Bayesian Estimation Method Research Articles

Flexible Bayesian estimation of incubation times.

The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps to plan public health strategies to keep an epidemic outbreak under control. Estimation of the incubation period distribution from reported exposure times and symptom onset times is challenging as the underlying data is coarse. We develop a new Bayesian methodology using Laplacian-P-splines that provides a semi-parametric estimation of the incubation density based on a Langevinized Gibbs sampler. A finite mixture density smoother informs a set of parametric distributions via moment matching and an information criterion arbitrates between competing candidates. Algorithms underlying our method find a natural nest within the EpiLPS package, which has been extended to cover estimation of incubation times. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on COVID-19, MERS and Mpox reveal results that are in alignment with what has been obtained in recent studies. The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.

Research on methods for estimating reference crop evapotranspiration under incomplete meteorological indicators.

Accurate estimation of reference crop evapotranspiration (ET0) is crucial for farmland hydrology, crop water requirements, and precision irrigation decisions. The Penman-Monteith (PM) model has high accuracy in estimating ET0, but it requires many uncommon meteorological data inputs. Therefore, an ideal method is needed that minimizes the number of input data variables without compromising estimation accuracy. This study aims to analyze the performance of various methods for estimating ET0 in the absence of some meteorological indicators. The Penman-Monteith (PM) model, known for its high accuracy in ET0 estimation, served as the standard value under conditions of adequate meteorological indicators. Comparative analyses were conducted for the Priestley-Taylor (PT), Hargreaves (H-A), McCloud (M-C), and FAO-24 Radiation (F-R) models. The Bayesian estimation method was used to improve the ET estimation model. Results indicate that, compared to the PM model, the F-R model performed best with inadequate meteorological indicators. It demonstrates higher average correlation coefficients (R2) at daily, monthly, and 10-day scales: 0.841, 0.937, and 0.914, respectively. The corresponding root mean square errors (RMSE) are 1.745, 1.329, and 1.423, and mean absolute errors (MAE) are 1.340, 1.159, and 1.196, with Willmott's Index (WI) values of 0.843, 0.862, and 0.859. Following Bayesian correction, R2 values remained unchanged, but significant reductions in RMSE were observed, with average reductions of 15.81%, 29.51%, and 24.66% at daily, monthly, and 10-day scales, respectively. Likewise, MAE decreased significantly, with average reductions of 19.04%, 34.47%, and 28.52%, respectively, and WI showed improvement, with average increases of 5.49%, 8.48%, and 10.78%, respectively. Therefore, the F-R model, enhanced by the Bayesian estimation method, significantly enhances the estimation accuracy of ET0 in the absence of some meteorological indicators.

A Comparison of Bayesian Approximation Methods for Analyzing Large Spatial Skewed Data

A Comparison of Bayesian Approximation Methods for Analyzing Large Spatial Skewed Data

Bayesian inference for multivariate probit model with latent envelope.

The response envelope model proposed by Cook etal. (2010) is an efficient method to estimate the regression coefficient under the context of the multivariate linear regression model. It improves estimation efficiency by identifying material and immaterial parts of responses and removing the immaterial variation. The response envelope model has been investigated only for continuous response variables. In this paper, we propose the multivariate probit model with latent envelope, in short, the probit envelope model, as a response envelope model for multivariate binary response variables. The probit envelope model takes into account relations between Gaussian latent variables of the multivariate probit model by using the idea of the response envelope model. We address the identifiability of the probit envelope model by employing the essential identifiability concept and suggest a Bayesian method for the parameter estimation. We illustrate the probit envelope model via simulation studies and real-data analysis. The simulation studies show that the probit envelope model has the potential to gain efficiency in estimation compared to the multivariate probit model. The real data analysis shows that the probit envelope model is useful for multi-label classification.

Massively parallel Bayesian estimation with Sequential Monte Carlo sampling for simultaneous estimation of earthquake fault geometry and slip distribution

In inverse analysis, Bayesian estimation is useful for understanding the reliability of the estimation result or prediction based on it because it can estimate not only optimal parameters but also their uncertainties. The estimation of an earthquake source fault based on observed crustal deformation is a typical inverse problem in the field of earthquake research. In this study, a method for simultaneous Bayesian estimation of earthquake fault plane geometry and spatially variable slip distribution on the plane has been developed. The developed method can be applied to stochastic models with arbitrary probability distribution settings, and it enables to incorporate appropriate constraints for slip distribution in the estimation process, which can lead to enhanced robustness and stability of estimation. Since this method is computationally more expensive than conventional methods, large-scale parallel computing was introduced to cope with the increased computational cost and a supercomputer was used for the analysis. To validate the proposed method, simultaneous Bayesian estimation of fault geometry and slip distribution with slip constraints was performed using the crustal deformation observed in the 2018 Hokkaido Eastern Iburi earthquake. Hierarchical parameterization and massively parallelized Bayesian inference used in this study have broad applicability not only in earthquake research but also in other scientific and engineering fields.

Quantitative Stylistic Analysis of Middle Chinese Texts Based on the Dissimilarity of Evolutive Core Word Usage

Stylistic analysis enables open-ended and exploratory observation of languages. To fill the gap in the quantitative analysis of the stylistic systems of Middle Chinese, we construct lexical features based on the evolutive core word usage and scheme a Bayesian method for feature parameters estimation. The lexical features are from the Swadesh list, each of which has different word forms along with the language evolution during the Middle Ages. We thus count the varied word of those entries along with the language evolution as the linguistic features. With the Bayesian formulation, the feature parameters are estimated to construct a high-dimensional random feature vector to obtain the pair-wise dissimilarity matrix of all the texts based on different distance measures. Finally, we perform the spectral embedding and clustering to visualize, categorize, and analyze the linguistic styles of Middle Chinese texts. The quantitative result agrees with the existing qualitative conclusions and, furthermore, betters our understanding of the linguistic styles of Middle Chinese from both the inter-category and intra-category aspects. It also helps unveil the special styles induced by the indirect language contact.

