, CH, SL, SG and FM, respectively. The direct additive genetic correlations ranged from -0.33 to 0.36. More specifically, the direct additive genetic correlations between BW and CH, SL, SG and FM were 0.19 ± 0.13, 0.15 ± 0.15, 0.36 ± 0.15 and - 0.33 ± 0.21, respectively. The genetic correlations of FM with SL, SG and CH were - 0.15 ± 0.15, -0.08 ± 0.17 and 0.18 ± 0.15, respectively. The direct genetic correlations between CH and SG and SL were - 0.02 ± 0.11 and - 0.20 ± 0.11, respectively, and that between SL and SG was 0.19 ± 0.11. The total heritabilities and maternal additive genetic correlations ranged from 0.16 to 0.44 and from -0.13 to 0.61, respectively. The third model also included the maternal permanent environmental effect for BW. The estimates of direct heritability, direct additive genetic correlation, total heritability and maternal additive genetic correlation were only slightly different from those based on the second model. Therefore, the maternal additive genetic effect has a large effect on the estimation of genetic parameters, and it is better to consider this effect in the genetic evaluation of these five traits. Relatively high direct and maternal additive genetic correlations for most trait pairs suggested that it is better to jointly evaluate these five traits in breeding programmes.

Bayesian tensor logistic regression with applications to neuroimaging data analysis of Alzheimer's disease.

Alzheimer's disease (AD) can be diagnosed by utilizing traditional logistic regression models to fit magnetic resonance imaging (MRI) data of brain, which is regarded as a vector of covariates. But its parameter estimation is inefficient and computationally extensive due to ultrahigh dimensionality and complicated structure of MRI data. To overcome this deficiency, this paper proposes a tensor logistic regression model (TLRM) for AD's MRI data by regarding MRI tensor as covariates. Under this framework, a tensor candecomp/parafac (CP) decomposition tool is employed to reduce ultrahigh dimensional tensor to a high dimensional level, a novel Bayesian adaptive Lasso method is developed to simultaneously select important components of tensor and estimate model parameters by incorporating the Plya-Gamma method leading a closed-form likelihood and avoiding the usage of the Metropolis-Hastings algorithm, and Gibbs sampler technique in Markov chain Monte Carlo (MCMC). A tensor's product technique is utilized to optimize the calculation program and speed up the calculation of MCMC. Bayes factor together with the path sampling approach is presented to select tensor rank in CP decomposition. Effectiveness of the proposed method is illustrated on simulation studies and an MRI data analysis.

A data-driven method for anomaly detection and aging model parameter estimation of capacitors based on condition monitoring

The reliability of capacitor is a crucial problem affecting power electronics system. However, the sudden failure caused by parameter mutation cannot be identified from normal aging and the aging model parameters obtained from prior knowledge cannot accurately describe the aging process of the capacitor under practical operating conditions. Therefore, a data-driven method for anomaly detection and aging model parameter estimation of capacitors is proposed. Firstly, Mahalanobis distance is introduced to analyse the correlation between capacitance loss and equivalent series resistance (ESR) and eliminate the dimensional effect. The anomaly is detected when there is a sudden change of the distance between the current monitoring value and the historical data. Then, parameter estimation method of aging model based on Bayesian linear regression is proposed to modify model parameters in real time, combining the prior knowledge and posterior data. The Markov chain Monte Carlo (MCMC) algorithm according to Gibbs sampling is introduced to obtain parameter posterior distribution. Finally, the superiority of the method is verified by accelerated aging test.

Controlling outlier contamination in multimessenger time-domain searches for supermasssive binary black holes

ABSTRACT Time-domain data sets of many varieties can be prone to statistical outliers that result from instrumental or astrophysical anomalies. These can impair searches for signals within the time series and lead to biased parameter estimation. Versatile outlier mitigation methods tuned toward multimessenger time-domain searches for supermassive binary black holes have yet to be fully explored. In an effort to perform robust outlier isolation with low computational costs, we propose a Gibbs sampling scheme. This provides structural simplicity to outlier modelling and isolation, as it requires minimal modifications to adapt to time-domain modelling scenarios with pulsar-timing array or photometric data. We robustly diagnose outliers present in simulated pulsar-timing data sets, and then further apply our methods to pulsar J1909−3744 from the NANOGrav 9-year Data set. We also explore the periodic binary-AGN candidate PG1302−102 using data sets from the Catalina Real-time Transient Survey, All-Sky Automated Survey for Supernovae, and the Lincoln Near-Earth Asteroid Research. We present our findings and outline future work that could improve outlier modelling and isolation for multimessenger time-domain searches.

