Sequential Bayesian Estimation Research Articles

Real-time gamma-ray energy spectrum / dose monitor with k-α method based on sequential bayesian estimation

Medical applications of radiation have been widely spread until now. However, the exposure of medical staff is sometimes overlooked, because treatment of patients is the first priority. The purpose of this study is to develop a small and light monitor that can measure the energy spectrum and dose of gamma-rays at the same time in real-time for medical applications. Using the monitor, the medical staff could be guided to be more aware ofthe risk of radiation, and finally the exposure to them could be substantially suppressed. So far, a CsI scintillator has been chosen as a detection device of gamma-rays and combined with a Multi-Pixel Photon Counter (MPPC) to develop a prototype monitor. Then we confirmed its basic performance with standard gamma-ray sources. To achieve the real-time measurement, α method (sequential Bayesian estimation) was adopted and improved to propose a new unfolding process, named k-α method, with which the convergence speed could really be accelerated to realize real-time measurement. Also, gamma-ray measurements with a mixed source of 133Ba, 137Cs and 60Co were carried out to confirm the validity of the present monitor. As a result, it was found that gamma-ray energy spectrum could be estimated successfully in several-tens seconds in the field of around 6 μSv/h. For the dose estimation, the correct values could be estimated just after starting measurement.

Balancing Performance and Portability: A Study on CsI(Tl) Crystal Sizes for Real-Time Gamma-Ray Spectrum and Dose Monitoring

Current radiation dosimeters sometimes face accuracy limitations or provide only cumulative doses over long periods. To contribute to this area, we developed a portable monitor that measures the energy spectrum and dose of gamma rays in real time. To achieve this, we used an improved sequential Bayesian estimation algorithm. The dose rate was then derived from the energy spectrum by applying a flux-to-dose conversion coefficient. The monitor consists mainly of a CsI(Tl) scintillator and a multi-pixel photon counter (MPPC). In developing this device, we focused on striking a balance between measurement accuracy, ease of use, and portability. As an essential aspect of the research, we investigated the influence of the CsI(Tl) crystal size on the performance of the monitor to determine an optimal size. This was accomplished by calculating the detection efficiency and energy resolution through experimental measurements using standard gamma-ray sources and simulations using MCNP5. Within the scope of the research, detector response functions were created for each crystal size for an energy range of 10 keV to 3 MeV. Considering an optimal balance of detection efficiency and energy resolution alongside a compact size suitable for portable applications, the crystal measuring 2.6 × 2.6 × 1.3 cm3 was deemed preferable.

A Possibilistic Formulation of Autonomous Search for Targets.

Autonomous search is an ongoing cycle of sensing, statistical estimation, and motion control with the objective to find and localise targets in a designated search area. Traditionally, the theoretical framework for autonomous search combines sequential Bayesian estimation with information theoretic motion control. This paper formulates autonomous search in the framework of possibility theory. Although the possibilistic formulation is slightly more involved than the traditional method, it provides a means for quantitative modelling and reasoning in the presence of epistemic uncertainty. This feature is demonstrated in the paper in the context of partially known probability of detection, expressed as an interval value. The paper presents an elegant Bayes-like solution to sequential estimation, with the reward function for motion control defined to take into account the epistemic uncertainty. The advantages of the proposed search algorithm are demonstrated by numerical simulations.

Video-based sequential Bayesian homography estimation for soccer field registration

A novel Bayesian framework is proposed, which explicitly relates the homography of one video frame to the next through an affine transformation while explicitly modelling keypoint uncertainty. The literature has previously used differential homography between subsequent frames, but not in a Bayesian setting. In cases where Bayesian methods have been applied, camera motion is not adequately modelled, and keypoints are treated as deterministic. The proposed method, Bayesian Homography Inference from Tracked Keypoints (BHITK), employs a two-stage Kalman filter and significantly improves existing methods. Existing keypoint detection methods may be easily augmented with BHITK. It enables less sophisticated and less computationally expensive methods to outperform the state-of-the-art approaches in most homography evaluation metrics. Furthermore, the homography annotations of the WorldCup and TS-WorldCup datasets have been refined using a custom homography annotation tool that has been released for public use. The refined datasets are consolidated and released as the consolidated and refined WorldCup (CARWC) dataset.

Rapid-IAF: Rapid Identification of Individual Alpha Frequency in EEG Data Using Sequential Bayesian Estimation.

