Bayesian Estimation Procedure Research Articles

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.

Multispecies initial numerical validation of an efficient algorithm prototype for auditory brainstem response hearing threshold estimation.

The auditory brainstem response (ABR) can be used to evaluate hearing sensitivity of animals. However, typical measurement protocols are time-consuming. Here, an adaptive algorithm is proposed for efficient ABR threshold estimation. The algorithm relies on the update of the predicted hearing threshold from a Gaussian process model as ABR data are collected using iteratively optimized stimuli. To validate the algorithm, ABR threshold estimation is simulated by adaptively subsampling pre-collected ABR datasets. The simulated experiment is performed on 5 datasets of mouse, budgerigar, gerbil, and guinea pig ABRs (27 ears). The datasets contain 68-106 stimuli conditions, and the adaptive algorithm is configured to terminate after 20 stimuli conditions. The algorithm threshold estimate is compared against human rater estimates who visually inspected the full waveform stacks. The algorithm threshold matches the human estimates within 10 dB, averaged over frequency, for 15 of the 27 ears while reducing the number of stimuli conditions by a factor of 3-5 compared to standard practice. The intraclass correlation coefficient is 0.81 with 95% upper and lower bounds at 0.74 and 0.86, indicating moderate to good reliability between human and algorithm threshold estimates. The results demonstrate the feasibility of a Bayesian adaptive procedure for rapid ABR threshold estimation.

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.

Accounting for ground-motion uncertainty in empirical seismic fragility modeling

Seismic fragility models provide a probabilistic relation between ground-motion intensity and damage, making them a crucial component of many regional risk assessments. Estimating such models from damage data gathered after past earthquakes is challenging because of uncertainty in the ground-motion intensity the structures were subjected to. Here, we develop a Bayesian estimation procedure that performs joint inference over ground-motion intensity and fragility model parameters. When applied to simulated damage data, the proposed method can recover the data-generating fragility functions, while the traditionally used method, employing fixed, best-estimate, intensity values, fails to do so. Analyses using synthetic data with known properties show that the traditional method results in flatter fragility functions that overestimate damage probabilities for low-intensity values and underestimate probabilities for large values. Similar trends are observed when comparing both methods on real damage data. The results suggest that neglecting ground-motion uncertainty manifests in apparent dispersion in the estimated fragility functions. This undesirable feature can be mitigated through the proposed Bayesian procedure.

Methods for measuring career readiness of high school students: based on multidimensional item response theory and text mining

In contemporary society, career readiness holds paramount significance for individual life, exerting a direct influence on initial employment, job satisfaction, and the sense of career identity. Framed within multidimensional item response theory and text mining, this study embarks on exploring assessment methodologies for high school students’ career readiness by revising the “Career Readiness Questionnaire – Adolescent Version” and employing text mining techniques. Study One collected 1261 valid data points through cluster sampling. With the aid of Bayesian multivariate item response theory parameter estimation procedures and R language, the career readiness measurement tool was revised, yielding a concise scale that aligns with psychometric requirements. The research findings indicated that the concept of “career readiness” is more suitable for the multidimensional graded response model than for the bifactor model. The dataset’s discrimination parameters fell within the range of [1.59, 3.84], the difficulty parameters fell between [−2.91, 2.24], and the peak values of the maximum information functions fell within [0.24, 2.35]. After six items with the lowest peaks were removed (Items 4, 5, 6, 31, 32, and 33), the remaining 30 items composed the Chinese concise version “Career Readiness Questionnaire – Adolescent Version,” with discrimination parameters ranging from [1.45, 3.38], difficulty parameters between [−3.31, 1.76], and maximum information function peaks within [0.50, 2.64]. Building upon the effective participants from Study One, Study Two matched questionnaire data with textual information, resulting in 1012 valid participants. Leveraging text mining, a machine learning model was constructed to predict high school students’ career readiness based on essay texts. The results of Study 2 prove that the revised lexicon was more accurate in feature extraction. Building upon this, the machine learning model for essay text demonstrated excellent performance in predicting career readiness, with random forest outperforming the other algorithms. This study provides a novel approach for schools and parents to comprehend the state of career readiness among high school students, offering a convenient and effective tool for educational activities related to students’ career development.

