Bayesian Parameter Estimation Research Articles

Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution.

In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto Distribution (GPD), only the observations above a certain threshold are considered; therefore, a big amount of information is wasted. The aim of this work is to make the most of the information provided by the observations in order to improve the accuracy of Bayesian parameter estimation. We present two new Bayesian methods to estimate the parameters of the GPD, taking into account the whole data set from the baseline distribution and the existing relations between the baseline and the limit GPD parameters in order to define highly informative priors. We make a comparison between the Bayesian Metropolis–Hastings algorithm with data over the threshold and the new methods when the baseline distribution is a stable distribution, whose properties assure we can reduce the problem to study standard distributions and also allow us to propose new estimators for the parameters of the tail distribution. Specifically, three cases of stable distributions were considered: Normal, Lévy and Cauchy distributions, as main examples of the different behaviors of the tails of a distribution. Nevertheless, the methods would be applicable to many other baseline distributions through finding relations between baseline and GPD parameters via studies of simulations. To illustrate this situation, we study the application of the methods with real data of air pollution in Badajoz (Spain), whose baseline distribution fits a Gamma, and show that the baseline methods improve estimates compared to the Bayesian Metropolis–Hastings algorithm.

Minimally-modeled search of higher multipole gravitational-wave radiation in compact binary coalescences

As the Advanced LIGO and Advanced Virgo interferometers, soon to be joined by the KAGRA interferometer, increase their sensitivity, they detect an ever-larger number of gravitational waves with a significant presence of higher multipoles (HMs) in addition to the dominant (2, 2) multipole. These HMs can be detected with different approaches, such as the minimally-modeled burst search methods, and here we discuss one such approach based on the coherent WaveBurst (cWB) pipeline. During the inspiral phase the HMs produce chirps whose instantaneous frequency is a multiple of the dominant (2, 2) multipole, and here we describe how cWB can be used to detect these spectral features. The search is performed within suitable regions of the time-frequency representation; their shape is determined by optimizing the receiver operating characteristics. This novel method has already been used in the GW190814 discovery paper (Abbott et al 2020 Astrophys. J. Lett. 896 L44) and is very fast and flexible. Here we describe in full detail the procedure used to detect the (3, 3) multipole in GW190814 as well as searches for other HMs during the inspiral phase, and apply it to another event that displays HMs, GW190412, replicating the results obtained with different methods. The procedure described here can be used for the fast analysis of HMs and to support the findings obtained with the model-based Bayesian parameter estimates.

Fundamental tools for developing likelihood functions within ACT-R

Likelihood functions are an integral component of statistical approaches to parameter estimation and model evaluation. However, likelihood functions are rarely used in cognitive architectures due, in part, to challenges in their derivation, and the lack of accessible tutorials. In this tutorial, we present fundamental concepts and tools for developing analytic likelihood functions for the ACT-R cognitive architecture. These tools are based on statistical concepts such as serial vs. parallel process, convolution, minimum/maximum processing time, and mixtures. Importantly, these statistical concepts are highly composable, allowing them to be combined to form likelihood functions for many models. We demonstrate how to apply these tools within the context of Bayesian parameter estimation using five models taken from the standard ACT-R tutorial. Although the tutorial focuses on ACT-R due to its prevalence, the concepts covered within the tutorial are applicable to other cognitive architectures.

Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application

In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one‐selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.

Bayesian Parameter Estimation and Model Selection for Gallbladder Cancer Data of two Countries

Bayesian Parameter Estimation and Model Selection for Gallbladder Cancer Data of two Countries

Using voltammetry augmented with physics-based modeling and Bayesian hypothesis testing to identify analytes in electrolyte solutions

