Bayesian Parameter Estimation Method Research Articles

Energy-dependent intrinsic time delay of gamma-ray bursts on testing Lorentz invariance violation

High-energy photons of gamma-ray bursts (GRBs) might be emitted at different intrinsic times with energy dependence at the source. In this letter, we expand the model from previous works on testing the Lorentz Invariance Violation (LV) with the observed GRB data from the Fermi Gamma-ray Space Telescope. We reanalyze the previous data with the full Bayesian parameter estimation method and get consistent results by assuming that the time delays are due to an LV term and a constant intrinsic time delay term. Subsequently, we neglect the LV effect and only consider the intrinsic time delay effect. We assume a common intrinsic time delay term along with a source energy correlated time delay of high-energy photons. We find that the energy-dependent emission times can also explain the observed GRB data of high-energy photon events. Finally, we integrate these two physical mechanisms into a unified model to distinguish and evaluate their respective contributions using the observed GRB data.

Bayesian parameter estimation using truncated normal distributions as priors for parameters in fundamental models of chemical processes

AbstractModellers of chemical processes with knowledge about plausible parameter values use Bayesian parameter estimation methods to account for their prior beliefs. Some modellers specify prior distributions with finite parameter ranges, such as uniform distributions and truncated normal distributions, because they better account for knowledge about realistic parameter ranges than normal prior distributions with parameter values ranging between and . We derive closed‐form objective functions for Bayesian parameter estimation with truncated normal priors and uniform priors, for the first time, so that parameter estimation can be performed by solving simple optimization problems rather than using complex sampling‐based techniques. A parametric bootstrapping method that considers truncated normal priors and model nonlinearity is proposed to determine 95% confidence intervals and joint confidence regions. A pharmaceutical case study is used to show the effectiveness of the proposed objective functions and bootstrapping methodology. Confidence regions from bootstrapping are similar to linearization‐based confidence regions that do not account for truncation when truncated areas in normal prior distributions are relatively small. More truncation, which corresponds to more‐precise prior knowledge about the parameters, results in smaller joint confidence regions. The proposed methods will be attractive for parameter estimation in complex process models because they can be less computationally intensive than Markov chain Monte Carlo methods that provide similar results.

Evaluation of Sampling Algorithms Used for Bayesian Uncertainty Quantification of Molecular Dynamics Force Fields.

New Bayesian parameter estimation methods have the capability to enable more physically realistic and reliable molecular dynamics (MD) simulations by providing accurate estimates of uncertainties of force-field (FF) parameters and associated properties. However, the choice of which Bayesian parameter estimation algorithm to use has not been widely investigated, despite its impact on the effective exploration of parameter space. Here, using a case example of the Embedded Atom Method (EAM) FF parameters, we investigated the ramifications of several of the algorithm choices. We found that Ensemble Slice Sampling (ESS) and Affine-Invariant Ensemble Sampling (AIES) demonstrate a new level of superior performance, culminating in more accurate parameter and property estimations with tighter uncertainty bounds, compared to traditional methods such as Metropolis-Hastings (MH), Gradient Search (GS), and Uniform Random Sampler (URS). We demonstrate that Bayesian Uncertainty Quantification with ESS and AIES leads to significantly more accurate and reliable predictions of the FF parameters and properties. The results suggest that ESS and AIES should be used to obtain more accurate parameter and uncertainty estimations while providing deeper physical insights.