Rapid and robust identification of the individual alpha frequency (IAF) in electroencephalogram (EEG) is an essential factor for successful brain-computer interface (BCI) use. Here we demonstrate an algorithm to determine the IAF from short-term resting-state scalp EEG data. First, we outlined the algorithm to determine IAF from short-term resting scalp EEG data and evaluated its reliability using a large-scale dataset of scalp EEG during motor imagery-based BCI use and independent dataset for generalizability confirmation (N = 147). Next, we characterized the relationship between IAF and responsive frequency band of sensorimotor rhythm, which exhibits prominent event-related desynchronization (SMR-ERD) while attempting unilateral and movement. The proposed sequential Bayesian estimation algorithm (Rapid-IAF) determined IAF from less than 26-second resting EEG data among 95% of participants, indicating a clear advance over the conventional methods, which uses 2-15 minutes of data in previous literatures. We confirmed that the determined IAF corresponded to the frequency of SMR, which exhibits the most prominent event-related desynchronization during BCI use (individual SMR-ERD frequency, ISF). Moreover, intraclass correlation revealed that the estimated IAF was more stable than ISF across sessions, suggesting its reliability and utility for robust BCI use without intermittent recalibration. Conclusion In summary, our method rapidly and reliably determined IAF compared to the conventional method using the spectral power change based on task-related response. The method can be utilized to quick BCI initialization. The demonstration of rapid, task-free parametrization of individual variability of neural responses would be of importance for future BCI systems including neural communication via a cursor, an avatar or robots, and closed-loop neurofeedback training.

Bayesian sequential estimation of the proportion of damage in maize seeds

Bayesian sequential estimation of the proportion of damage in maize seeds

Bernoulli Filter for Extended Target Tracking in the Framework of Possibility Theory

Extended objects give rise to a varying number of noisy measurements from its reflection (scattering or feature) points. Due to imperfect detection, only some of the feature points are detected in each scan of input data, while false alarms can also be present. The optimal sequential Bayesian state estimator in the framework of random set theory is the Bernoulli filter for an extended target (BF-X). In this paper we formulate and derive the analog of the BF-X in the framework of possibility theory, where uncertainty is represented using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">possibility</i> functions, rather than <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probability</i> distributions. Possibility functions have the capacity to model partial (imprecise) probabilistic specifications and thus the main advantage of the proposed possibilistic BF-X, is enhanced robustness in the absence of precise measurements or dynamic models.

Sequential Bayesian Ability Estimation Applied to Mixed-Format Item Tests.

Large-scale tests often contain mixed-format items, such as when multiple-choice (MC) items and constructed-response (CR) items are both contained in the same test. Although previous research has analyzed both types of items simultaneously, this may not always provide the best estimate of ability. In this paper, a two-step sequential Bayesian (SB) analytic method under the concept of empirical Bayes is explored for mixed item response models. This method integrates ability estimates from different item formats. Unlike the empirical Bayes method, the SB method estimates examinees' posterior ability parameters with individual-level sample-dependent prior distributions estimated from the MC items. Simulations were used to evaluate the accuracy of recovery of ability and item parameters over four factors: the type of the ability distribution, sample size, test length (number of items for each item type), and person/item parameter estimation method. The SB method was compared with a traditional concurrent Bayesian (CB) calibration method, EAPsum, that uses scaled scores for summed scores to estimate parameters from the MC and CR items simultaneously in one estimation step. From the simulation results, the SB method showed more accurate and reliable ability estimation than the CB method, especially when the sample size was small (150 and 500). Both methods presented similar recovery results for MC item parameters, but the CB method yielded a bit better recovery of the CR item parameters. The empirical example suggested that posterior ability estimated by the proposed SB method had higher reliability than the CB method.

Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach.

Decentralized stochastic control (DSC) is a stochastic optimal control problem consisting of multiple controllers. DSC assumes that each controller is unable to accurately observe the target system and the other controllers. This setup results in two difficulties in DSC; one is that each controller has to memorize the infinite-dimensional observation history, which is not practical, because the memory of the actual controllers is limited. The other is that the reduction of infinite-dimensional sequential Bayesian estimation to finite-dimensional Kalman filter is impossible in general DSC, even for linear-quadratic-Gaussian (LQG) problems. In order to address these issues, we propose an alternative theoretical framework to DSC-memory-limited DSC (ML-DSC). ML-DSC explicitly formulates the finite-dimensional memories of the controllers. Each controller is jointly optimized to compress the infinite-dimensional observation history into the prescribed finite-dimensional memory and to determine the control based on it. Therefore, ML-DSC can be a practical formulation for actual memory-limited controllers. We demonstrate how ML-DSC works in the LQG problem. The conventional DSC cannot be solved except in the special LQG problems where the information the controllers have is independent or partially nested. We show that ML-DSC can be solved in more general LQG problems where the interaction among the controllers is not restricted.