Voltammetry is a foundational electrochemical technique that can qualitatively and quantitatively probe electroactive species in solutions and as such has been used in numerous fields of study. Recently, automation has been introduced to extend the capabilities of voltammetric analysis through approaches such as Bayesian parameter estimation and compound identification. However, opportunities exist to enable more versatile methods across a wider range of solution compositions and experimental conditions. Here, we present a protocol that uses experimental voltammetry, physics-driven models, binary hypothesis testing, and Bayesian inference to enable robust labeling of analytes in multicomponent solutions across multiple techniques. We first describe the development of this protocol, and we subsequently validate the methodology in a case study involving five N-functionalized phenothiazine derivatives. In this analysis, the protocol correctly labels solutions each containing 10H-phenothiazine and 10-methylphenothiazine from both cyclic voltammograms and cyclic square wave voltammograms, demonstrating the ability to identify redox-active constituents of a multicomponent solution. Finally, we identify areas of further improvement—such as achieving greater detection accuracy—and future applications to potentially enhance in situ or operando diagnostic workflows.

Adsorption of Praziquantel Enantiomers on Chiral Cellulose Tris 3-Chloro, 4-Methylphenylcarbamate by Frontal Analysis: Fisherian and Bayesian Parameter Estimation and Inference

Adsorption of Praziquantel Enantiomers on Chiral Cellulose Tris 3-Chloro, 4-Methylphenylcarbamate by Frontal Analysis: Fisherian and Bayesian Parameter Estimation and Inference

Effects of Sentence Output Tasks on EFL Vocabulary Learning from a Bayesian Perspective

This article builds on the growing line of inquiry into the relative effectiveness of different tasks for vocabulary learning. Specifically, the study compares the efficacy of several sentence output tasks in EFL vocabulary learning through reading. To this end, evidence was weighed for one hypothesis over the alternative from a Bayesian perspective rather than in light of the commonly used null hypothesis significance testing (NHST), which depends heavily on the <i>p</i> values for statistical conclusions. Ninety-one EFL learners were randomly assigned to one of three word-focused sentence output tasks (i.e., L2-L1 translating, paraphrasing and writing), and were subsequently tested on their initial learning and retention of newly-encountered EFL words. Both Bayes factor analysis and Bayesian parameter estimation were employed to find evidence for task effects. With respect to initial word learning, moderate evidence was in favor of no difference between translating and paraphrasing, whilst weak evidence in favor of no difference between translating and writing as well as between paraphrasing and writing. For pedagogical purposes, no good evidence was for or against task effects. Regarding word retention, moderate evidence supported no task difference, and all the tasks fared equally well pedagogically. The results partially support the involvement load hypothesis and are discussed in terms of task difficulty, context generation and semantic elaboration.

External Evaluation of a Bayesian Warfarin Dose Optimization Based on a Kinetic-Pharmacodynamic Model.

Warfarin is a representative anticoagulant with large interindividual variability. The published kinetic-pharmacodynamic (K-PD) model allows the prediction of warfarin dose requirement in Swedish patients; however, its applicability in Japanese patients is not known. We evaluated the model's predictive performance in Japanese patients with various backgrounds and relationships using Bayesian parameter estimation and sampling times. A single-center retrospective observational study was conducted at Tokyo Women's Medical University, Medical Center East. The study population consisted of adult patients aged >20 years who commenced warfarin with a prothrombin time-international normalized ratio (PT-INR) from June 2015 to June 2019. The published K-PD model modified by Wright and Duffull was assessed using prediction-corrected visual predictive checks, focusing on clinical characteristics, including age, renal function, and individual prediction error. The external dataset included 232 patients who received an initial warfarin daily dose of 3.2 ± 1.28 mg with 2278 PT-INR points (median [range] follow-up period of 23 d [7-28]). Prediction-corrected visual predictive checks carried a propensity for underprediction. Additionally, age >60 years, body mass index ≤25 kg/m2, and estimated glomerular filtration rate ≤60 mL/min/1.73 m2 had a pronounced tendency to underpredict PT-INR. However, Bayesian prediction using four prior observations reduced underprediction. To improve the prediction performance of these special populations, further studies are required to construct a model to predict warfarin dose requirements in Japanese patients.

