Bayesian Estimation Research Articles

Statistical physical view of statistical inference in Bayesian linear regression model.

This paper considers similarities between statistical physics and Bayes inference through the Bayesian linear regression model. Some similarities have been discussed previously, such as the analogy between the marginal likelihood in Bayes inference and the partition function in statistical mechanics. In particular, this paper considers the proposal to associate discrete sample size with inverse temperature [C. H. LaMont and P. A. Wiggins, Phys. Rev. E 99, 052140 (2019)2470-004510.1103/PhysRevE.99.052140]. The previous study suggested that incorporating this similarity motivates the derivation of analogs of thermodynamic functions such as energy and entropy. The study also anticipated that those analogous functions have potential to describe Bayes estimation from physical points of view and to provide physical insights into mechanisms of estimation. This paper incorporates a macroscopic perspective as an asymptotics similar to the thermodynamic limit into the previous suggestion. Its motivation stems from the statistical mechanical concept of deriving thermodynamic functions that characterize macroscopic properties of macroscopic systems. This incorporation not only allows analogs of macroscopic thermodynamic functions to be considered but also suggests a candidate for an analog of inverse temperature with continuity, which is partly consistent with the previous proposal to associate the discrete sample size with inverse temperature. On the basis of this suggestion, we analyze analogs of macroscopic thermodynamic functions for a Bayesian linear regression model which is the basis of various machine learning models. We further investigate, through the behavior of these functions, how Bayes estimation is described from the perspective of physics and what kind of physical insight is obtained. As a result, the estimation of regression coefficients, which is the primary task of regression, appears to be described by the physical picture of balance between decreasing energy and increasing entropy as in equilibrium states of thermodynamic systems. More specifically we observe the physical view of Bayes inference as follows: the estimation succeeds where the effect of decreasing energy is dominant at low temperature. On the other hand, the estimation fails where the effect of increasing entropy is dominant at high temperature.

Estimation and Analysis of Trigonometric Models under Bayesian Approach

In this study, we explore three innovative trigonometric models within the Bayesian framework, utilizing the inverse Weibull distribution as our foundation. These models—namely the Sine inverse Weibull, Cosine inverse Weibull, and Tan inverse Weibull—are crafted from distinct distribution families. We employ both maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) simulation techniques to estimate parameters, drawing upon a comprehensive dataset. By scrutinizing posterior samples numerically and graphically, we evaluate the efficacy of our models, generating Bayes estimates for parameters, examining reliability and hazard functions, and establishing credible intervals. Furthermore, we assess the predictive capacity of all three models through posterior predictive checks. We also conduct comparative analyses, pitting our models against competing ones using real-world data. Notably, our results reveal that the proposed trio of models exhibit strikingly similar performance in terms of fitting the data.

Different estimation techniques and data analysis for constant-partially accelerated life tests for power half-logistic distribution

Partial accelerated life tests (PALTs) are employed when the results of accelerated life testing cannot be extended to usage circumstances. This work discusses the challenge of different estimating strategies in constant PALT with complete data. The lifetime distribution of the test item is assumed to follow the power half-logistic distribution. Several classical and Bayesian estimation techniques are presented to estimate the distribution parameters and the acceleration factor of the power half-logistic distribution. These techniques include Anderson–Darling, maximum likelihood, Cramér von-Mises, ordinary least squares, weighted least squares, maximum product of spacing and Bayesian. Additionally, the Bayesian credible intervals and approximate confidence intervals are constructed. A simulation study is provided to compare the outcomes of various estimation methods that have been provided based on mean squared error, absolute average bias, length of intervals, and coverage probabilities. This study shows that the maximum product of spacing estimation is the most effective strategy among the options in most circumstances when adopting the minimum values for MSE and average bias. In the majority of situations, Bayesian method outperforms other methods when taking into account both MSE and average bias values. When comparing approximation confidence intervals to Bayesian credible intervals, the latter have a higher coverage probability and smaller average length. Two authentic data sets are examined for illustrative purposes. Examining the two real data sets shows that the value methods are workable and applicable to certain engineering-related problems.

