Non-blind image blur removal method based on a Bayesian hierarchical model with hyperparameter priors

Blind image deconvolution, i.e., estimating both the latent image and the blur kernel from the only observed blurry image, is a severely ill-posed inverse problem. In this paper, we propose a blur kernel estimation method for blind motion deblurring using sparse representation and cross-scale self-similarity of image patches as priors to recover the latent sharp image from a single blurry image. Sparse representation indicates that image patches can always be represented well as a sparse linear combination of atoms in an appropriate dictionary. Cross-scale self-similarity results in that any image patch can in some way be well approximated by a number of other similar patches across different image scales. Our method is based on the observations that almost any image patch in a natural image has multiple similar patches in down-sampled versions of the image, and down-sampling produces image patches that are sharper than those in the blurry image itself. In our method, the dictionary for sparse representation is trained adaptively from sharper patches sampled from the down-sampled latent image estimate to make the similar patches of the latent sharp image well represented sparsely, and meanwhile, all patches from the latent image estimate are optimized to be as close to the sharper similar patches searched from the down-sampled version to enforce the sharp recovery of the latent image by constructing a non-local regularization. Experimental results on both simulated and real blurry images demonstrate that our method outperforms state-of-the-art blind deblurring methods.

A deep variational Bayesian framework for blind image deblurring

Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.

This paper describes procedures for forecasting countries' output growth rates and medians of a set of output growth rates using Hierarchical Bayesian (HB) models. The purpose of this paper is to show how the γ‐shrinkage forecast of Zellner and Hong (1989) emerges from a hierarchical Bayesian model and to describe how the Gibbs sampler can be used to fit this model to yield possibly improved output growth rate and median output growth rate forecasts. The procedures described in this paper offer two primary methodological contributions to previous work on this topic: (1) the weights associated with widely‐used shrinkage forecasts are determined endogenously, and (2) the posterior predictive density of the future median output growth rate is obtained numerically from which optimal point and interval forecasts are calculated. Using IMF data, we find that the HB median output growth rate forecasts outperform forecasts obtained from variety of benchmark models. Copyright © 2001 John Wiley & Sons, Ltd.

BackgroundVaccines constitute a fundamental component of public health interventions, preventing the transmission of numerous diseases. Nevertheless, vaccines remain underutilized in various regions globally, particularly in East African nations, where high mortality rates among children under 5 years of age are predominantly attributable to vaccine‐preventable diseases. Consequently, this investigation is aimed at evaluating children′s vaccination coverage and its associated determinants in East Africa utilizing Bayesian hierarchical modeling based on Demographic and Health Survey (DHS) data (2019–2022).MethodsThis study analyzed nationally representative data from the DHS, a standardized cross‐sectional household survey program that collects health and population data using stratified two‐stage cluster sampling. Data were drawn from surveys conducted between 2019 and 2022 in five East African countries: Ethiopia (2019), Kenya (2022), Mozambique (2022), Rwanda (2019/20), and Tanzania (2022). A Bayesian hierarchical regression model was applied to identify factors influencing vaccination coverage, evaluating four candidate models using leave‐one‐out cross‐validation to select the best fit. Statistical significance was assessed using 95% posterior credible intervals (CrIs) after confirming model convergence.ResultsA total of 15,703 weighted children aged 12–23 months were included, with an overall survey response rate of 97.2%. A substantial proportion of children (73.81%) were only partially immunized, highlighting a critical gap in achieving full vaccination coverage. The Bayesian hierarchical ordinal logistic regression showed that several factors were significantly associated with the odds of being in a higher vaccination category versus a lower one. Children residing in Kenya had 3.10 times higher odds of being in a higher vaccination category compared with those in Ethiopia (AOR = 3.10; 95% CrI: 2.49–3.86). Maternal media exposure (AOR = 1.25, 95% CrI: 1.15, 1.38), maternal education (secondary or above) (AOR = 1.42, 95% CrI: 1.21, 1.67), health facility delivery (AOR = 1.53, 95% CrI: 1.19, 1.96), postnatal care visit (AOR = 1.28, 95% CrI: 1.15, 1.43), skilled birth attendance (AOR = 1.61, 95% CrI: 1.24, 2.079), and antenatal care (ANC) visits (four and above) (AOR = 4.08, 95% CrI: 3.44, 4.84) were all positively associated with higher odds of being in a higher vaccination category.ConclusionsVaccination coverage remains low across East Africa, with significant regional disparities. These results highlight the need for focused interventions in high‐risk areas and addressing key determinants to improve childhood vaccination rates.