Bayesian analysis of longitudinal binary responses based on the multivariate probit model: A comparison of five methods.

Dichotomous response data observed over multiple time points, especially data that exhibit longitudinal structures, are important in many applied fields. The multivariate probit model has been an attractive tool in such situations for its ability to handle correlations among the outcomes, typically by modeling the covariance (correlation) structure of the latent variables. In addition, a multivariate probit model facilitates controlled imputations for nonignorable dropout, a phenomenon commonly observed in clinical trials of experimental drugs or biologic products. While the model is relatively simple to specify, estimation, particularly from a Bayesian perspective that relies on Markov chain Monte Carlo sampling, is not as straightforward. Here we compare five sampling algorithms for the correlation matrix and discuss their merits: a parameter-expanded Metropolis-Hastings algorithm (Zhang et al., 2006), a parameter-expanded Gibbs sampling algorithm (Talhouk et al., 2012), a parameter-expanded Gibbs sampling algorithm with unit constraints on conditional variances (Tang, 2018), a partial autocorrelation parameterization approach (Gaskins et al., 2014), and a semi-partial correlation parameterization approach (Ghosh et al., 2021). We describe each algorithm, use simulation studies to evaluate their performance, and focus on comparison criteria such as computational cost, convergence time, robustness, and ease of implementations. We find that the parameter-expanded Gibbs sampling algorithm by Talhouk et al. (2012) often has the most efficient convergence with relatively low computational complexity, while the partial autocorrelation parameterization approach is more flexible for estimating the correlation matrix of latent variables for typical late phase longitudinal studies.

Genetic evaluation of semen traits in Holstein-Friesian purebred, Holstein-Friesian crossbred and indigenous bulls under hot and semi-arid conditions of India

Genetic parameters of semen production traits were evaluated in Holstein-Friesian (HF) purebred, HF crossbred and indigenous bulls using Bayesian univariate and bivariate models. Data from 486 bulls on 164,962 ejaculates collected from Bharatiya Agro Industries Foundation (BAIF) was utilized for this study. Six semen production traits viz. ejaculate volume (EV- ml), sperm concentration (SC- 109/ml), initial sperm motility (ISM- %), post-thaw motility (PTM- %), total number of spermatozoa per ejaculate (TNS- 109/ejaculate) and the theoretical number of semen doses (TNSD) were included in the analysis. Gibbs sampling was done to implement a Bayesian framework where 200,000 and 500,000 Gibbs samples were obtained for univariate and bivariate analyses respectively. In general, the estimates of the means for semen production traits were lower in indigenous bulls except for ISM. Heritability estimates ranged between 0.023 (ISM) to 0.340 (SC) in HF purebreds, 0.011 (PTM) to 0.076 (EV) in HF crossbreds and 0.025 (ISM) to 0.153 (TNS) in indigenous bulls. Repeatability estimates ranged between 0.030 (PTM) to 0.412 (SC) in HF purebreds, 0.012 (PTM) to 0.391 (SC) in HF crossbreds and 0.067 (ISM) to 0.333 (EV) in indigenous bulls. Highly negative genetic correlations were obtained between EV and SC whereas they were highly positive between ISM and PTM. Precise genetic parameter estimates could be obtained for the semen production traits using a Bayesian framework which will further facilitate in the improvement of semen traits and bull fertility.