Monetary and fiscal policies in Brazil and the behavioral approach

PurposeThis study aims to elucidate the dynamics of monetary and fiscal policy interactions in Brazil, focusing on the impacts of positive shocks in government consumption and interest rates. By comparing rational and behavioral agent responses, it clarifies how these frameworks influence gross domestic product (GDP), inflation, private and government consumption and nominal interest rates.Design/methodology/approachThe study employs a new Keynesian dynamic stochastic general equilibrium (DSGE) model with Bayesian estimation from 2000Q1 to 2022Q4, capturing rational and behavioral behaviors with adjustments for Brazilian economic idiosyncrasies. Impulse response functions (IRF) assess the dynamic effects of policy shocks, providing a comparative analysis of the two frameworks.FindingsBehavioral agents show greater initial sensitivity to policy shocks, causing more pronounced fluctuations in GDP, inflation and private consumption compared to rational agents. Over time, the behavioral approach leads to a more robust recovery, while the rational approach results in a quicker return to equilibrium but less pronounced long-term recovery. The study also finds fiscal policy can partially offset the negative impacts of monetary tightening, with a more delayed effect in the behavioral model.Originality/valueThis paper provides insights into the interplay between monetary and fiscal policies under different agent expectations, emphasizing the importance of incorporating behavioral elements into macroeconomic models to better capture policy dynamics in emerging markets.

Addressing accuracy by prescribing precision: Bayesian error estimation of point defect energetics

With density functional theory (DFT), it is possible to calculate the formation energy of charged point defects and in turn to predict a range of experimentally relevant quantities, such as defect concentrations, charge transition levels, or recombination rates. While prior efforts have led to marked improvements in the accuracy of such calculations, comparatively modest effort has been directed at quantifying their uncertainties. However, in the broader DFT research space, the development of Bayesian Error Estimation Functionals (BEEF) has enabled uncertainty quantification (UQ) for other properties. In this paper, we investigate the utility of BEEF as a tool for UQ of defect formation energies. We build a pipeline for propagating BEEF energies through a formation-energy calculation and test it on intrinsic defects in several materials systems spanning a variety of chemistries, bandgaps, and crystal structures, comparing to prior published results where available. We also assess the impact of aligning to a deep-level transition rather than to the VBM (valence band maximum). We observe negligible dependence of the estimated uncertainty upon a supercell size, though the relationship may be obfuscated by the fact that finite-size corrections cannot be computed separately for each member of the BEEF ensemble. Additionally, we find an increase in estimated uncertainty with respect to the absolute charge of a defect and the relaxation around the defect site without deep-level alignment, but this trend is absent when the alignment is applied. While further investigation is warranted, our results suggest that BEEF could be a useful method for UQ in defect calculations.

Estimation of Bonferroni Curve and Bonferroni Index of the Pareto Distribution

Abstract In this article, we consider classical and Bayesian estimations of some economic measures, specially Bonferroni Curve and Bonferroni Index of the Pareto distribution. We obtain the Maximum Likelihood Estimator and Uniform Minimum Variance Unbiased Estimator in the classical setup, and their properties are studied. Additionally, we conduct Bayesian estimation procedures based on symmetric loss functions and a truncated gamma prior. The precision of the estimators is evaluated under different sample sizes via Monte Carlo simulation. Furthermore, a real dataset is provided to compute all the estimators.