BAYES ESTIMATION OF EXPONENTIALLY DISTRIBUTED SURVIVAL DATA UNDER SYMMETRIC AND ASYMMETRIC LOSS FUNCTIONS

In a research study, population data are often not available, so the population parameter is unknown. Meanwhile, knowledge about the population parameter is needed to know the characteristics of the studied population. Therefore, it is needed to estimate the parameter of the population which can be estimated by sample data. There are several methods of parameter estimation which are generally classified into classical and Bayesian method. This research studied the Bayesian parameter estimation method to determine the parameters of the exponentially distributed survival data associated with the reliability measure of the estimates under symmetric and asymmetric loss functions for complete sample data in a closed form. The symmetric loss functions used in this research are Squared Error Loss Function (SELF) and Minimum Expected Loss Function (MELF). The asymmetric loss functions used are the General Entropy Loss Function (GELF) and Linex Loss Function (LLF). Performance of some loss functions used in this research are then compared through numerical simulation to select the best loss function in determining the parameter estimation of the exponentially distributed survival data. We also studied which loss function is best for underestimation and overestimation modeling. Based on simulation results, the Bayes estimates using MELF is the best method to estimate population parameters of the exponentially distributed survival data for the overestimation modeling, while LLF is the best for the underestimation modeling. We provided direct application in a case study of fluorescence lamp survival data. The results show that the best method to estimate the parameter of the standard fluorescence life data is using LLF for underestimation with and MELF for overestimation with .

Bayesian Parameter Estimation for Geometric Process with Rayleigh Distribution

The main purpose of this study is to deal with the parameter estimation problem for the geometric process (GP) when the distribution of the first occurrence time of an event is assumed to be Rayleigh. For this purpose, maximum likelihood and Bayesian parameter estimation methods are discussed. Lindley and MCMC approximation methods are used in Bayesian calculations. Additionally, a novel method called the Modified-Lindley approximation has been proposed as an alternative to the Lindley approximation. An extensive simulation study was conducted to compare the performances of the prediction methods. Finally, a real data set is analyzed for illustrative purposes.

Behaviour Analysis of Modeling and Model Evaluating Methods in System Identification for a Multiprocess Station

Systems are designed to perform specific task by giving certain input which produces the required output in an orderly manner known as process. The input, output, and the state variables should be known that will help in interacting with the system. The relation between these variables can be brought out by building a model that resembles or expresses the original performance of the system. The parameters of the model are estimated using the least squares approximation, maximum likelihood, maximum log-likelihood, and Bayesian parameter estimation methods by utilizing the experimental data from the multiprocess station. The selected parameters are converted to nine different transfer function models that represent the given dynamic system. The models framed are analyzed by the criterion curve technique using seven criterion functions evaluating the fitness of the model. Order of the model is found from Hankel matrix representation methods such as singular value decomposition and determinant method. Response of the models is compared with the original response to choose the best fit model by calculating ISE standard. All the above methods are used to model the system without physical and theoretical laws which is known as system identification.

A Bayesian Collocation Integral Method for Parameter Estimation in Ordinary Differential Equations

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on basis functions or Gaussian processes to approximate the ODE solution and its derivatives. Due to the sensitivity of the ODE solution to its derivatives, these methods can be hindered by estimation error, especially when only sparse time-course observations are available. We present a Bayesian collocation framework that operates on the integrated form of the ODEs and also avoids the expensive use of numerical solvers. Our methodology has the capability to handle general nonlinear ODE systems. We demonstrate the accuracy of the proposed method through simulation studies, where the estimated parameters and recovered system trajectories are compared with other recent methods. A real data example is also provided. Supplementary materials for this article are available online.

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.

Embracing uncertainty in cerebrospinal fluid dynamics: A Bayesian approach to analysing infusion studies

IntroductionCerebrospinal fluid (CSF) infusion test analysis allows recognizing and appropriately evaluating CSF dynamics in the context of normal pressure hydrocephalus (NPH), which is crucial for effective diagnosis and treatment. However, existing methodology possesses drawbacks that may compromise the precision and interpretation of CSF dynamics parameters. Research questionThis study aims to circumvent these constraints by introducing an innovative analysis method grounded in Bayesian inference. Material and methodsA single-centre retrospective cohort study was conducted on 858 patients who underwent a computerized CSF infusion test between 2004 and 2020. We developed a Bayesian framework-based method for parameter estimation and compared the results to the current, gradient descent-based approach. We evaluated the accuracy and reliability of both methods by analysing erroneous prediction rates and curve fitting errors. ResultsThe Bayesian method surpasses the gradient descent approach, reflected in reduced inaccurate prediction rates and an improved goodness of model fit. On whole cohort level both techniques produced comparable results. However, the Bayesian method holds an added advantage by providing uncertainty intervals for each parameter. Sensitivity analysis revealed significance of the CSF production rate parameter and its interplay with other variables. The resistance to CSF outflow demonstrated excellent robustness. Discussion and conclusionThe proposed Bayesian approach offers a promising solution for improving robustness of CSF dynamics assessment in NPH, based on CSF infusion tests. Additional provision of the uncertainty measure for each diagnostic metric may perhaps help to explain occasional poor diagnostic performance of the test, offering a robust framework for improved understanding and management of NPH.