How cognitive modeling can benefit from hierarchical Bayesian models

Global climate change (GCC) may be causing distribution range shifts in many organisms worldwide. Multiple efforts are currently focused on the development of models to better predict distribution range shifts due to GCC. We addressed this issue by including intraspecific genetic structure and spatial autocorrelation (SAC) of data in distribution range models. Both factors reflect the joint effect of ecoevolutionary processes on the geographical heterogeneity of populations. We used a collection of 301 georeferenced accessions of the annual plant Arabidopsis thaliana in its Iberian Peninsula range, where the species shows strong geographical genetic structure. We developed spatial and nonspatial hierarchical Bayesian models (HBMs) to depict current and future distribution ranges for the four genetic clusters detected. We also compared the performance of HBMs with Maxent (a presence-only model). Maxent and nonspatial HBMs presented some shortcomings, such as the loss of accessions with high genetic admixture in the case of Maxent and the presence of residual SAC for both. As spatial HBMs removed residual SAC, these models showed higher accuracy than nonspatial HBMs and handled the spatial effect on model outcomes. The ease of modelling and the consistency among model outputs for each genetic cluster was conditioned by the sparseness of the populations across the distribution range. Our HBMs enrich the toolbox of software available to evaluate GCC-induced distribution range shifts by considering both genetic heterogeneity and SAC, two inherent properties of any organism that should not be overlooked.

Multivariate Bayesian hierarchical modeling of the non-stationary traffic conflict extremes for crash estimation

ABSTRACTStroke is a disturbance in blood supply to the brain resulting in the loss of brain functions, particularly motor function. A study was conducted by the UCI Neurorehabilitation Lab to investigate the impact of stroke on motor-related brain regions. Functional MRI (fMRI) data were collected from stroke patients and healthy controls while the subjects performed a simple motor task. In addition to affecting local neuronal activation strength, stroke might also alter communications (i.e., connectivity) between brain regions. We develop a hierarchical Bayesian modeling approach for the analysis of multi-subject fMRI data that allows us to explore brain changes due to stroke. Our approach simultaneously estimates activation and condition-specific connectivity at the group level, and provides estimates for region/subject-specific hemodynamic response functions. Moreover, our model uses spike-and-slab priors to allow for direct posterior inference on the connectivity network. Our results indicate that motor-control regions show greater activation in the unaffected hemisphere and the midline surface in stroke patients than those same regions in healthy controls during the simple motor task. We also note increased connectivity within secondary motor regions in stroke subjects. These findings provide insight into altered neural correlates of movement in subjects who suffered a stroke. Supplementary materials for this article are available online.

ABSTRACTDue to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common for the full data set, with most parameters being group specific. Thus, parallel Bayesian MCMC methods that take into account the structure of the model and split the full data set by groups rather than by observations are a more natural approach for analysis. Here, we adapt and extend a recently introduced two-stage Bayesian hierarchical modeling approach, and we partition complete data sets by groups. In stage 1, the group-specific parameters are estimated independently in parallel. The stage 1 posteriors are used as proposal distributions in stage 2, where the target distribution is the full model. Using three-level and four-level models, we show in both simulation and real data studies that results of our method agree closely with the full data analysis, with greatly increased MCMC efficiency and greatly reduced computation times. The advantages of our method versus existing parallel MCMC computing methods are also described.