Assessment of reliability and availability of a system by using a bivariate stochastic model

AbstractIn the present age of industrial revolution where the smart manufacturing and smart production are being used in the developed countries, the production systems are still vulnerable to disruptions and outages that affect the reliability and availability of the systems. Certain scientific and probabilistic approaches are required to study the inter‐failure times and repair times and find the possible solutions for maximum production and minimum losses. In this article, we propose a bivariate Power Pareto distribution to model the inter‐failure times and repair times of a system along with some of its characteristics. The model parameters are estimated by employing the maximum likelihood estimation, Bayesian estimation and ant colony optimization algorithm. A simulation study is conducted for different sample sizes to assess the stability of the model parameters. Moreover, we derive the distribution of convolution from our proposed bivariate stochastic distribution and compute its quantiles that help to determine the total time of availability and recovery of a certain system. To demonstrate the efficacy of our model, we use real data set of inter‐failure times and repair times of a certain system.

Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

Bayesian reliability estimation of weighted exponential-lindley distribution with intuitionistic fuzzy lifetime data

Tests of human auditory temporal resolution: Simulations of Bayesian threshold estimation for auditory gap detection.

In an attempt to develop tests of auditory temporal resolution using gap detection, we conducted computer simulations of Zippy Estimation by Sequential Testing (ZEST), an adaptive Bayesian threshold estimation procedure, for measuring gap detection thresholds. The results showed that the measures of efficiency and precision of ZEST changed with the mean and standard deviation (SD) of the initial probability density function implemented in ZEST. Appropriate combinations of mean and SD values led to efficient ZEST performance; i.e., the threshold estimates converged to their true values after 10 to 15 trials.

Spectral decomposition for collective Thomson scattering based on an improved genetic algorithm.

Collective Thomson scattering (CTS) is a diagnostic technique that obtains ion temperature and ion composition of plasma by spectral decomposition from scattering spectra. Bayesian estimation and least squares fitting are usually applied in this spectral decomposition process. Nevertheless, these spectral decomposition methods strongly rely on measurements of other diagnostic systems, and the measurement errors of other systems would influence the spectral decomposition results. In this article, an improved genetic algorithm is applied to decompose the scattering spectra of CTS. By analyzing the sensitivity of plasma parameters, the width and slope of the scattering spectrum are found to be strongly associated with ion temperature. Based on this correlation relation, a new fitness function is designed to provide a more precise estimation of ion temperature. Meanwhile, adaptive crossover and mutation operators are introduced to solve the premature convergence problem. This improved genetic algorithm with the new fitness function can obtain a more precise ion temperature from scattering spectra of CTS and does not rely on the measurement of other diagnostic systems, which has an extensive application prospect in data processing of CTS.

Fast likelihood-free reconstruction of gravitational wave backgrounds

We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based) techniques for reconstructing the spectral shape of a gravitational wave background (GWB). We focus on the reconstruction of an arbitrarily shaped signal (approximated by a piecewise power-law in many frequency bins) by the LISA detector, but the method can be easily extended to either template-dependent signals, or to other detectors, as long as a characterisation of the instrumental noise is available. As proof of the technique, we quantify the ability of LISA to reconstruct signals of arbitrary spectral shape (blind reconstruction), considering a diversity of frequency profiles, and including astrophysical backgrounds in some cases. As a teaser of how the method can reconstruct signals characterised by a parameter-dependent template (template reconstruction), we present a dedicated study for power-law signals. While our technique has several advantages with respect to traditional MCMC methods, we validate it with the latter for concrete cases. This work opens the door for both fast and accurate Bayesian parameter estimation of GWBs, with essentially no computational overhead during the inference step. Our set of tools are integrated into the package GWBackFinder, which is publicly available in GitHub.

