Bayesian Parameter Estimation Research Articles

Generating and Transferring Priors for Causal Bayesian Network Parameter Estimation in Robotic Tasks

Generating and Transferring Priors for Causal Bayesian Network Parameter Estimation in Robotic Tasks

Simultaneous estimation of a model-derived input function for quantifying cerebral glucose metabolism with [18F]FDG PET

BackgroundQuantification of the cerebral metabolic rate of glucose (CMRGlu) by dynamic [18F]FDG PET requires invasive arterial sampling. Alternatives to using an arterial input function (AIF) include the simultaneous estimation (SIME) approach, which models the image-derived input function (IDIF) by a series of exponentials with coefficients obtained by fitting time activity curves (TACs) from multiple volumes-of-interest. A limitation of SIME is the assumption that the input function can be modelled accurately by a series of exponentials. Alternatively, we propose a SIME approach based on the two-tissue compartment model to extract a high signal-to-noise ratio (SNR) model-derived input function (MDIF) from the whole-brain TAC. The purpose of this study is to present the MDIF approach and its implementation in the analysis of animal and human data.MethodsSimulations were performed to assess the accuracy of the MDIF approach. Animal experiments were conducted to compare derived MDIFs to measured AIFs (n = 5). Using dynamic [18F]FDG PET data from neurologically healthy volunteers (n = 18), the MDIF method was compared to the original SIME-IDIF. Lastly, the feasibility of extracting parametric images was investigated by implementing a variational Bayesian parameter estimation approach.ResultsSimulations demonstrated that the MDIF can be accurately extracted from a whole-brain TAC. Good agreement between MDIFs and measured AIFs was found in the animal experiments. Similarly, the MDIF-to-IDIF area-under-the-curve ratio from the human data was 1.02 ± 0.08, resulting in good agreement in grey matter CMRGlu: 24.5 ± 3.6 and 23.9 ± 3.2 mL/100 g/min for MDIF and IDIF, respectively. The MDIF method proved superior in characterizing the first pass of [18F]FDG. Groupwise parametric images obtained with the MDIF showed the expected spatial patterns.ConclusionsA model-driven SIME method was proposed to derive high SNR input functions. Its potential was demonstrated by the good agreement between MDIFs and AIFs in animal experiments. In addition, CMRGlu estimates obtained in the human study agreed to literature values. The MDIF approach requires fewer fitting parameters than the original SIME method and has the advantage that it can model the shape of any input function. In turn, the high SNR of the MDIFs has the potential to facilitate the extraction of voxelwise parameters when combined with robust parameter estimation methods such as the variational Bayesian approach.

Monitoring of Poisson multi-stage process in Phase II with Bayesian estimation of parameters

Monitoring of Poisson multi-stage process in Phase II with Bayesian estimation of parameters

Monitoring of Poisson multi-stage process in Phase II with Bayesian estimation of parameters

Monitoring of Poisson multi-stage process in Phase II with Bayesian estimation of parameters

Using Gravitational Waves to Determine if Primordial Black Holes are Sources of Dark Matter

Scientists do not have much information about or evidence of dark matter. Dark matter does not emit electromagnetic radiation and does not interact with normal matter, but some researchers have found evidence of its existence throughout the universe. Scientists have narrowed down to two possible sources of dark matter: Massive Compact Halo Objects (MACHOs) and Weakly Interacting Massive Particles (WIMPs). In our research, we analyzed MACHOs, which are primordial black holes, using gravitational wave data from the LIGO/Virgo collaboration. We hypothesized that MACHOs may be dark matter due to the higher black hole mass formed from binary mergers between primordial black holes, compared to the black hole mass between binary mergers from simulated stellar black holes. Using the data derived from primordial black hole pairs, we used Python to perform Bayesian inference parameter estimation to generate another set of simulated datasets (which are stellar black hole pairs) to compare the final masses of the black hole mergers in the simulated and original gravitational wave datasets. Our results showed that primordial black holes (MACHOs) may not be dark matter, but in the future, based on the research on dark matter, astrophysicists’ can further improve understanding of primordial black holes and their effect in the universe.