BAYESIAN SEQUENTIAL ESTIMATION OF PROPORTION OF ORTHOPEDIC SURGERY OF TYPE 2 DIABETIC PATIENTS AMONG DIFFERENT AGE GROUPS –A CASE STUDY OF GOVERNMENT MEDICAL COLLEGE, JAMMU-INDIA

A study to determine the proportion of diabetic cases handled by the hospitals in Jammu regarding orthopedic surgeries, especially among different age group, by employing a Bayesian model called Beta-binomial conjugate model using Bayesian sequential estimation method. From the hospital record of Government Medical College (GMC), Jammu. Data was collected and collated over a period of 3 years from 2014-2016 in terms of 4 quarters (Jan-March, April-June, July-Sep and OctDec). The study also compares the computed sample and Empirical Bayes estimates over the three year period and also the variances of the computed estimates and it has been strongly advocated that Empirical Bayes estimators are better estimators on the basis of efficiency and consistency and the proposed method can be employed successfully in any suitable location globally.

Estimation of Soil–Structure Model Parameters for the Millikan Library Building Using a Sequential Bayesian Finite Element Model Updating Technique

We present a finite element model updating technique for soil–structure system identification of the Millikan Library building using the seismic data recorded during the 2002 Yorba Linda earthquake. A detailed finite element (FE) model of the Millikan Library building is developed in OpenSees and updated using a sequential Bayesian estimation approach for joint parameter and input identification. A two-step system identification approach is devised. First, the fixed-base structural model is updated to estimate the structural model parameters (including effective elastic modulus of structural components, distributed floor mass, and Rayleigh damping parameters) and some uncertain components of the foundation-level motion. Then, the identified structural model is used for soil–structure model updating wherein the Rayleigh damping parameters, the stiffness and viscosity of the soil subsystem (modeled using a substructure approach), and the foundation input motions (FIMs) are estimated. The identified model parameters are compared with state-of-practice recommendations. While a specific application is made for the Millikan Library, the present work offers a framework for integrating large-scale FE models with measurement data for model inversion. By utilizing this framework for different civil structures and earthquake records, key structural model parameters can be estimated from the real-world recorded data, which can subsequently be used for assessing and improving, as necessary, state-of-the-art seismic analysis and structural modeling techniques. This paper presents an effort towards using real-world measurements for large-scale FE model updating in the soil and structure, uniform soil time domain for joint parameter and input estimation, and thus paves the way for future applications in system identification, health monitoring, and diagnosis of civil structures.

Moving horizon estimator for nonlinear and non-Gaussian stochastic disturbances

Over the last two decades, moving horizon estimation (MHE) has increasingly been used by researchers and industrial practitioners of nonlinear model predictive control as an alternative to recursive Bayesian estimation schemes. The MHE formulations available in the literature assume that uncertainties in the state dynamics can be modelled as additive and Gaussian stochastic processes. In practice, the unmeasured disturbances affect the system dynamics in a much more complex way and Gaussian assumption may prove inadequate to represent their behaviour. However, unlike the recursive Bayesian estimation area, handling of non-additive and non-Gaussian state disturbances has not received much attention in the MHE literature. In this work, a novel formulation of MHE is proposed in the Bayesian framework to solve state estimation problems associated with systems subjected to nonlinear non-Gaussian stochastic disturbances. To begin with, a Bayesian formulation that maximizes the joint posterior density function of the initial state and stochastic inputs is developed for a batch of data, which is further extended to the moving horizon framework. The proposed formulation associates the random fluctuations affecting the system dynamics with the unmeasured inputs entering the systems. The probabilistic formulation of MHE together with modelling of the state disturbances arising from physical sources enables us to work with any (non-Gaussian or Gaussian) probability density function (PDF) and systematically handle the stochastic inputs affecting the dynamics in a nonlinear manner without making any simplifying assumptions. We proceed to show that the disturbances/states with constraints can also be incorporated in our proposed formulation and can be interpreted as following truncated probability density functions. Efficacy of the proposed MHE approach is demonstrated using three benchmark simulation case studies and an experimental case study. Simulation studies show that the proposed MHE framework is able to perform similar to EnKF, a sampling based sequential Bayesian estimation approach which is capable of handling nonlinear non-Gaussian disturbances. It is further shown that the proposed MHE performs much better than the conventional MHE approach which assumes additive Gaussian noise in the state dynamics. Thus, the proposed MHE scheme provides an optimization based alternative to sampling based estimation schemes, such as Ensemble Kalman filtering, which can handle state estimation problems when state and measurement densities are non-Gaussian.