A Relationship between Classical and Bayesian Estimation Procedures through Fisher Information

The aim of this article is to investigate the association between the classical and Bayesian approaches through Fisher information. For any particular distribution, the computation of Fisher information is quite significant, as it provides the amount of information about the unknown parameter inferred from the observed data and is related to classical methods of estimation. Also, in the light of some prior knowledge, we may estimate the unknown parameter through Bayesian approach. Specifically, we want to see a relationship between information and Bayes estimation. In this article, the scale parameter of the one-parameter exponential distribution is estimated under the weighted squared error and Kullback-Leibler distance loss functions. The information acquired from both the classical and Bayesian methodologies have been connected through the risk intensity and error intensity which have been introduced in this article. The results of extensive simulation studies using these intensity measures show that the Bayes estimator performs more intensely as the amount of Fisher information increases. It is seen that the Fisher information, which is pivotal to many classical estimation methods, has a relationship with the Bayesian method depending on prior distribution, at least in this case, as the intensity measures of the Bayes estimator decrease with the increase in information. Further, to comprehend the theoretical notion of association, two real-life datasets have been included to show usefulness in practical field.

The Role of the Social Network in Adopting New Turfgrass Varieties: An Analysis of Twitter Data

This study examines the effect of social learning on new turfgrass variety adoption decisions using data from 231 turfgrass professionals’ Twitter accounts between 1 Jun 2018 and 31 Dec 2019. To determine the social learning effect, we decompose networking effects into social learning, individual-level and group-level similarities, herd behavior, and clustering effects. Our study estimates a spatial autoregressive probit model that directly incorporates the social network structure to account for unobservable networking effects and potential reflection problem. A Bayesian estimation procedure is used to alleviate the convergence problem caused by the complexity of model specification. Empirical results show that the social learning effect positively influences the new technology adoption and was greater than herd behavior effect. The results also suggest that turf professionals rely more on suggestions and information from online social networking among themselves than recommendations from advisors.

Efficient Bayesian inference for a defect rate based on completely censored data

This paper discusses the challenging issues that reliability practitioners face in conducting destructive tests that lead to completely censored lifetimes, especially in estimating the defect rate of products. Manufacturers need to measure the defect rate for quality control purposes, but obtaining enough defective devices for accurate estimation is not easy when the defect rate is relatively low. To address the issues, a Bayesian approach for estimating the defect rate is proposed in this paper. The proposed method is devised to make up for the heavy computational burdens of the Metropolis-Hastings algorithm. To quantify the uncertainty in the Bayesian estimation, a nonparametric bootstrap technique is employed to construct a credible interval for the defect rate. The performance of the proposed method is evaluated through a variety of Monte Carlo simulation studies. The efficiency of the proposed Bayesian estimation procedure is validated using a real-world dataset of return-springs in DC motor systems under an accelerated destructive degradation test.

Bayesian Estimation of a New Pareto-Type Distribution Based on Mixed Gibbs Sampling Algorithm

In this paper, based on the mixed Gibbs sampling algorithm, a Bayesian estimation procedure is proposed for a new Pareto-type distribution in the case of complete and type II censored samples. Simulation studies show that the proposed method is consistently superior to the maximize likelihood estimation in the context of small samples. Also, an analysis of some real data is provided to test the Bayesian estimation.

A Dynamic Spatiotemporal Stochastic Volatility Model with an Application to Environmental Risks

A dynamic spatiotemporal stochastic volatility (SV) model is introduced, incorporating explicit terms accounting for spatial, temporal, and spatiotemporal spillover effects. Alongside these features, the model encompasses time-invariant site-specific factors, allowing for differentiation in volatility levels across locations. The statistical properties of an outcome variable within this model framework are examined, revealing the induction of spatial dependence in the outcome variable. Additionally, a Bayesian estimation procedure employing the Markov Chain Monte Carlo (MCMC) approach, complemented by a suitable data transformation, is presented. Simulation experiments are conducted to assess the performance of the proposed Bayesian estimator. Subsequently, the model is applied in the domain of environmental risk modeling, addressing the scarcity of empirical studies in this field. The significance of climate variation studies is emphasized, illustrated by an analysis of local air quality in Northern Italy during 2021, which underscores pronounced spatial and temporal clusters and increased uncertainties/risks during the winter season compared to the summer season.

Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data

PurposeA progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS.Design/methodology/approachIn this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques.FindingsThe Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study.Originality/valueThe ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature.

Tests of human auditory temporal resolution: preliminary investigation of ZEST parameters for amplitude modulation detection.

