Distribution Of Model Parameters Research Articles

A parametric distribution model of electrostatic spray rotating bell and application for automobile painting

A parametric distribution model of electrostatic spray rotating bell and application for automobile painting

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.

Impact study of numerical discretization accuracy on parameter reconstructions and model parameter distributions

In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.

A Bayesian Augmented-Learning framework for spectral uncertainty quantification of incomplete records of stochastic processes

A novel Bayesian Augmented-Learning framework, quantifying the uncertainty of spectral representations of stochastic processes in the presence of missing data, is developed. The approach combines additional information (prior domain knowledge) of the physical processes with real, yet incomplete, observations. Bayesian deep learning models are trained to learn the underlying stochastic process, probabilistically capturing temporal dynamics, from the physics-based pre-simulated data. An ensemble of time domain reconstructions are provided through recurrent computations using the learned Bayesian models. Models are characterized by the posterior distribution of model parameters, whereby uncertainties over learned models, reconstructions and spectral representations are all quantified. In particular, three recurrent neural network architectures, (namely long short-term memory, or LSTM, LSTM-Autoencoder, LSTM-Autoencoder with teacher forcing mechanism), which are implemented in a Bayesian framework through stochastic variational inference, are investigated and compared under many missing data scenarios. An example from stochastic dynamics pertaining to the characterization of earthquake-induced stochastic excitations even when the source load data records are incomplete is used to illustrate the framework. Results highlight the superiority of the proposed approach, which adopts additional information, and the versatility of outputting many forms of results in a probabilistic manner.

Power Modified Lindley Distribution: Properties, Classical and Bayesian Estimation and Regression Model with Applications

In this article, we explore a new probability density function, called the power modified Lindley distribution. Its main feature is to operate a simple trade-off among the generalized exponential, Weibull and gamma distributions, offering an alternative to these three well-established distributions. The proposed model turns out to be quite flexible: its probability density function can be right skewed and its associated hazard rate function may be increasing, decreasing, unimodal and constant. First the model parameters of the proposed distribution are obtained by the maximum likelihood method. Next, Bayes estimators of the unknown parameters are obtained under different loss functions. In addition, bootstrap confidence intervals are provided to compare with Bayes credible intervals. Besides, log power modified Lindley regression model for censored data is proposed. Two real data sets are analyzed to illustrate the flexibility and importance of the proposed model.

Hierarchical Bayesian model for predicting small-strain stiffness of sand

This paper develops a hierarchical Bayesian model (HBM) that integrates the physical knowledge and the test data to predict the small-strain shear modulus Gmax for a target sand type. The limited target-specific data are combined with the abundant generic data through a hierarchical structure so that the variability of Gmax within one sand type and across different sand types can be captured. The hyperparameters that characterize the same underlying distribution of physical model parameters across all the sand types are first estimated from the abundant generic data. The model parameters for the new sand type are then updated as the limited site-specific data become available. The approach is illustrated using a generic database and two real examples not covered by the generic database. Multiple possible hierarchical models are compared in terms of model complexity and goodness-of-fit. The results show that the hierarchical modeling of small-strain shear modulus data is reasonable and necessary. The hierarchical model can provide less biased and more accurate predictions of Gmax compared to the commonly used complete pooling model, especially in cases where the site-specific data are quite different from the overall average of the generic database.

CHOICE OF STARTING VALUES OF PARTICLE-SIZE DISTRIBUTION PARAMETERS FOR THEIR CALCULATION FROM SMALL-ANGLE X-RAY SCATTERING DATA

Simple methods are proposed for determining the starting values of the parameters of particle-size distribution models (mean radius and its standard deviation), calculated from small-angle X-ray scattering curves. Estimates of these parameters from above based on the obtained analytical expression for the Guinier region of the scattering curve from a polydisperse system obeying the Schultz distribution are proposed for systems with narrow distributions. It is proposed to estimate the parameters and range of sizes from below based on the obtained expression of the Porod asymptotics for a polydisperse system. A method for calculating the generalized Guinier–Porod approximation in Kratky coordinates, from which independent estimates of the average size and variance can also be obtained, is proposed. The efficiency of the developed approach is demonstrated by an example of analyzing the scattering intensity from aqueous solutions of silicasol nanoparticles.

Bayesian Subset Selection of Seasonal Autoregressive Models

Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture–normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm.