Joint Bayesian Channel Estimation and Data Detection for Underwater Acoustic Communications

Joint Bayesian Channel Estimation and Data Detection for Underwater Acoustic Communications

Greedy Selection of Sensors for Linear Bayesian Estimation under Correlated Noise

Greedy Selection of Sensors for Linear Bayesian Estimation under Correlated Noise

Gender effects for loss aversion: A reconsideration

Gender differences in decision making is a topic that has attracted much attention in the literature and the debate seems to be inconclusive. In a recent study, Bouchouicha et al. (2019) using data from an incentivised experiment with almost 3000 students and 30 different countries, estimate gender effects assuming four commonly employed definitions of loss aversion. Despite the fact that their analysis is based on the same data and the same functional forms and econometric setup, their results are inconclusive regarding the existence and the direction of gender effects for loss aversion. In this study, we investigate two extensions of their work in an effort to shed some light on the potential reasons behind this contradictory result. In particular, we explore whether: (1) a more flexible estimation method that allows for individual heterogeneity and generates more robust estimates in the presence of noise and; (2) a different utility function, can generate more robust inference regarding gender effects. We show that while a more flexible Hierarchical Bayesian estimation method is not sufficient to explain the contradictory results, an alternative utility function detects a uniform gender effect, with women being always more loss-averse, regardless the adopted definition of loss aversion.

측정오차 공변량을 고려한 포아송 소지역 모델의 준모수적 계층적 베이즈 추정

In the sample survey, it is impossible to obtain sufficient samples in relatively small areas, which makes it difficult to estimate accurate statistics for small areas. For this reason, various studies on small area estimation are constantly being conducted, and in particular, the Fay-Herriot (1979) model has been expanded to various forms as one of the most widely used small area estimation models. In this study, we developed a semiparametric regression model based on a radial basis function that can consider nonlinear relationships between the resulting variables and covariates, extended from the model considering the measurement error of the covariate in the Poisson distribution proposed by Nam, Hwang(2021). Also, parameter estimation and model fit were performed through hierarchical Bayesian estimation using Gibbs sampling and Metropolis-Hastings algorithm among Markov chain Monte Carlo techniques. Simulations were conducted under various conditions to confirm the suitability of the model developed in this study, and the excellence of the developed model was further verified through empirical analysis using data from the 8th Korean longitudinal study of aging.

Bayesian estimation of some reliability characteristics for Nakagami model using adaptive progressive censoring

The focus of this research is to clarify both conventional and Bayesian parametric estimation methods for the Nakagami distribution making use of adaptive progressive Type II censored data. From a classical estimation perspective, two estimation methods are considered: maximum likelihood and least squares estimations. Along with the model parameters, three reliability metrics are estimated using point and interval estimation. Bayes estimates with gamma and inverse gamma priors are investigated by employing the squared error loss function. The Bayes computations are created using the Markov Chain Monte Carlo technique. Moreover, the classical and Bayesian intervals are also taken into consideration. For evidence of the effectiveness of the given methodologies, a simulation study and three applications from the physics, chemistry, and engineering domains are explored. Lastly three optimality criteria are applied to the stated data sets to pick the best progressive censoring strategy.

Modeling construct change over time amidst potential changes in construct measurement: A longitudinal moderated factor analysis approach.

In analyzing longitudinal data with growth curve models, a critical assumption is that changes in the observed measures reflect construct changes and not changes in the manifestation of the construct over time. However, growth curve models are often fit to a repeated measure constructed as a sum or mean of scale items, making an implicit assumption of constancy of measurement. This practice risks confounding actual construct change with changes in measurement (i.e., differential item functioning [DIF]), threatening the validity of conclusions. An improved method that avoids such confounding is the second-order growth curve (SGC) model. It specifies a measurement model at each occasion of measurement that can be evaluated for invariance over time. The applicability of the SGC model is hindered by key limitations: (a) the SGC model treats time as continuous when modeling construct growth but as discrete when modeling measurement, reducing interpretability and parsimony; (b) the evaluation of DIF becomes increasingly error-prone given multiple timepoints and groups; (c) DIF associated with continuous covariates is difficult to incorporate. Drawing on moderated nonlinear factor analysis, we propose an alternative approach that provides a parsimonious framework for including many time points and DIF from different types of covariates. We implement this model through Bayesian estimation, allowing for incorporation of regularizing priors to facilitate efficient evaluation of DIF. We demonstrate a two-step workflow of measurement evaluation and growth modeling, with an empirical example examining changes in adolescent delinquency over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