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.

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.

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.

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.

Metode Bayesian untuk Estimasi Parameter Distribusi Eksponensial pada Data Tersensor

Parameter is a value that describe the characteristics of a population. But the parameterof a real data, the value is unknown. To estimate the value of the parameter,there are several methods, which are maximum likelihood estimation method (MLE)and Bayesian parameter estimation method. In Bayesian method, the prior informationis applied to update the current data. The prior is determined based on the informationin the data. This mini thesis is using censored data with exponential distribution, andusing the conjugate prior. Followed by squared error loss function (SELF), the estimatedvalue function ot the λ parameter is ˆλ =α+Σ_{i=1}^{n}δ_{i}β+Σ_{i=1}^{n}t_{i}with α and β are hyperparameters,Σ_{i=1}^{n}δ_{i} is the number of objects that experienced the event and Σ_{i=1}^{n}t_{i} is the numberof the survival time. When the function was applied on Stanford heart transplant data,the value of ˆλ = 0.00089, which means the patient’s failure (death) probability is lowand the patient’s probability to survive is high.

An advanced Bayesian parameter estimation methodology for concrete dams combining an improved extraction technique of hydrostatic component and hybrid response surface method

It is very important to estimate the mechanical parameters based on monitoring data for investigating the operation behavior of concrete dams. In this paper, an advanced Bayesian parameter estimation method for concrete dams is proposed. The Empirical Mode Decomposition (EMD) is adopted to extract the aging component of the observed deformation sequence, and the hydrostatic component is separated from the remaining periodic term through the statistical regression model (SRM). A hybrid response surface method (HRSM) is proposed as a surrogate model for finite element method (FEM) simulation. The likelihood function, which reflects the error between the observed and simulated deformation, is constructed, then the Bayesian formula for parameter estimation is established. The transitional Markov chain Monte Carlo (TMCMC) algorithm is used to obtain the parameter posterior distribution. The proposed method is applied to estimate the elastic modulus of the GD concrete dam, the parameter posterior distribution is obtained through the fusion of monitoring information and parameter prior information. This method can also avoid the issues of multiple solutions and unreasonable parameter combinations, which may exist in traditional deterministic inversion methods. The case study shows that the proposed method has good applicability in the parameter estimation of concrete dams.

Experimental Bayesian Calibration of Trapped-Ion Entangling Operations

The performance of quantum gate operations is experimentally determined by how correct operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multi-dimensional parameter estimation procedure is crucial to calibrate even medium sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used Molmer-Sorensen entangling gate operation in a trapped ion quantum information processor. The protocol exploits Bayesian parameter estimation methods which includes a stopping criterion based on a desired gate infidelity. We experimentally demonstrate a median gate infidelity of $1.3(1)\cdot10^{-3}$, requiring only $1200\pm500$ experimental cycles, while completing the entire gate calibration procedure in less than one minute. This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.

Mental speed is high until age 60 as revealed by analysis of over a million participants.