Reweighted variational full-waveform inversions

Starting from an initial model and predefined priors, a variational full-waveform inversion (VFWI) seeks posterior distributions of model parameters via optimization using a Bayesian theorem. Thus, VFWI is useful in estimating uncertainties in full-waveform inversions (FWIs). However, the resolution of the inverted models from VFWIs is usually not as good as those from conventional FWIs. We decompose the loss function in a VFWI into two terms: the complexity cost and the data misfit. The data variance, which balances these two terms, is expected to decrease during an iterative optimization to gradually put higher weight on the data misfit. We develop and compare two reweighting schemes in VFWI that can produce high-resolution velocity models and the associated uncertainties. Inversions are performed efficiently in a deep-learning framework to take advantage of automatic differentiation. Tests using synthetic data and blind data indicate that reweighted VFWIs are less sensitive to initial models and can generate inversion results that have higher resolution than those from conventional FWIs.

Monte Carlo characterization of Si ring modulator PAM-4 eye diagram performance

The eye diagram performance of the Si ring modulator (RM) is Monte Carlo characterized with the RM equivalent circuit model. Inter-die statistical distributions of Si-RM model parameters are determined from simple RM optical transmission and electrical reflection coefficient measurement, and the correlated model parameter sets are randomly generated for Monte Carlo simulation of 40-Gbps 4-level pulse AM (PAM-4) eye diagrams within simulation program with IC emphasis. From the resulting Monte Carlo simulated eye diagrams, the yield for the Si RMs that satisfy optical modulation amplitude and the ratio of level mismatch requirements can be corroborated with measurement. With these, the eye diagrams of Si electronic-photonic integrated PAM-4 transmitters with RMs and driver electronics are Monte Carlo characterized. This approach allows the extension of the standard Si IC characterization technique to the electronic-photonic ICs and can produce better-performing solutions with better yields in the design stage.

A Stochastic Analysis of the Effect of Trading Parameters on the Stability of the Financial Markets Using a Bayesian Approach

The purpose of this study was to identify and measure the impact of the different effects of entropy states over the high-frequency trade of the cryptocurrency market, especially in Bitcoin, using and selecting optimal parameters of the Bayesian approach, specifically through approximate Bayesian computation (ABC). ABC corresponds to a class of computational methods rooted in Bayesian statistics that could be used to estimate the posterior distributions of model parameters. For this research, ABC was applied to estimate the daily prices of the Bitcoin cryptocurrency from May 2013 to December 2021. The findings suggest that the behaviour of the parameters for our tested trading algorithms, in which sudden jumps are observed, can be interpreted as changes in states of the generated time series. Additionally, it is possible to identify and model the effects of the COVID-19 pandemic on the series analysed in the research. Finally, the main contribution of this research is that we have characterised the relationship between entropy and the evolution of parameters defining the optimal selection of trading algorithms in the financial industry.

Mapping the risk of Rift Valley fever in Uganda using national seroprevalence data from cattle, sheep and goats.

Uganda has had repeated outbreaks of Rift Valley fever (RVF) since March 2016 when human and livestock cases were reported in Kabale after a long interval. The disease has a complex and poorly described transmission patterns which involves several mosquito vectors and mammalian hosts (including humans). We conducted a national serosurvey in livestock to determine RVF virus (RVFV) seroprevalence, risk factors, and to develop a risk map that could be used to guide risk-based surveillance and control measures. A total of 3,253 animals from 175 herds were sampled. Serum samples collected were screened at the National Animal Disease Diagnostics and Epidemiology Centre (NADDEC) using a competition multispecies anti-RVF IgG ELISA kit. Data obtained were analyzed using a Bayesian model that utilizes integrated nested Laplace approximation (INLA) and stochastic partial differential equation (SPDE) approaches to estimate posterior distributions of model parameters, and account for spatial autocorrelation. Variables considered included animal level factors (age, sex, species) and multiple environmental data including meteorological factors, soil types, and altitude. A risk map was generated by projecting fitted (mean) values, from a final model that had environmental factors onto a spatial grid that covered the entire domain. The overall RVFV seroprevalence was 11.3% (95% confidence interval: 10.2-12.3%). Higher RVFV seroprevalences were observed in older animals compared to the young, and cattle compared to sheep and goats. RVFV seroprevalence was also higher in areas that had (i) lower precipitation seasonality, (ii) haplic planosols, and (iii) lower cattle density. The risk map generated demonstrated that RVF virus was endemic in several regions including those that have not reported clinical outbreaks in the northeastern part of the country. This work has improved our understanding on spatial distribution of RVFV risk in the country as well as the expected burden of the disease in livestock.