Sparsity enforced time–frequency decomposition in the Bayesian framework for bearing fault feature extraction under time-varying conditions

Fault characteristic extraction of rolling bearings is essential for fault diagnosis. Rolling bearings are usually operated at changing speeds, and the nonstationary signals of the bearings are covered by the heavy background noise, making the extraction task of fault features very difficult. To address this issue, a robust fault characteristic extraction approach based on the time–frequency analysis under variable speed conditions is proposed in this paper. Firstly, the sparse property of the time-variant fault characteristics and low-rankness of background noise are explored and utilized in the time–frequency representation (TFR). Then, the sparse and the low-rank components are integrated into a hierarchical Bayesian model, and a random error term is considered to make the Bayesian model more robust. The Gibbs sampler is applied to extract the desired sparsity-enhanced component of the TFR in the Bayesian framework. Eventually, the time–frequency reassignment technique is adopted further to optimize the time–frequency resolution of the sparse component. Two simulated scenarios and a real-data experiment are used to evaluate the suggested approach’s performance. It turns out that the proposed approach is robust to noise and can extract the bearing time-varying fault features effectively.

A model and a numerical scheme for the description of distribution and abundance of individuals.

We introduce a model in the context of ecology that can be used to describe the distribution and abundance of individuals when data from field work is extremely limited (for example, in the case of endangered species). Our procedure is based on an intuitive understanding of the physical properties of phenomena. The idea is that individuals have the tendency to be attracted (or repulsed) to certain properties of the environment. At the same time, they are spread in such a way that if there is no reason for them to be in some specific locations, then they are uniformly distributed throughout the region. Our model draws from quantum mechanics, by using quantum Hamiltonians in the context of classical statistical mechanics. The equilibrium between the spreading and the attractive (or repulsive) forces determines the behavior of the species that we model, and this is expressed in terms of a global control problem of an energy operator which is the sum of a kinetic term (spreading) and a potential (attraction or repulsion). We focus on the full probability measure and a global control of the model (instead of looking at conditional measures that generate a global measure). Furthermore, we propose a numerical solution to this global control problem that overcomes the well-known major difficulty of Gibbs sampling (annealing) which is the fact that a global control is hardly reachable when the number of variables is large (the algorithms get stuck in non-optimal states).

Bayesian Markov-Switching Tensor Regression for Time-Varying Networks

Modeling time series of multilayer network data is challenging due to the peculiar characteristics of real-world networks, such as sparsity and abrupt structural changes. Moreover, the impact of external factors on the network edges is highly heterogeneous due to edge- and time-specific effects. Capturing all these features results in a very high-dimensional inference problem. A novel tensor-on-tensor regression model is proposed, which integrates zero-inflated logistic regression to deal with the sparsity, and Markov-switching coefficients to account for structural changes. A tensor representation and decomposition of the regression coefficients are used to tackle the high-dimensionality and account for the heterogeneous impact of the covariate tensor across the response variables. The inference is performed following a Bayesian approach, and an efficient Gibbs sampler is developed for posterior approximation. Our methodology applied to financial and email networks detects different connectivity regimes and uncovers the role of covariates in the edge-formation process, which are relevant in risk and resource management. Code is available on GitHub. Supplementary materials for this article are available online.

The Performance of Bayesian Analysis in Structural Equation Modelling to Construct The Health Behaviour During Pandemic COVID-19

Originating from Wuhan, China, COVID-19 is spreading rapidly throughout the world. The epidemiological model is required to provide evidence for public health policymakers to reduce the spread of COVID-19. Health behaviour is assumed could reduce the spread of this virus. This study purposes to construct an acceptable model of health behaviour. To achieve this goal, a Bayesian structural equation modelling (SEM) is implemented. This current study is also purposed to evaluate the performance of Bayesian SEM, including the sensitivity, adequacy, and the acceptability of parameters estimated with the result that the acceptable model is obtained. The sensitivity of the Bayesian SEM estimator is evaluated by choosing several types of prior and the model results are compared. The adequacy of the Bayesian SEM estimate is checked by doing the convergence test of the corresponding model parameters. The acceptability of the Bayesian approach and its associated algorithm in recovering the true parameters are monitored by the Bootstrap simulation study. The Bayesian SEM applies the Gibbs sample approach in estimating model parameters. This method is applied to the primary data gathered from an online survey from March to May 2020 during COVID-19 to individuals living in West Sumatera, Indonesia. It is found that health motivation is significantly related to health behaviour. Whereas socio-demographic and perceived susceptibility has no significant effect on health behaviour.