Bayesian Parameter Estimation for Linear Parameter-varying Systems with Outliers and Missing Observations

Bayesian Parameter Estimation for Linear Parameter-varying Systems with Outliers and Missing Observations

Research on dynamic polarization control in continuous variable quantum key distribution systems

In a commercial fiber-based quantum key distribution system, the local and signal optical fields are transmitted through long distance fibers by using time division multiplexing and polarization multiplexing. The state of polarization of the optical field is inevitably disturbed by random birefringence of the standard single-mode fiber caused by external complex environments. This drift of the state of polarization significantly affects the balanced homodyne detection results and the secret key rate. Therefore, the key technology of the dynamic polarization control unit is crucial for the system in a large-scale commercial application. We theoretically analyze and prove that the polarization control unit only needs the combination of two degrees of freedom when considering the result of an arbitrary polarization extinction ratio at the receiver of the system. To overcome the influence of polarization variations, we propose a chaotic monkey algorithm based on Bayesian parameter estimation method and implement intelligence algorithm on field programmable gate array (FPGA) hardware under pulsed light with an integral-type detector for the dynamic polarization control unit. The simulation results show that the optimal combination is four degrees of freedom and the optimal prior distribution is an exponential distribution among various distributions in the dynamic polarization control unit. According to the simulation results, the experimental results show that the achieved polarization extinction ratio is over 30 dB and the average time of polarization control is 400 μs for a single random polarization scrambling. By combining the dynamic polarization control unit with the system, we demonstrate the continuous variable quantum key distribution (CV-QKD) under a continuous polarization scrambling scope of 0－2 krad/s and verify its effectiveness. In addition, the methods presented will improve the performance of the system and expand the range of applications even under strong external disturbance.

Amortized Bayesian Parameter Estimation Approach for WECC Composite Load Model

Calibrating the composite load model with distributed generation (CMPLDWG) is of a great challenge due to the presence of high-dimension parameters. This paper proposes an amortized Bayesian parameter estimation method for the CMPLDWG model. A prior distribution restrictor is developed via a classifier to filter out invalid simulations because of the unsuitable parameter combinations during the offline training stage. A sparse polynomial chaos expansion (SPCE) enabled global sensitivity analysis is also developed to identify the importance of each parameter's response to the captured system dynamics. This allows us to narrow down the problematic parameters and reduce the problem's complexity. Finally, the multi-fidelity trajectory statistics constructor is proposed to extract the representations from post-disturbance dynamic responses. The representations are further used by conditional masked autoregressive flow (CMAF) to learn the parameter posterior distribution. Comparative results with state-of-the-art approaches on the IEEE 39-bus power system demonstrate the high accuracy and robustness of the proposed method.

A new extension of Poisson distribution for asymmetric count data: theory, classical and Bayesian estimation with application to lifetime data.

Several research investigations have stressed the importance of discrete data analysis and its relevance to actual events. The current work focuses on a new discrete distribution with a single parameter that can be derived using the Poisson mixing technique. The new distribution is named the Poisson Entropy-Based Weighted Exponential Distribution. It is useful for discussing asymmetric "right-skewed" data with "heavy" tails. Its failure rate function can be used to explain situations with increasing failure rates. The statistical properties of the new distribution are expressed explicitly. The proposed model is simple to manage for under-, equal-, and over-dispersed datasets. The model parameters are estimated using the maximum likelihood method. We consider the parameter estimation for the new model based on right-censored data with a cure fraction. One more focus of the present study is the Bayesian estimation of the model parameters. In the end, three real-world dataset examples were utilized to show the value of the new distribution. These applications revealed that the new model outperforms other standard discrete models.

Improved analytic method for outrigger structures considering floor stiffness

SummaryCurrent analytical models for outrigger structures in super high‐rise buildings tend to oversimplify by not considering the stiffness of individual floors. This paper introduces a more refined calculation model, based on the substructure method, which takes floor stiffness into account. To verify our proposed approach, we derived a mathematical algorithm and developed a finite element model using ANSYS. When compared to traditional methods that only account for outrigger stiffness, our model, which incorporates both outrigger and floor stiffness, provides improved accuracy in calculating vertex displacement. It also suggests an upward shift in the optimal position for the outrigger and bolsters the overall building's lateral stiffness. To further our analysis, we introduced an equivalent stiffness calculation formula, using the Bayesian parameter estimation method. When applied to dynamic analysis, this formula aligns closely with the results from the finite element simulations. Furthermore, the suggested algorithm for determining the best position for the outrigger is consistent with theoretical calculations. By considering the contribution of regular floors to the overall structure, we found that the fitted equivalent core tube stiffness offers a reliable reflection of structural stiffness. Lastly, when this equivalent stiffness was applied to a dynamic analysis based on Rayleigh's energy method, there was a noticeable reduction in computational effort. This yields not only more efficient calculations but also precise results, rendering it particularly valuable during the initial design phases of high‐rise buildings.