Omics data for sampling thermodynamically feasible kinetic models

Kinetic models are key to understanding and predicting the dynamic behaviour of metabolic systems. Traditional models require kinetic parameters which are not always available and are often estimated in vitro. Ensemble models overcome this challenge by sampling thermodynamically feasible models around a measured reference point. However, it is unclear if the convenient distributions used to generate the ensemble produce a natural distribution of model parameters and hence if the model predictions are reasonable.In this paper, we produced a detailed kinetic model for the central carbon metabolism of Escherichia coli. The model consists of 82 reactions (including 13 reactions with allosteric regulation) and 79 metabolites. To sample the model, we used metabolomic and fluxomic data from a single steady-state time point for E. coli K-12 MG1655 growing on glucose minimal M9 medium (average sampling time for 1000 models: 11.21 ± 0.14 min). Afterwards, in order to examine whether our sampled models are biologically sound, we calculated Km, Vmax and kcat for the reactions and compared them to previously published values. Finally, we used metabolic control analysis to identify enzymes with high control over the fluxes in the central carbon metabolism.Our analyses demonstrate that our platform samples thermodynamically feasible kinetic models, which are in agreement with previously published experimental results and can be used to investigate metabolic control patterns within cells. This renders it a valuable tool for the study of cellular metabolism and the design of metabolic pathways.

Real-world abnormal event detection via super-resolution and few-shot learning

The performance of abnormal event detection has been greatly improved in recent years. However, due of the problems of low resolution and few labeled training samples, it is difficult to apply in practice. To address these issues, we propose a few-shot scene-adaptive abnormal event detection method. First, to restore high-quality video from low-quality video, we propose a weighted recurrent backprojection network (WRBPN). WRBPN selectively extracts supplementary information from adjacent frames based on their similarity, which is beneficial to the reconstruction of the target frame and suppresses the interference of irrelevant frames. Second, we propose an abnormal event detection network to detect abnormal events in high-quality surveillance videos. The network extracts multiscale features to obtain more discriminative representations and uses variance attention to suppress the interference of background noise. On this basis, the video frame is predicted, and abnormal event detection is performed according to the prediction error. Finally, in order to quickly adapt the model to new scenarios, we propose a metalearning-based approach. During the training process, the distribution of model parameters is learned, and the specific parameters of the model are obtained via distribution sampling. Experiments on benchmark datasets demonstrate the effectiveness of our method.

Probabilistic Assessment of Conservation Voltage Reduction Using Static Load Model Parameter in the Presence of Uncertainties

Higher penetration of solar PV and wind generation in distribution networks may change the conservation voltage reduction (CVR) capabilities. The uncertainties associated with the renewable generations and system loads are neglected in the deterministic CVR assessment. In this paper, a probabilistic framework for CVR assessment has been presented to assess the impact of uncertainties associated with renewable generations and system loads. A theoretical framework has been presented by establishing a mathematical relationship between the probability distribution of renewable generations (solar PV and wind) and the probability distribution of static exponential load model parameters. The simulation results have confirmed that the penetration of non-Gaussian solar PV and wind generation leads to non-Gaussian static exponential load model parameter distribution, which is validated by the normality tests (quantile-quantile plot, skewness, and kurtosis). Subsequently, the magnitude and probability distribution of the CVR capabilities of the network changes with the penetration of renewable generations, where the higher renewable penetration scenarios lead to higher CVR values and non-Gaussian (asymmetric) distribution.

Sea Clutter Measurement Test and Amplitude Characteristics Analysis in the South China Sea Nearshore Area

To address the problem of sea clutter amplitude distribution characteristics varying with bandwidth, this paper obtains the raw data of clutter under different polarization methods of HH and VV in X and Ka bands based on the sea clutter measurement experiment carried out in June 2022 in the near-shore waters of South China Sea. For the data in X-band HH polarization mode, the goodness-of-fit test was conducted based on the classical models of Rayleigh, Weibull, log-normal and K distribution for the amplitude distribution characteristics of the sea clutter, and the variation of the estimated parameters of the distribution model with the bandwidth was analyzed. The test data show that: 1, with the increase of bandwidth sea clutter amplitude decreases; 2, with the increase of bandwidth Weibull distribution model parameters are decreasing trend, k distribution parameters are increasing trend; 3, the test conditions, the offshore sea clutter amplitude distribution is the optimal K distribution. The conclusions of this paper can provide a comparison and reference for the subsequent study on the characteristics of sea clutter distribution.