Microstructure modelling quantifies subvoxel tissue features by combining an MRI acquisition with a mathematical model, which is typically fitted voxel-by-voxel with least-squares (LSQ) minimisation to give voxelwise maps of microstructural quantities such as diffusivity and compartmental fractions. Such approaches are susceptible to voxelwise noise, which can lead to erroneous values in parameter maps. Hierarchical Bayesian modelling (HBM) can address this limitation but has only been demonstrated for simple models. We previously derived an HBM approach for an arbitrary microstructure model with flexible parameter constraints, utilising a Markov chain Monte Carlo algorithm for parameter estimation; here, the method is demonstrated and evaluated using simulated and human data for two previously unexplored diffusion MRI techniques, namely, diffusion kurtosis imaging and blood-brain barrier filter exchange imaging. When compared with LSQ minimisation, HBM increased the accuracy, precision, contrast-to-noise ratio and parameter map quality in both simulated and human data. HBM was also able to resolve local parameter variations associated with white matter lesions in a small sample of cerebral small vessel disease subjects, which were obscured by high noise levels in the LSQ-derived parameter maps. Finally, a noise sensitivity assessment in simulations showed that HBM improved the contrast-to-noise ratio and parameter map quality even at low signal-to-noise ratios. This generalised HBM framework can improve parameter estimation for more complex diffusion MRI microstructural models that extend beyond linear combinations of exponentials.

A Bayesian hierarchical model was applied to acoustic backscattering data collected on Mysis relicta (opossum shrimp) populations in Lake Ontario in 2005 to estimate the combined uncertainty in mean density estimates as well as the individual contributions to that uncertainty from the various information sources involved in the calculation including calibration, target strength determination, threshold specification and survey sampling design. Traditional estimation approaches often only take into account the variability associated with the survey design, while assuming that all other intermediate parameter estimates used in the calculations are fixed and known. Unfortunately, unaccounted for variation in the steps leading up to the global density estimate may make significant contributions to the uncertainty of density estimates. While other studies have used sensitivity analyses to demonstrate the degree to which uncertainty in the various input parameters can influence estimates, including the uncertainty directly as demonstrated here using a Bayesian hierarchical approach allows for a more transparent representation of the true uncertainty and the mechanisms needed for its reduction. A Bayesian analysis of the mysid data examined here indicates that increasing the sample size of biological collections used in the target strength regression prove to be a more direct and practical way of reducing the overall variation in mean density estimates than similar steps employed to increase the number of transects surveyed. A doubling of target strength net tow samples resulted in a 23% reduction in variance relative to an 11% reduction that resulted from doubling the number of survey transects. This is an important difference as doubling the number of survey transects would add 5 days to the survey whereas doubling the number of net tows would add only one day. Although these results are specific to this particular data set, the method described is general.

Key-words: hierarchical Bayes model, backcalculation, fish, scales, Zingel asper Back-calculation allows to increase available data on fish growth. The accuracy of back-calculation models is of paramount importance for growth analysis. Frequentist and Bayesian hierarchical approaches were used for regression between fish body size and scale size for the rare fish species Zingel asper. The Bayesian approach permits more reliable estimation of back-calculated size, taking into account biological information and cohort variability. This method greatly improves estimation of backcalculated length when sampling is uneven and/or small.

Ecosystem health and water quality of rivers are dependent on their temperature. With ongoing human‐induced climate change causing increases in air temperature across the globe, it is anticipated the stream temperatures will rise too—in turn increasing the rates of biogeochemical stream processes and potentially threatening the viability and health of aquatic organisms. To understand the relationship between climate change and stream temperature response, the longer the records that can be analysed, the more the robust the analysis for detecting change. In this study, we analyse records from 263 catchments from across the United Kingdom for 45 years from 1974 to 2019 to assess the link between air temperature and stream temperature change. To give the most precise analysis of these long records, Bayesian hierarchical modelling was used and showed that: (i) The Bayesian hierarchical approach was 59% more precise, that is, reduced uncertainty on long‐term trends, than using simple linear regression. (ii) The increase in annual average air temperature over 45 years across the United Kingdom showed no significant differences between 22 weather stations and gave a 45‐year change of 1.35 ± 0.9°C. (iii) Trends in annual mean stream temperature change varied from −2.3 °C to 2.0 °C over 45 years, with the mean over 263 sites being 0.5 °C over 45 years. (iv) 1% of rivers showed a stream temperature trend significantly greater than the air temperature trend but 3% of sites showed a stream temperature trend significantly lower than zero. (v) 74% of all river sites showed no significant monotonic trend, either positive or negative, in water temperature even after 45 years. The observed declines in stream temperature could be ascribed to the closures of thermoelectric power stations but it is unclear why the stream temperature at some sites has risen faster than air temperature. The study shows that mean river temperature was well buffered against changes in air temperature—a 1°C rise in air temperature giving 0.37°C in mean stream temperature.

Multilevel data and Bayesian analysis in traffic safety