Bayes Estimator of Exponential Distribution Parameters of Type II Censored Data with Linear Exponential Loss Function Method Based on Jeffrey Priors

Survival analysis is often used in the application of analyzing the survival of an object such as living things or objects. This analysis is identical to data censoring which is divided into three, namely: type I, II, and III censored data. Type II censored data is data censoring done by determining the number of objects to be analyzed from the total number of observation objects . Type II censored data is used when the analysis is intended to maximize the results of the analysis. Bayesian Linear Exponential (LINEX) loss function is one method that can be used to estimate parameters in survival analysis by minimizing the expected value of LINEX. The purpose of this study is to determine the Bayesian LINEX loss function parameter estimation on type II censored data using exponential distribution. This method uses the concept of posterior distribution and prior distribution. The prior distribution used is the Jeffrey prior distribution which has objective properties and is based on Fisher information theory The application of the parameter estimation results is carried out on the survival data of lung cancer patients obtained from the North Central Cancer Treatment Group. Based on the results of parameter estimation, it is concluded that the greater the value of the controller (a) can produce a smaller value of parameter estimation results (θ^) . The results of this study can be used as a reference in conducting survival tests using type II censored exponential distribution data using the LINEX loss function method based on Jeffrey priors.

Multidimensional item response theory models for testlet-based doubly bounded data.

A testlet-based visual analogue scale (VAS) is a doubly bounded scaling approach (e.g., from 0% to 100% or from 0 to 1) composed of multiple adjectives, nouns, or sentences (statements/items) within testlets for measuring individuals' attitudes, opinions, or career interests. While testlet-based VASs have many advantages over Likert scales, such as reducing response style effects, the development of proper statistical models for analyzing testlet-based VAS data lags behind. This paper proposes a novel beta copula model and a competing logit-normal model based on the item response theory framework, assessed by Bayesian parameter estimation, model comparison, and goodness-of-fit statistics. An empirical career interest dataset based on a testlet-based VAS design was analyzed using the proposed models. Simulation studies were conducted to assess the two models' parameter recovery. The results show that the beta copula model had superior fit in the empirical data analysis, and also exhibited good parameter recovery in the simulation studies, suggesting that it is a promising statistical approach to testlet-based doubly bounded responses.

Fast Gravitational-wave Parameter Estimation without Compromises

We present a lightweight, flexible, and high-performance framework for inferring the properties of gravitational-wave events. By combining likelihood heterodyning, automatically differentiable, and accelerator-compatible waveforms, and gradient-based Markov Chain Monte Carlo sampling enhanced by normalizing flows, we achieve full Bayesian parameter estimation for real events like GW150914 and GW170817 within a minute of sampling time. Our framework does not require pretraining or explicit reparameterizations and can be generalized to handle higher dimensional problems. We present the details of our implementation and discuss trade-offs and future developments in the context of other proposed strategies for real-time parameter estimation. Our code for running the analysis is publicly available on GitHub at https://github.com/kazewong/jim.

Bayesian parameter estimation for characterising mobile ion vacancies in perovskite solar cells

To overcome the challenges associated with poor temporal stability of perovskite solar cells, methods are required that allow for fast iteration of fabrication and characterisation, such that optimal device performance and stability may be actively pursued. Currently, establishing the causes of underperformance is both complex and time-consuming, and optimisation of device fabrication is thus inherently slow. Here, we present a means of computational device characterisation of mobile halide ion parameters from room temperature current–voltage () measurements only, requiring ∼2 h of computation on basic computing resources. With our approach, the physical parameters of the device may be reverse-modelled from experimental measurements. In a drift-diffusion (DD) model, the set of coupled DD partial differential equations cannot be inverted explicitly, so a method for inverting the DD simulation is required. We show how Bayesian Parameter Estimation coupled with a DD perovskite solar cell model can determine the extent to which device parameters affect performance measured by characteristics. Our method is demonstrated by investigating the extent to which device performance is influenced by mobile halide ions for a specific fabricated device. The ion vacancy density N 0 and diffusion coefficient DI were found to be precisely characterised for both simulated and fabricated devices. This result opens up the possibility of pinpointing origins of degradation by finding which parameters most influence device curves as the cell degrades.