Determination of the impact parameter distribution of low-intermediate energy heavy ion collisions using machine learning

<p indent="0mm">The impact parameter is an important quantity for reasonably simulating heavy ion collisions (HIC) using the transport model, because many HIC observables obviously depend on it in the simulation. However, the impact parameter cannot be directly measured or determined from HIC observables, so reconstructing impact parameter distributions from HIC observables is highly desired. For intermediate energy HICs, impact parameters distribute in a wide range for the selected events due to the strong fluctuation mechanism. In this work, three methods for reconstructing impact parameter distributions are discussed, namely sharp cut-off approximation, Bayesian estimation, and neural network estimation of impact parameters. The dataset used for reconstructing the impact parameter distribution by machine learning methods are generated from an improved quantum molecular dynamics model (ImQMD). Finally, we propose to use an unsupervised machine learning method, namely the K-means algorithm, to sort the centrality of heavy ion collisions and its validity is also proved in theory.

Statistical Analysis Based on Progressive Type‐I Censored Scheme from Alpha Power Exponential Distribution with Engineering and Medical Applications

Using a progressive Type‐I censoring technique, this article will explore how to estimate unknown parameters of the alpha power exponential distribution (APED) (Type‐I PCS). The squared error loss function and the LINEX loss function are used to get the maximum likelihood estimate as well as the Bayesian estimation of the unknown parameters, respectively. It was our intention to use the Markov chain Monte Carlo method in conjunction with the Bayes estimation strategy. We are able to calculate the approximately accurate confidence intervals for the parameters whose values are unknown. In addition to this, we discussed the estimation challenges of reliability and the hazard rate function of the APED while using Type‐I PCS, as well as the approximate confidence intervals that relate to these problems. In the last step, the theoretical findings that were acquired are evaluated and compared with the distributions of all of its rivals by making use of two actual datasets that represent the disciplines of engineering and medicine.

Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

AbstractMany different equations have been proposed to describe quantitatively one‐dimensional soil water infiltration. The unknown coefficients of these equations characterize soil hydraulic properties and may be estimated from a n record, , of cumulative infiltration measurements using curve fitting techniques. The two‐term infiltration equation, , of Philip has been widely used to describe measured infiltration data. This function enjoys a solid mathematical–physical underpinning and admits a closed‐form solution for the soil sorptivity, S [L T−1/2], and multiple, c [−], of the saturated hydraulic conductivity, Ks [L T−1]. However, Philip's two‐term equation has a limited time validity, tvalid [T], and thus cumulative infiltration data, , beyond will corrupt the estimates of S and Ks. This paper introduces a novel method for estimating S, c, Ks, and tvalid of Philip's two‐term infiltration equation. This method, coined parasite inversion, use as vehicle Parlange's three‐parameter infiltration equation. As prerequisite to our method, we present as secondary contribution an exact, robust and efficient numerical solution of Parlange's infiltration equation. This solution admits Bayesian parameter estimation with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and yields as byproduct the marginal distribution of Parlange's β parameter. We evaluate our method for 12 USDA soil types using synthetic infiltration data simulated with HYDRUS‐1D. An excellent match is observed between the inferred values of S and Ks and their “true” values known beforehand. Furthermore, our estimates of c and tvalid correlate well with soil texture, corroborate linearity of the relationship for , and fall within reported ranges. A cumulative vertical infiltration of about 2.5 cm may serve as guideline for the time‐validity of Philip's two‐term infiltration equation.

Bayesian parameter estimation for phosphate dynamics during hemodialysis.

Hyperphosphatemia in patients with renal failure is associated with increased vascular calcification and mortality. Hemodialysis is a conventional treatment for patients with hyperphosphatemia. Phosphate kinetics during hemodialysis may be described by a diffusion process and modeled by ordinary differential equations. We propose a Bayesian model approach for estimating patient-specific parameters for phosphate kinetics during hemodialysis. The Bayesian approach allows us to both analyze the full parameter space using uncertainty quantification and to compare two types of hemodialysis treatments, the conventional single-pass and the novel multiple-pass treatment. We validate and test our models on synthetic and real data. The results show limited identifiability of the model parameters when only single-pass data are available, and that the Bayesian model greatly reduces the relative standard deviation compared to existing estimates. Moreover, the analysis of the Bayesian models reveal improved estimates with reduced uncertainty when considering consecutive sessions and multiple-pass treatment compared to single-pass treatment.