SB-ETAS: using simulation based inference for scalable, likelihood-free inference for the ETAS model of earthquake occurrences

The rapid growth of earthquake catalogs, driven by machine learning-based phase picking and denser seismic networks, calls for the application of a broader range of models to determine whether the new data enhances earthquake forecasting capabilities. Additionally, this growth demands that existing forecasting models efficiently scale to handle the increased data volume. Approximate inference methods such as inlabru, which is based on the Integrated nested Laplace approximation, offer improved computational efficiencies and the ability to perform inference on more complex point-process models compared to traditional MCMC approaches. We present SB-ETAS: a simulation based inference procedure for the epidemic-type aftershock sequence (ETAS) model. This approximate Bayesian method uses sequential neural posterior estimation (SNPE) to learn posterior distributions from simulations, rather than typical MCMC sampling using the likelihood. On synthetic earthquake catalogs, SB-ETAS provides better coverage of ETAS posterior distributions compared with inlabru. Furthermore, we demonstrate that using a simulation based procedure for inference improves the scalability from O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(n^2)$$\\end{document} to O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(n\\log n)$$\\end{document}. This makes it feasible to fit to very large earthquake catalogs, such as one for Southern California dating back to 1981. SB-ETAS can find Bayesian estimates of ETAS parameters for this catalog in less than 10 h on a standard laptop, a task that would have taken over 2 weeks using MCMC. Beyond the standard ETAS model, this simulation based framework allows earthquake modellers to define and infer parameters for much more complex models by removing the need to define a likelihood function.

Optimal variable acceptance sampling plan for exponential distribution using Bayesian estimate under Type-I hybrid censoring

Acceptance sampling plans with censoring schemes are crucial for improving quality control by efficiently managing incomplete information. This approach improves cost and time effectiveness compared to traditional methods, providing a more accurate assessment of product quality. In this study, a variable acceptance sampling plan under Type-I hybrid censoring is designed for a lot of independent and identical units with exponential lifetimes using Bayesian estimation of the mean life. This novel approach diverges from conventional methods in acceptance sampling plans, which rely on maximum likelihood estimation and the minimization of Bayes risk. Bayesian estimation is obtained using both squared error loss and Linex loss functions. Under each method, a nonlinear optimization problem is solved to minimize the testing cost, and the optimal values of the plan parameters are determined. The proposed plans are illustrated using various numerical examples, with each plan presented in tables. The acceptance sampling plan using the squared error loss function proves to be more cost-effective than the plan using the Linex loss function. A comparative analysis of the proposed plans with existing work in the literature demonstrates that our cost is much lower than the cost of existing plans using maximum likelihood estimation. Additionally, a real-life case study is conducted to validate the approach.

Estimation of the Reliability Function of the Generalized Rayleigh Distribution under Progressive First-Failure Censoring Model

This study investigates the statistical inference of the parameters, reliability function, and hazard function of the generalized Rayleigh distribution under progressive first-failure censoring samples, considering factors such as long product lifetime and challenging experimental conditions. Firstly, the progressive first-failure model is introduced, and the maximum likelihood estimation for the parameters, reliability function, and hazard function under this model are discussed. For interval estimation, confidence intervals have been constructed for the parameters, reliability function, and hazard function using the bootstrap method. Next, in Bayesian estimation, considering informative priors and non-information priors, the Bayesian estimation of the parameters, reliability function, and hazard function under symmetric and asymmetric loss functions is obtained using the MCMC method. Finally, Monte Carlo simulation is conducted to compare mean square errors, evaluating the superiority of the maximum likelihood estimation and Bayesian estimation under different loss functions. The performance of the estimation methods used in the study is illustrated through illustrative examples. The results indicate that Bayesian estimation outperforms maximum likelihood estimation.