Development of a Predictive Statistical Pharmacological Model for Local Anesthetic Agent Effects with Bayesian Hierarchical Model Parameter Estimation.

As an alternative to animal use, computer simulations are useful for predicting pharmacokinetics and cardiovascular activities. For this purpose, we constructed a statistical model to simulate the effects of local anesthetic agents. To train the model, animal experiments were performed on 6-week-old male Hartley guinea pigs. Firstly, the guinea pigs' backs were shaved, then local anesthetic agents were subcutaneously injected, with subsequent stimulation of the anesthetized site with a needle six times at regular intervals. The number of reactions (score value) was counted. In this statistical model, the probability of reacting to needle stimulation was calculated using the elapsed time, type of local anesthetic agent, and presence or absence of adrenaline. Score values were assumed to follow a binomial distribution at the calculated probability. Parameters were estimated using the Bayesian hierarchical model and Hamiltonian Monte Carlo method. The predicted curves using the estimated parameters fitted well the observed animal values. When score values were predicted using randomly generated parameters, the median of duration was similar between animal experiments and simulations (Procaine: 55 min vs. 50 min, Lidocaine: both 60 min, and Mepivacaine: both 85 min). This approach effectively modeled the effects of local anesthetic agents. It is possible to create the simulator using the parameter values estimated in this study.

베이지안 방식의 데이터 증강을 이용한 지도학습 기반 인지진단평가 연구

Objectives The purposes of this study were to propose and validate a method for applying supervised learning for cognitive diagnostic assessment by augmenting expert-labeled dataset using Bayesian parameter estimation techniques. Methods The method was evaluated with a simulation study and an application to real data. The simulation study was conducted to compare the diagnostic accuracy of neural networks trained with both ‘Bayesian-based aug-mented dataset’ and ‘expert-labeled dataset’ across four factors: ‘item quality’, ‘expert labeling error rate’, ‘size of the expert labeled dataset’, and ‘size of the augmented dataset’. Additionally, the real data consists of the binary responses of 936 middle-school students to 24 arithmetic problems on linear equations and linear inequalities. Results The performance of supervised learning trained on the ‘Bayesian-based augmented dataset’ showed significant improvements in all conditions compared to solely using the ‘expert-labeled dataset’. The effect of the labeling error rate and the size of the expert-labeled dataset was trivial. As the quality of the items increased and the size of the augmented dataset grew, accuracy improved, though beyond a certain size N=3,000 of the aug-mented dataset, the difference was negligible. For the real data on linear equations and inequalities, supervised learning trained on the ‘Bayesian-based augmented dataset’ showed enhanced accuracy over just on the ‘ex-pert-labeled dataset’. It is also evident that students understand solving linear equations better than solving linear inequalities. Conclusions When performing supervised learning based cognitive diagnosis with a small expert-labeled data-set, the diagnostic performance can be enhanced through Bayesian-based data augmentation method. Moreover, students tend to find understanding inequalities more challenging than equations, suggesting the need for opportunities to master cognitive attributes related to inequalities.

Lithospheric strength of the Anatolian plateau and implications for strong earthquake activity in Turkey

On February 6, 2023, the doublet earthquake including two main shocks with magnitudes MW7.8 and MW7.5, occurred near the western side of the East Anatolian Fault at the southeast boundary of the Anatolian Plateau in Turkey. Based on the WGM2012 Bouguer gravity anomaly data and the Etopo1 topography data, this study first introduced a joint inversion of admittance and coherence functions and used the Bayesian optimal parameter estimation method to obtain the effective elastic thickness Te and loading ratio F of the lithosphere for various tectonic units in the Anatolian Plateau. Secondly, we discussed the characteristics and influencing factors of the lithospheric mechanical strength and analyzed its relationship with seismic activity. The lithospheric mechanical strength of the Anatolian Plateau showed clear lateral heterogeneity and a "weak-strong-weak" spatial pattern from east to west, reflecting various tectonic processes. At last, the strong seismic activity was found where the lithospheric strength was low in the Anatolian Plate. We also incorporated GPS strain rate and other results to investigate the tectonic background and primary causes of the MW7.8 and MW7.5 doublet earthquakes in Turkey. The results have a good insight into urban safety design in the Turkish region, including post-disaster rehabilitation, earthquake hazard assessment, and loss reduction.