Collaborative Task Offloading and Service Caching Strategy for Mobile Edge Computing

Mobile edge computing (MEC), which sinks the functions of cloud servers, has become an emerging paradigm to solve the contradiction between delay-sensitive tasks and resource-constrained terminals. Task offloading assisted by service caching in a collaborative manner can reduce delay and balance the edge load in MEC. Due to the limited storage resources of edge servers, it is a significant issue to develop a dynamical service caching strategy according to the actual variable user demands in task offloading. Therefore, this paper investigates the collaborative task offloading problem assisted by a dynamical caching strategy in MEC. Furthermore, a two-level computing strategy called joint task offloading and service caching (JTOSC) is proposed to solve the optimized problem. The outer layer in JTOSC iteratively updates the service caching decisions based on the Gibbs sampling. The inner layer in JTOSC adopts the fairness-aware allocation algorithm and the offloading revenue preference-based bilateral matching algorithm to get a great computing resource allocation and task offloading scheme. The simulation results indicate that the proposed strategy outperforms the other four comparison strategies in terms of maximum offloading delay, service cache hit rate, and edge load balance.

Hierarchical modeling of microstructural images for porosity prediction in metal additive manufacturing via two-point correlation function

Porosity is one of the most critical quality issues in Additive Manufacturing (AM). As process parameters are closely related to porosity formation, it is vitally important to study their relationship for better process optimization. In this article, motivated by the emerging application of metal AM, a three-level hierarchical mixed-effects modeling approach is proposed to characterize the relationship between microstructural images and process parameters for porosity prediction and microstructure reconstruction. Specifically, a Two-Point Correlation Function (TPCF) is used to capture the morphology of the pores quantitatively. Then, the relationship between the TPCF profile and process parameters is established. A blocked Gibbs sampling approach is developed for parameter inference. Our modeling framework can reconstruct the microstructure based on the predicted TPCF through a simulated annealing optimization algorithm. The effectiveness and advantageous features of our method are demonstrated by both the simulation study and the case study with real-world data from metal AM applications.

Bayesian dynamic network modelling: an application to metabolic associations in cardiovascular diseases

We propose a novel approach to the estimation of multiple Graphical Models to analyse temporal patterns of association among a set of metabolites over different groups of patients. Our motivating application is the Southall And Brent REvisited (SABRE) study, a tri-ethnic cohort study conducted in the UK. We are interested in identifying potential ethnic differences in metabolite levels and associations as well as their evolution over time, with the aim of gaining a better understanding of different risk of cardio-metabolic disorders across ethnicities. Within a Bayesian framework, we employ a nodewise regression approach to infer the structure of the graphs, borrowing information across time as well as across ethnicities. The response variables of interest are metabolite levels measured at two time points and for two ethnic groups, Europeans and South-Asians. We use nodewise regression to estimate the high-dimensional precision matrices of the metabolites, imposing sparsity on the regression coefficients through the dynamic horseshoe prior, thus favouring sparser graphs. We provide the code to fit the proposed model using the software Stan, which performs posterior inference using Hamiltonian Monte Carlo sampling, as well as a detailed description of a block Gibbs sampling scheme.

Analysis of presence-only data via exact Bayes, with model and effects identification

This paper provides an exact modeling approach for the analysis of presence-only ecological data. Our proposal is also based on frequently used inhomogeneous Poisson processes but does not rely on model approximations, unlike other approaches. Exactness is achieved via a data augmentation scheme. One of the augmented processes can be interpreted as the unobserved occurrences of the relevant species, and its posterior distribution can be used to make predictions of the species over the region of study beyond the observer bias. The data augmentation also leads to a natural Gibbs sampler to make Bayesian inference through MCMC. The proposal shows better performance than the currently standard method based on Poisson process with intensity function depending log-linearly on the covariates. Additionally, an identification problem that arises in the traditional model does not seem to affect our proposal in the analyses of real ecological data.