Response speeds in simple decision-making tasks begin to decline from early and middle adulthood. However, response times are not pure measures of mental speed but instead represent the sum of multiple processes. Here we apply a Bayesian diffusion model to extract interpretable cognitive components from raw response time data. We apply our model to cross-sectional data from 1.2 million participants to examine age differences in cognitive parameters. To efficiently parse this large dataset, we apply a Bayesian inference method for efficient parameter estimation using specialized neural networks. Our results indicate that response time slowing begins as early as age 20, but this slowing was attributable to increases in decision caution and to slower non-decisional processes, rather than to differences in mental speed. Slowing of mental speed was observed only after approximately age 60. Our research thus challenges widespread beliefs about the relationship between age and mental speed.

Variance-based sensitivity analysis of dynamic systems with both input and model uncertainty

This paper develops a methodology to compute variance-based sensitivity indices for dynamic systems with time series inputs and outputs, while accounting for both aleatory and epistemic uncertainty sources, and both random process and random variable inputs. We present semi-analytical methods for computing sensitivity indices for linear systems with Gaussian random process inputs, and for the general case of nonlinear systems with non-Gaussian random process inputs. The novel elements in this approach are the treatment of model form error, quantifying the cumulative effects of uncertainty sources over time, and evaluating sensitivity indices for multi-physics models. Bayesian state and parameter estimation methods are incorporated to quantify the model uncertainty arising from unknown model parameters and model form errors, and sensitivity indices are computed before and after model updating. The proposed methods are illustrated for (a) a linear Timoshenko beam erroneously modeled as an Euler-Bernoulli beam, and (b) hypersonic flow behavior of a flexible panel represented by a coupled multi-physics nonlinear model.

GWBENCH: a novel Fisher information package for gravitational-wave benchmarking

We present a new Python package, gwbench, implementing the well-established Fisher information formalism as a fast and straightforward tool for the purpose of gravitational-wave benchmarking, i.e. the estimation of signal-to-noise ratios and measurement errors of gravitational waves observed by a network of detectors. Such an infrastructure is necessary due to the high computational cost of Bayesian parameter estimation methods which renders them less effective for the scientific assessment of gravitational waveforms, detectors, and networks of detectors, especially when determining their effects on large populations of gravitational-wave sources spread throughout the Universe. gwbench further gives quick access to detector locations and sensitivities, while including the effects of Earth’s rotation on the latter, as well as waveform models and their derivatives, while giving access to the host of waveforms available in the LSC Algorithm Library. With the provided functionality, gwbench is relevant for a wide variety of applications in gravitational-wave astronomy such as waveform modeling, detector development, cosmology, and tests of general relativity.

Bayesian parameter estimation in the oral minimal model of glucose dynamics from non-fasting conditions using a new function of glucose appearance

Background and objectiveThe oral minimal model (OMM) of glucose dynamics is a prominent method for assessing postprandial glucose metabolism. The model yields estimates of insulin sensitivity and the meal-related appearance of glucose from insulin and glucose data after an oral glucose challenge. Despite its success, the OMM approach has several weaknesses that this paper addresses. MethodsA novel procedure introducing three methodological adaptations to the OMM approach is proposed. These are: (1) the use of a fully Bayesian and efficient method for parameter estimation, (2) the model identification from non-fasting conditions using a generalised model formulation and (3) the introduction of a novel function to represent the meal-related glucose appearance based on two superimposed components utilising a modified structure of the log-normal distribution. The proposed modelling procedure is applied to glucose and insulin data from subjects with normal glucose tolerance consuming three consecutive meals in intervals of four hours. ResultsIt is shown that the glucose effectiveness parameter of the OMM is, contrary to previous results, structurally globally identifiable. In comparison to results from existing studies that use the conventional identification procedure, the proposed approach yields an equivalent level of model fit and a similar precision of insulin sensitivity estimates. Furthermore, the new procedure shows no deterioration of model fit when data from non-fasting conditions are used. In comparison to the conventional, piecewise linear function of glucose appearance, the novel log-normally based function provides an improved model fit in the first 30 min of the response and thus a more realistic estimation of glucose appearance during this period. The identification procedure is implemented in freely accesible MATLAB and Python software packages. ConclusionsWe propose an improved and freely available method for the identification of the OMM which could become the future standardard for the oral minimal modelling method of glucose dynamics.