Too small to fail: characterizing sub-solar mass black hole mergers with gravitational waves

The detection of a sub-solar mass black hole could yield dramatic new insights into the nature of dark matter and early-Universe physics, as such objects lack a traditional astrophysical formation mechanism. Gravitational waves allow for the direct measurement of compact object masses during binary mergers, and we expect the gravitational-wave signal from a low-mass coalescence to remain within the LIGO frequency band for thousands of seconds. However, it is unclear whether one can confidently measure the properties of a sub-solar mass compact object and distinguish between a sub-solar mass black hole or other exotic objects. To this end, we perform Bayesian parameter estimation on simulated gravitational-wave signals from sub-solar mass black hole mergers to explore the measurability of their source properties. We find that the LIGO/Virgo detectors during the O4 observing run would be able to confidently identify sub-solar component masses at the threshold of detectability; these events would also be well-localized on the sky and may reveal some information on their binary spin geometry. Further, next-generation detectors such as Cosmic Explorer and the Einstein Telescope will allow for precision measurement of the properties of sub-solar mass mergers and tighter constraints on their compact-object nature.

High-Precision DOA Estimation Based on Synthetic Aperture and Sparse Reconstruction.

The direction-of-arrival (DOA) estimation is predominantly influenced by the antenna's aperture size. However, space constraints on flight platforms often necessitate the use of antennas with smaller apertures and fewer array elements. This inevitably imposes limitations on the DOA estimation's resolution and degrees of freedom. To address these precision constraints, we introduce an accurate DOA estimation method based on spatial synthetic aperture model. This method adopts a two-stage strategy to ensure both efficiency and precision in DOA estimation. Initially, the orthogonal matching pursuit (OMP) reconstruction algorithm processes the original aperture data, providing a rough estimate of target angles that guides the aircraft's flight direction. Subsequently, the early estimations merge with the aircraft's motion space samples, forming equivalent spatially synthesized array samples. The refined angle estimation then employs the OMP-RELAX algorithm. Moreover, with the off-grid issue in mind, we devise an estimation method integrating Bayesian parameter estimation with dictionary sequence refinement. The proposed technique harnesses the spatial synthetic aperture for pinpoint estimation, effectively addressing the challenges of atomic orthogonality and angular off-grid on estimation accuracy. Importantly, the efficiency of deploying sparse reconstruction for angle estimation is bolstered by our phased strategy, eliminating the necessity for fine grid analysis across the entire observation scene. Moreover, the poor estimation accuracy caused by coherent source targets and angular-flickering targets is improved by sparse reconstruction. Through simulation and experiment, we affirm the proposed method's efficacy in angle estimation. The results indicate that target angle estimation errors are limited to within 1°. Furthermore, we assess the impact of variables such as target state, heading angle, spatial sampling points, and target distance on the estimation accuracy of our method, showcasing its resilience and adaptability.

Multi-axial load spectrum extrapolation method for fatigue durability of special vehicles based on extreme value theory

A method for the multi-axial load spectrum extrapolation based on extreme value theory has been proposed herein, for the first time to the best of our knowledge. The relationship between the internal damage of the structure with the external multi-axial load spectrum is first established prior to extrapolation. The multi-axial load spectrum is then equivalently synthesized into a uni-axial load spectrum based on the interaction between the external forces and the internal stress state of the structure. The basic theory of the time-domain multi-axial load spectrum extrapolation method is developed, including (1) the multi-axial load spectrum extrapolation model establishment; (2) the optimal threshold determination based on grey relational analysis (GRA); (3) the fitting of the distribution function parameters based on the Bayesian parameter estimation method; and (4) the judgment of phase relationship between each channel of the multi-axial load spectrum. The rationality of the method proposed in this paper is verified through an application example. In the example, the multi-axial load spectrum measurement of a special vehicle is introduced, and the proposed multi-axial extrapolation method is applied. Finally, the validation of the multi-axial load spectrum extrapolation method – in terms of the characterized comparison and the durability simulation – is performed.