Auditory temporal resolution plays a critical role in the everyday experience of listening to complex acoustic patterns. Amplitude modulation detection thresholds are widely used to measure auditory temporal resolution. In an attempt to develop a standardized clinical test of auditory temporal resolution, we used ZEST (Zippy Estimation by Sequential Testing, a Bayesian threshold estimation procedure, to measure amplitude modulation detection thresholds. ZEST utilizes prior knowledge about a listener's thresholds, as represented by a probability density function of the thresholds, and psychometric functions of the listener's responses. This paper reports a preliminary study in which ZEST parameters that could be used for measurements of amplitude modulation detection thresholds were sought. For this purpose, we created histograms of the detection thresholds for a wide range of modulation frequencies, measured the psychometric functions of amplitude modulation detection, and performed computer simulations of ZEST threshold estimation. The results suggested that, with appropriately-set parameters, ZEST allows for the accurate estimation of amplitude modulation detection thresholds within 20 trials.

1336-P: Predicting the Progression of Stages of Neuropathy Using Routine Eye and Kidney Tests—An Application of Novel Statistical Methods in the Diabetes Control and Complications Trial (DCCT)

Despite recent advances, neuropathy screening is not consistently performed in clinical practice. We aimed to determine if neuropathy risk could be predicted using the trajectories of routinely-performed eye and kidney screening tests in T1D. We used 28-year data from the DCCT/EDIC study, available via the NIH public repository. We used the Early Treatment Diabetic Retinopathy Study Research (ETDRS) Group 23-point scale, albumin excretion rate (AER), and eGFR treated as longitudinal outcomes. Simultaneously, we represented neuropathy as a 3-state progressive multistate outcome using nerve conduction studies and the Michigan Neuropathy Screening Instrument (MNSI) for early-stage neuropathy and the occurrence of serious foot ulcer or amputation for late-stage neuropathy. To model these interrelated disease processes, we used and developed joint models with multistate submodels. Our “joint multistate model” accounted for interval censoring: due to the visit schedule, the exact time of transition to early-stage neuropathy was known only to occur in between consecutive visits. A Bayesian estimation procedure was used. We found that the risk of transition from no to early-stage neuropathy was affected by the current value of ETDRS, the current slope of ETDRS, and the current value of AER. For example, controlling for all covariates including eGFR, the there was a 23% higher rate of occurrence of this early-stage for a 3-step higher ETDRS scale. In the same model controlling for all covariates, progression from early-stage to late-stage neuropathy was affected mainly by AER (11% higher rate for a doubling of AER). Routinely-performed clinical eye and kidney test results can be leveraged to help identify the risk of neuropathy. Future work will develop dynamic predictions integrated into an electronic medical record. Disclosure L.Lovblom: None. L.Briollais: None. G.Tomlinson: None. B.A.Perkins: Advisory Panel; Dexcom, Inc., Insulet Corporation, Novo Nordisk, Sanofi, Vertex Pharmaceuticals Incorporated, Other Relationship; Abbott, Medtronic, Sanofi, Research Support; Novo Nordisk, Bank of Montreal (BMO).

Quantile regression based on the skewed exponential power distribution

Bayesian quantile regression generally relies on the asymmetric Laplace distribution (ALD) as the error distribution. We consider methods for Lp -quantile regression based on the skewed exponential power distribution (SEPD). Both Bayesian and frequentist estimation procedures are outlined and compared with previous work based on the SEPD. We find that our proposed methods greatly outperform a previous method in terms of quantile estimation. Further, compared with standard quantile regression, we find that our proposed methods generally perform better in terms of root mean square error (RMSE). Empirical evidence of the statistical properties of the proposed models is provided through a simulation study. Further, a real data application illustrates their performance.

Correlated compound geometric frailty models based on reversed hazard rate

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times (e.g. matched pairs experiments, twin or family data), the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the correlated compound geometric frailty models based on reversed hazard rate with three different baseline distributions namely, the generalized log-logistic type I, the generalized log-logistic type II and the modified inverse Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.