Longitudinal Data Analysis Based on Bayesian Semiparametric Method

A Bayesian semiparametric model framework is proposed to analyze multivariate longitudinal data. The new framework leads to simple explicit posterior distributions of model parameters. It results in easy implementation of the MCMC algorithm for estimation of model parameters and demonstrates fast convergence. The proposed model framework associated with the MCMC algorithm is validated by four covariance structures and a real-life dataset. A simple Monte Carlo study of the model under four covariance structures and an analysis of the real dataset show that the new model framework and its associated Bayesian posterior inferential method through the MCMC algorithm perform fairly well in the sense of easy implementation, fast convergence, and smaller root mean square errors compared with the same model without the specified autoregression structure.

Machine learning assisted identification of grey-box hot metal desulfurization model

ABSTRACT Hot metal desulfurization operates as an extraction process in steel production after the blast furnace. Mathematical modeling of the process provides the basis for control and optimization solutions. Owing to complex dynamics, an exhaustive physico-chemical description of the process is computationally infeasible. Thus, a model with a gray–box structure is considered. In the model, a neural network model for sulfide capacity of the slag is implemented in series with the reaction model. The network is trained using an independent data set. The parameters for the reaction model are identified using genetic algorithm with real-encoded population and hybrid selection and recombination operators. The gray-box model parameter distributions are estimated using Metropolis Hastings Algorithm. This study suggests that a sufficiently low mean absolute error can be achieved for the end sulfur content. The relative contribution of the permanent contact reaction to overall reaction rate under industrial conditions remains uncertain.

Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications

In this paper, we present the half logistic inverted Nadarajah–Haghigh (HL-INH) distribution, a novel extension of the inverted Nadarajah–Haghigh (INH) distribution. The probability density function (PDF) for the HL-INH distribution might have a unimodal, right skewness, or heavy-tailed shape for numerous parameter values; however, the shape forms of the hazard rate function (HRF) for the HL-INH distribution may be decreasing. Four specific entropy measurements were investigated. Some useful expansions for the HL-INH distribution were investigated. Several statistical and computational features of the HL-INH distribution were calculated. Using simple (SRS) and ranked set sampling (RSS), the parameters for the HL-INH distribution were estimated using the maximum likelihood (ML) technique. A simulation analysis was executed in order to determine the model parameters of the HL-INH distribution using the SRS and RSS methods, and RSS was shown to be more efficient than SRS. We demonstrate that the HL-INH distribution is more adaptable than the INH distribution and other statistical distributions when utilizing three real-world datasets.

Frequency-dependent site amplification functions for key geological units in Iceland from a Bayesian hierarchical model for earthquake strong-motions

A fundamental modeling assumption in engineering seismology is that seismic ground motion is affected by source, propagation path and site effects. Contrary to the first two, comprehensive studies on site effects, the localized amplification effects on seismic ground motion due to the uppermost geological structure, have been limited in Iceland. As a result, site amplification has been modeled in ground motion models in a simplistic and qualitative way. In this study, we address this limitation by using the new Bayesian hybrid GMM proposed by Kowsari et al. (2020) to model the recorded ground motions at regional strong-motion stations in southwest Iceland, specifically the peak ground acceleration and pseudo-acceleration response spectra as a function of oscillator period (i.e., PGA and PSA at T=0.01-3.0 s), earthquake magnitude, distance and hypocentral depth, and at first, we omit a site-term. Then, we incorporate the GMM in a Bayesian Hierarchical Model (BHM) that allows prior distributions of model parameters to be used and we partition the model residuals into various terms associated with the source, propagation path and station terms. Through Bayesian inference of the model parameters the results show that the station term residuals reveal a frequency-dependent site amplification at the recording sites. By inspecting this systematic behaviour, we propose four groups of station terms by their characteristics. We then carefully inspect the station locations in terms of their associated geological unit and observe that the geological units and station term groups are qualitatively correlated. By combining the two, we propose the first frequency-dependent average site amplification functions associated with key geological units in Iceland based on age and formation. Provisionally we refer to them as hard rock, rock, (Holocene) lava rock, and (unspecified) soil site classes, respectively. We then update the GMM by incorporating these amplification functions so that it now enables the prediction of PGA and PSA at these four site classes. As a result, the new model standard deviations are considerably lower, with those associated with the event term being τ = 0.05, station terms φS2S = 0.10, intra-event φ = 0.17 and total σ = 0.18 in common logarithm units for PGA. The new site class-specific GMM now enables the site-specific ground motion for separate geological units which in turn improves site-specific seismic hazard assessment and informed site-specific engineering decision making in Iceland.