Research on the mechanical properties of the joint of the beam-column subassembly

In order to study the effect of high-performance fiber cement composites (HPFRCC) on the mechanical properties of the joint of the frame structure, pseudo-static tests were conducted on seven beam-column subassemblies. Compared with the RC subassembly, the shear capacity of the HPFRCC beam-column connection was increased by 11.4%, and the shear deformation was reduced by 10.3%. The contribution ratio of the shear deformation to the drift was reduced by 22.7%. The value of the coefficient ηc and the flange width of the slab had a significant impact on the shear deformation of the HPFRCC joint. The shear deformation corresponding to the peak load of the joint can be controlled at about 0.01 when the coefficient ηc is 1.6, or the flange width is eight times the width of the slab thickness. The shear strength-shear deformation calculation model of the joint was established through the Bayesian parameter estimation, and the model analysis results were in good agreement with the test results.

1109. Pharmacokinetics and Exposure of Cefepime in Critically Ill Patients Receiving Extracorporeal Membrane Oxygenation (ECMO)

BackgroundECMO is a life-saving tool utilized in critically ill patients that require respiratory and/or cardiac support. ECMO may also affect the pharmacokinetics (PK) of certain medications, including some antibiotics. Cefepime is a widely used antibiotic in this population due to its broad spectrum activity but limited data are available to guide dosing in patients requiring ECMO. MethodsThis was a prospective, single-center study of 6 critically ill adult patients requiring ECMO and receiving cefepime 2g q8h as a 3h infusion. After obtaining informed consent, 4-6 blood samples within the dosing interval were collected to determine cefepime concentrations. Population PK was conducted in Pmetrics using R. Final MAP Bayesian parameter estimates were used to simulate free time above MIC (%ƒT >MIC) for various cefepime dosing regimens. The target pharmacodynamic exposure was 70% fT >MIC.ResultsPatients were between 31-62 years old; 4/6 (66.7%) were on veno-venous (VV) ECMO and 2 veno-arterial (VA) ECMO. Two patients required continuous venovenous hemodiafiltration (CVVHDF) while the other 4 had a CrCL between 92-199 ml/min. A two compartment model fitted the data better than a one compartment model. Median (range) final population PK parameters were: clearance (CL), 9.8 L/h (7.6-33.1); volume of central compartment (VC ), 6.9 L (4.7-49.8); and intercompartment transfer constants (k12), 2.04 h-1 (1.48-2.29); and k21, 1.49 h-1 (0.75-1.71). The 2g q8h (3h infusion) regimen resulted in target exposure in all patients up to an MIC of 8 mg/L (the susceptibility breakpoint for Pseudomonas), with 5/6 patients achieving this at 16 mg/L. A standard 2g q12h (0.5h infusion) regimen would have resulted in 5/6 patients achieving 70% ƒT >MIC at 8 mg/L and 1/6 at 16 mg/L.ConclusionThese are the first data describing cefepime PK and exposure attainment in critically ill patients receiving ECMO. Cefepime 2g q8h (3h infusion) achieved target pharmacodynamic exposure up to the susceptibility breakpoint of 8 mg/L in all 6 patients, including 2 with concomitant CVVHDF. Additional studies are warranted to define cefepime PK in patients on ECMO across a robust range of CrCL to guide dosing.Disclosures David P. Nicolau, PharmD, Abbvie, Cepheid, Merck, Paratek, Pfizer, Wockhardt, Shionogi, Tetraphase (Other Financial or Material Support, I have been a consultant, speakers bureau member, or have received research funding from the above listed companies.) Joseph L. Kuti, PharmD, Allergan (Speaker’s Bureau)BioMérieux (Consultant, Research Grant or Support, Speaker’s Bureau)Contrafect (Scientific Research Study Investigator)GSK (Consultant)Merck (Research Grant or Support)Paratek (Speaker’s Bureau)Roche Diagnostics (Research Grant or Support)Shionogi (Research Grant or Support)Summit (Scientific Research Study Investigator)