Experimental verification of real-time gamma-ray energy spectrum and dose monitor

The purpose of this study is to develop a portable monitor that can measure the energy spectrum and dose of gamma-rays simultaneously in real time for the benefit of medical staff who must work in clinical radiation environments. For this purpose, we have developed a prototype monitor using a CsI (Tl) scintillator combined with a multi-pixel photon counter (MPPC). For real-time measurement, we employed an improved sequential Bayesian estimation (k-α method) to convert the measured pulse height spectrum into an energy spectrum. Then we confirmed that reconstruction of the energy spectrum and dose estimation could simultaneously be carried out in real time by the k-α method in a radiation field composed of mixed standard gamma-ray sources. In this study, we carried out measurements in a background gamma-ray field to confirm applicability of the prototype monitor to the weakest type of radiation field. In addition, we conducted measurements in front of a nuclear fuel storage room (∼2 μSv/h) in the authors’ laboratory to evaluate practicality of the monitor for measuring fields with a complex energy spectrum. As a result, it was found that the dose could be estimated in about 20 s after start of measurements even in the background field. For the energy spectrum, it was instantly reconstructed within 60 s in front of the fuel storage room. On the other hand, it could successfully be estimated within 10 min in the background gamma-ray field. Currently, the convergence of the energy spectrum is determined visually from time dependent change of the spectrum and dose. As a next step, we will attempt to develop a more quantitative procedure for determining the convergence.

Bayesian sequential joint detection and estimation under multiple hypotheses

We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The optimal method minimizes the expected number of samples while ensuring that the average detection/estimation errors do not exceed a certain level. After converting the constrained problem to an unconstrained one, we characterize the general solution by a nonlinear Bellman equation, which is parameterized by a set of cost coefficients. A strong connection between the derivatives of the cost function with respect to the coefficients and the detection/estimation errors of the sequential procedure is derived. Based on this fundamental property, we further show that for suitably chosen cost coefficients the solutions of the constrained and the unconstrained problem coincide. We present two approaches to finding the optimal coefficients. For the first approach, the final optimization problem is converted into a linear program, whereas the second approach solves it with a projected gradient ascent. To illustrate the theoretical results, we consider two problems for which the optimal schemes are designed numerically. Using Monte Carlo simulations, it is validated that the numerical results agree with the theory.

Greenland Ice Sheet Subsurface Temperature Estimation Using Ultrawideband Microwave Radiometry

Ice sheet subsurface temperature is important for understanding glacier dynamics, yet existing methods to obtain the temperature of the ice sheet column are limited to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> sources at present. The ultrawideband software-defined microwave radiometer (UWBRAD) has been developed to investigate the remote sensing of ice sheet internal temperatures. UWBRAD measures brightness temperature spectra from 0.5 to 2 GHz using 12 subchannels and employs a sophisticated algorithm for detection and mitigation of radio frequency interference (RFI). The instrument was deployed during a flight over northwestern Greenland in September 2017 and acquired the first wideband low-frequency brightness temperature spectra over the ice sheet and coastal regions. The results reveal strong spatial and spectral variations that correlate well with internal ice sheet temperature information. In this article, the section of the flight path ranging from the Camp Century to NEEM to NGRIP boreholes is used for subsurface temperature estimation. A “partially coherent” forward model is applied along with a Robin model for the temperature profile and a two-scale model of ice sheet density variations to describe measured brightness temperatures. Using this model, vertical temperature profiles are retrieved along the flight path using a sequential Bayesian estimator; borehole measurements at the three campsites are used to obtain Bayesian priors. The retrieved temperature profiles show reasonable behaviors and demonstrate the potential of ultrawideband microwave radiometry for remotely sensing internal ice sheet temperatures.