Parsimonious Bayesian factor analysis for modelling latent structures in spectroscopy data

In recent years, within the dairy sector, animal diet and management practices have been receiving increased attention, in particular, examining the impact of pasture-based feeding strategies on the composition and quality of milk and dairy products in line with the prevalence of premium grass-fed dairy products appearing on market shelves. To date, methods to thoroughly investigate the more relevant differences induced by the diet on milk chemical features are limited; enhanced statistical tools exploring these differences are required. Infrared spectroscopy techniques are widely used to collect data on milk samples and to predict milk related traits and characteristics. While these data are routinely used to predict the composition of the macro components of milk, each spectrum also provides a reservoir of unharnessed information about the sample. The accumulation and subsequent interpretation of these data present some challenges due to their high-dimensionality and the relationships amongst the spectral variables. In this work, directly motivated by a dairy application, we propose a modification of the standard factor analysis to induce a parsimonious summary of spectroscopic data. Our proposal maps the observations into a low-dimensional latent space while simultaneously clustering the observed variables. The method indicates possible redundancies in the data, and it helps disentangle the complex relationships among the wavelengths. A flexible Bayesian estimation procedure is proposed for model fitting, providing reasonable values for the number of latent factors and clusters. The method is applied on milk mid-infrared (MIR) spectroscopy data from dairy cows on distinctly different pasture and nonpasture based diets, providing accurate modelling of the correlation, clustering of variables, and information on differences among milk samples from cows on different diets.

Joint classification and prediction of random curves using heavy‐tailed process functional regression

We propose a heavy-tailed process functional regression to jointly perform classification and prediction of time-varying functional data. We use two independent scale mixtures of Gaussian Processes to respectively model random effects and random errors, yielding robust inferences against both magnitude and shape outliers. We classify random curves by posterior predictive probabilities of class labels and offer a weighted prediction of future curve trends. A Bayesian estimation procedure is implemented through an MCMC sampling algorithm. The performance of classification and prediction of the proposed model is evaluated using simulated studies and some real data sets.

Non-intrusive estimation of model error and discrepancy in dynamics models

Errors in formulating the system physics model, due to inability to rigorously account for nonlinear behavior, boundary conditions, and multi-component and multi-physics interactions result in discrepancies between model predictions of system responses and the corresponding experimentally measured values. In our previous work, we have developed a Bayesian state estimation-based framework for the estimation of these model errors, and the subsequent prediction of model discrepancies at unmeasured locations, for untested inputs, and for untested configurations. In this approach, we represent model errors as external inputs in the dynamic system model, and estimate them using Bayesian state estimation. However, this approach is intrusive in the sense that it requires access to the governing system of equations, the ability to modify the system model by introducing an external system input, and the ability to represent system inputs and responses as probabilistic quantities. In this paper, we develop semi-intrusive and non-intrusive approaches to extend the model error estimation to black-box models. The semi-intrusive method does not need access to the governing equations, but requires the ability to interrupt the simulation at any time instant, update the system responses at that moment, and resume the simulation using the updated value of system responses. For situations where this is not permitted, we propose a fully non-intrusive approach where, a surrogate model is constructed and used in the Bayesian state estimation procedure. The proposed approaches are illustrated with three examples: structural deformation of a Timoshenko beam, heat transfer across a rigid bar, and deformation of a Timoshenko beam subjected to heating.

Inference for reliability in a multicomponent stress-strength model from generalized inverted exponential lifetime distribution under progressive first failure censoring

This article considers the non-Bayesian and Bayesian estimation procedures for multicomponent stress-strength reliability (MSSR) from generalized inverted exponential lifetime distributions using a progressively first failure censoring scheme. For the non-Bayesian estimation method of MSSR, the maximum likelihood estimation method is used, and for the Bayesian estimation method, the Metropolis-Hastings algorithm is taken into account. Also, the highest posterior density credible interval and the asymptotic confidence interval for MSSR in the case of Bayesian and non-Bayesian estimation methods, respectively, are obtained. A Monte Carlo numerical study is conducted to compare different types of estimates. For illustrative purposes, a real data analysis is carried out.

Peer-induced beliefs regarding college participation

We study the heterogeneity of peer effects on the formation of beliefs regarding college participation. We present a structural model of learning in friendship networks. We show that the model is identified and we present a Bayesian estimation procedure. We estimate the model using data on teenagers’ beliefs regarding college participation, controlling for preferences and academic achievement. While we find that, on average, friends’ beliefs account for about 8% of the updating process, we also find strong heterogeneity among schools and individuals. In particular, we find substantial unobserved individual heterogeneity (ranging from close to 0 to more than 75%), which casts doubt on the efficiency of network-targeted public policies.