Co-clustering of multivariate functional data for the analysis of air pollution in the South of France

Nowadays, air pollution is a major threat for public health with clear relationships with many diseases, especially cardiovascular ones. The spatiotemporal study of pollution is of great interest for governments and local authorities when deciding for public alerts or new city policies against pollution increase. The aim of this work is to study spatiotemporal profiles of environmental data collected in the south of France (Région Sud) by the public agency AtmoSud. The idea is to better understand the exposition to pollutants of inhabitants on a large territory with important differences in term of geography and urbanism. The data gather the recording of daily measurements of five environmental variables, namely, three pollutants (PM10, NO2, O3) and two meteorological factors (pressure and temperature) over six years. Those data can be seen as multivariate functional data: quantitative entities evolving along time for which there is a growing need of methods to summarize and understand them. For this purpose a novel co-clustering model for multivariate functional data is defined. The model is based on a functional latent block model which assumes for each co-cluster a probabilistic distribution for multivariate functional principal component scores. A stochastic EM algorithm, embedding a Gibbs sampler, is proposed for model inference as well as a model selection criteria for choosing the number of co-clusters. The application of the proposed co-clustering algorithm on environmental data of the Région Sud allowed to divide the region, composed by 357 zones, into six macroareas with common exposure to pollution. We showed that pollution profiles vary accordingly to the seasons, and the patterns are similar during the six years studied. These results can be used by local authorities to develop specific programs to reduce pollution at the macroarea level and to identify specific periods of the year with high pollution peaks in order to set up specific health prevention programs. Overall, the proposed co-clustering approach is a powerful resource to analyse multivariate functional data in order to identify intrinsic data structure and to summarize variables profiles over long periods of time.

Quantum algorithms for structured prediction

We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in $$\tilde{O}\left (1/\epsilon \right )$$ with respect to the precision, 𝜖, of the solution. Motivated by robust inference techniques in machine learning, we then introduce another quantum algorithm that solves a smooth approximation of the structured prediction problem with a similar quantum speedup in the size of the label space and a similar scaling in the precision parameter. In doing so, we analyze a variant of stochastic gradient descent for convex optimization in the presence of an additive error in the calculation of the gradients, and show that its convergence rate does not deteriorate if the additive errors are of the order $$O(\sqrt{\epsilon})$$ . This algorithm uses quantum Gibbs sampling at temperature Ω(𝜖) as a subroutine. Based on these theoretical observations, we propose a method for using quantum Gibbs samplers to combine feedforward neural networks with probabilistic graphical models for quantum machine learning. Our numerical results using Monte Carlo simulations on an image tagging task demonstrate the benefit of the approach.

On Posterior Consistency of Bayesian Factor Models in High Dimensions

As a principled dimension reduction technique, factor models have been widely adopted in applications. However, conducting a proper Bayesian factor analysis can be subtle in high-dimensional settings since it requires both a careful prescription of the prior distribution and a suitable computational strategy. We analyze issues of posterior inconsistency and sensitivity under different priors for high-dimensional sparse normal factor models, and show why adopting the n-orthonormal factor assumption can resolve these issues and lead to a more robust and efficient Bayesian analysis. We also provide an efficient Gibbs sampler to conduct the required computation, and show that it can be orders of magnitude more efficient than compared existing algorithms.

Perfect Sampling of the Posterior in the Hierarchical Pitman-Yor Process.

The predictive probabilities of the hierarchical Pitman-Yor process are approximated through Monte Carlo algorithms that exploits the Chinese Restaurant Franchise (CRF) representation. However, in order to simulate the posterior distribution of the hierarchical Pitman-Yor process, a set of auxiliary variables representing the arrangement of customers in tables of the CRF must be sampled through Markov chain Monte Carlo. This paper develops a perfect sampler for these latent variables employing ideas from the Propp-Wilson algorithm and evaluates its average running time by extensive simulations. The simulations reveal a significant dependence of running time on the parameters of the model, which exhibits sharp transitions. The algorithm is compared to simpler Gibbs sampling procedures, as well as a procedure for unbiased Monte Carlo estimation proposed by Glynn and Rhee. We illustrate its use with an example in microbial genomics studies.