Reliability estimation and parameter estimation for inverse Weibull distribution under different loss functions

In this paper, the classical and Bayesian estimators of the unknown parameters and the reliability function of the inverse Weibull distribution are considered. The maximum likelihood estimators (MLEs) and modified maximum likelihood estimators (MMLEs) are used in the classical parameter estimation. Bayesian estimators of the parameters are obtained by using symmetric and asymmetric loss functions under informative and non-informative priors. Bayesian computations are derived by using Lindley approximation and Markov chain Monte Carlo (MCMC) methods. The asymptotic confidence intervals are constructed based on the maximum likelihood estimators. The Bayesian credible intervals of the parameters are obtained by using the MCMC method. Furthermore, the performances of these estimation methods are compared concerning their biases and mean square errors through a simulation study. It is seen that the Bayes estimators perform better than the classical estimators. Finally, two real-life examples are given for illustrative purposes.

Analysis of Change in the Precipitation Regime on the Territory of the Russian Federation in the Second Half of the 20th Century and the Early 21st Century Using Bayesian Estimation of Markov Chain Parameters

Analysis of Change in the Precipitation Regime on the Territory of the Russian Federation in the Second Half of the 20th Century and the Early 21st Century Using Bayesian Estimation of Markov Chain Parameters

Constraints on the spatially dependent cosmic-ray propagation model from Bayesian analysis

The energy spectra of primary and secondary cosmic rays (CRs) generally harden at several hundreds of GeV, a finding which can be naturally interpreted by means of propagation effects. We adopt a spatially dependent CR propagation model to fit the spectral hardening, where a slow-diffusion disk (SDD) is assumed near the galactic plane. We aim to constrain the propagation parameters with a Bayesian parameter estimation based on a Markov chain Monte Carlo sampling algorithm. The latest precise measurements of carbon spectrum and B/C ratio are adopted in the Bayesian analysis. The $^{10}\mathrm{Be}/^{9}\mathrm{Be}$ and Be/B ratios are also included to break parameter degeneracies. The fitting result shows that all the parameters are well constrained. Especially, the thickness of the SDD is limited to 0.4--0.5 kpc above and below the galactic plane, which could be the best constraint for the slow-diffusion region among similar works. The $\overline{p}/p$ ratio and the amplitude of CR anisotropy predicted by the SDD model are consistent with the observations, while the predicted high-energy electron and positron fluxes are slightly and significantly lower than the observations, respectively, indicating the necessity of extra sources.

Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples

Front Cover: In article number 2100017, Michael Wulkow and co-workers refine and apply classical and Bayesian parameter estimation for polymerization. This article aims at showing the mathematical connection of both approaches and how their combination can and should be leveraged in a closed workflow to derive a strong understanding of a model and its parameters.

BESTP — An automated Bayesian modeling tool for asteroseismology

Asteroseismic observations are crucial to constrain stellar models with precision. Bayesian Estimation of STellar Parameters (BESTP) is a tool that utilizes Bayesian statistics and nested sampling Monte Carlo algorithm to search for the stellar models that best match a given set of classical and asteroseismic constraints from observations. The computation and evaluation of models are efficiently performed in an automated and multi-threaded way. To illustrate the capabilities of BESTP, we estimate fundamental stellar properties for the Sun and the red-giant star HD 222076. In both cases, we find models that are consistent with observations. We also evaluate the improvement in the precision of stellar parameters when the oscillation frequencies of individual modes are included as constraints, compared to the case when only the large frequency separation is included. For the solar case, the uncertainties of estimated masses, radii and ages are reduced by 0.7%, 0.3% and 8% respectively. For HD 222076, they are reduced even more noticeably by 2%, 0.5% and 4.7% respectively. We also note an improvement of 10% for the age of HD 222076 when the Gaia parallax is included as a constraint compared to the case when only the large separation is included as a constraint.