Deep Learning-Based Beam Tracking for Millimeter-Wave Communications Under Mobility

In this paper, we propose a deep learning-based beam tracking method for millimeter-wave (mmWave) communications. Beam tracking is employed for transmitting the known symbols using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sounding beams</i> and tracking time-varying channels to maintain a reliable communication link. When the pose of a user equipment (UE) device varies rapidly, the mmWave channels also tend to vary fast, which hinders seamless communication. Thus, models that can capture temporal behavior of mmWave channels caused by the motion of the device are required, to cope with this problem. Accordingly, we employ a deep neural network to analyze the temporal structure and patterns underlying in the time-varying channels and the signals acquired by inertial sensors. We propose a model based on long short term memory (LSTM) that predicts the distribution of the future channel behavior based on a sequence of input signals available at the UE. This channel distribution is used to 1) control the sounding beams adaptively for the future channel state and 2) update the channel estimate through the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">measurement update step</i> under a sequential Bayesian estimation framework. Our experimental results demonstrate that the proposed method achieves a significant performance gain over the conventional beam tracking methods under various mobility scenarios.

Probabilistic focalization for shallow water localization.

Localizing and tracking an underwater acoustic source is a key task for maritime situational awareness. This paper presents a sequential Bayesian estimation method for passive acoustic source localization in shallow water. The proposed probabilistic focalization approach associates detected directions of arrival (DOAs) to modeled DOAs and jointly estimates the time-varying source location. Embedded ray tracing makes it possible to incorporate environmental parameters that characterize the acoustic waveguide. Due to its statistical model, the proposed method can provide robustness in scenarios with severe environmental uncertainty. We demonstrate performance advantages compared to matched field processing using data collected during the SWellEx-96 experiment.

Second-order extended particle filter with exponential family observation model

Particle filter is the most widely used Bayesian sequential state estimation method for nonlinear dynamic systems. When importance sampling is adopted, it is still a challenge to select an appropriate importance function for sampling to avoid particle degeneracy. This paper suggests a novel particle filter, called second-order extended particle filter, which uses conditional normal distribution to approximate the theoretical optimal importance function in sequential state estimation. The approximation is fulfilled through taking logarithm to the optimal importance function and implementing second-order Taylor expansion. This method is suitable for exponential family observation models, which have numerous applications in state estimation research field.

Adaptive Bayesian Learning and Forecasting of Epidemic Evolution—Data Analysis of the COVID-19 Outbreak

Since the beginning of 2020, the outbreak of a new strain of Coronavirus has caused hundreds of thousands of deaths and put under heavy pressure the world’s most advanced healthcare systems. In order to slow down the spread of the disease, known as COVID-19, and reduce the stress on healthcare structures and intensive care units, many governments have taken drastic and unprecedented measures, such as closure of schools, shops and entire industries, and enforced drastic social distancing regulations, including local and national lockdowns. To effectively address such pandemics in a systematic and informed manner in the future, it is of fundamental importance to develop mathematical models and algorithms to predict the evolution of the spread of the disease to support policy and decision making at the governmental level. There is a strong literature describing the application of Bayesian sequential and adaptive dynamic estimation to surveillance (tracking and prediction) of objects such as missiles and ships; and in this article, we transfer some of its key lessons to epidemiology. We show that we can reliably estimate and forecast the evolution of the infections from daily — and possibly uncertain — publicly available information provided by authorities, e.g., daily numbers of infected and recovered individuals. The proposed method is able to estimate infection and recovery parameters, and to track and predict the epidemiological curve with good accuracy when applied to real data from Lombardia region in Italy, and from the USA. In these scenarios, the mean absolute percentage error computed after the lockdown is on average below 5% when the forecast is at 7 days, and below 10% when the forecast horizon is 14 days.

Sequential Poisson Regression in Diffusion Networks

The Poisson regression is a popular model for positive integer random variables determined by known explanatory variables. This letter studies the problem of its collaborative Bayesian sequential estimation under potentially slowly time-varying regression coefficients. We assume networks where agents share their information about the inferred quantities with adjacent neighbors in order to improve the overall estimation performance. The communication strategy is the information diffusion, i.e., only one information exchange per time instant is allowed.