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

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

Utilizing Bayesian inference in accelerated testing models under constant stress via ordered ranked set sampling and hybrid censoring with practical validation

This research investigates the application of the ordered ranked set sampling (ORSSA) procedure in constant-stress partially accelerated life-testing (CSPALTE). The study adopts the assumption that the lifespan of a specific item under operational stress follows a half-logistic probability distribution. Through Bayesian estimation methods, it concentrates on estimating the parameters, utilizing both asymmetric loss function and symmetric loss function. Estimations are conducted using ORSSAs and simple random samples, incorporating hybrid censoring of type-I. Real-world data sets are utilized to offer practical context and validate the theoretical discoveries, providing concrete insights into the research findings. Furthermore, a rigorous simulation study, supported by precise numerical calculations, is meticulously conducted to gauge the Bayesian estimation performance across the two distinct sampling methodologies. This research ultimately sheds light on the efficacy of Bayesian estimation techniques under varying sampling strategies, contributing to the broader understanding of reliability analysis in CSPALTE scenarios.

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space.An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias.For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

Myocardial T1 mapping using an instantaneous signal loss simulation modeling and a Bayesian estimation method: A robust T1 extraction method free of tuning parameters

The Instantaneous Signal Loss Simulation (InSiL) model is a promising alternative to the classical mono-exponential fitting of the Modified Look-Locker Inversion-recovery (MOLLI) sequence in cardiac T1 mapping applications, which achieves better accuracy and is less sensitive to heart rate (HR) variations. Classical non-linear least squares (NLLS) estimation methods require some parameters of the model to be fixed a priori in order to give reliable T1 estimations and avoid outliers. This introduces further bias in the estimation, reducing the advantages provided by the InSiL model. In this paper, a novel Bayesian estimation method using a hierarchical model is proposed to fit the parameters of the InSiL model. The hierarchical Bayesian modeling has a shrinkage effect that works as a regularizer for the estimated values, by pulling spurious estimated values toward the group-mean, hence reducing greatly the number of outliers. Simulations, physical phantoms, and in-vivo human cardiac data have been used to show that this approach estimates accurately all the InSiL parameters, and achieve high precision estimation of the T1 compared to the classical MOLLI model and NLLS InSiL estimation.

Bayesian mixture modelling with ranked set samples.

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation-Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS-based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.

A comparison of Bayesian and score methods for interval estimates of positive/negative likelihood ratios in support of diagnostic device performance evaluation

ABSTRACT Background Positive and negative likelihood ratios (PLR and NLR) are important metrics of accuracy for diagnostic devices with a binary output. However, the properties of Bayesian and frequentist interval estimators of PLR/NLR have not been extensively studied and compared. In this study, we explore the potential use of the Bayesian method for interval estimation of PLR/NLR, and, more broadly, for interval estimation of the ratio of two independent proportions. Methods We develop a Bayesian-based approach for interval estimation of PLR/NLR for use as a part of a diagnostic device performance evaluation. Our approach is applicable to a broader setting for interval estimation of any ratio of two independent proportions. We compare score and Bayesian interval estimators for the ratio of two proportions in terms of the coverage probability (CP) and expected interval width (EW) via extensive experiments and applications to two case studies. A supplementary experiment was also conducted to assess the performance of the proposed exact Bayesian method under different priors. Results Our experimental results show that the overall mean CP for Bayesian interval estimation is consistent with that for the score method (0.950 vs. 0.952), and the overall mean EW for Bayesian is shorter than that for score method (15.929 vs. 19.724). Application to two case studies showed that the intervals estimated using the Bayesian and frequentist approaches are very similar. Discussion Our numerical results indicate that the proposed Bayesian approach has a comparable CP performance with the score method while yielding higher precision (i.e. a shorter EW).

A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models.

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis-Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method.

A Two‐stage Bayesian Small Area Estimation Approach for Proportions

SummaryWith the rise in popularity of digital Atlases to communicate spatial variation, there is an increasing need for robust small area estimates. However, current small area estimation methods suffer from various modelling problems when data are very sparse or when estimates are required for areas with very small populations. These issues are particularly heightened when modelling proportions. Additionally, recent work has shown significant benefits in modelling at both the individual and area levels. We propose a two‐stage Bayesian hierarchical small area estimation approach for proportions that can account for survey design, reduce direct estimate instability and generate prevalence estimates for small areas with no survey data. Using a simulation study, we show that, compared with existing Bayesian small area estimation methods, our approach can provide optimal predictive performance (Bayesian mean relative root mean squared error, mean absolute relative bias and coverage) of proportions under a variety of data conditions, including very sparse and unstable data. To assess the model in practice, we compare modelled estimates of current smoking prevalence for 1,630 small areas in Australia using the 2017–2018 National Health Survey data combined with 2016 census data.

Simulation Study for Estimating the Parameters and Reliability Function of Weighted Exponential Distribution with Fuzzy Data

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information availableisin the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function linksequalimportance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently

A computational framework for probabilistic modeling of galvanic corrosion for automotive applications

Abstract To address the need for reduced vehicle weight and improved environmental sustainability, the automotive industry has increasingly turned to mixing lightweight materials and alloys with metal alloys. However, this integration of dissimilar materials has heightened the risk of galvanic corrosion. This study addresses the gap in modeling of galvanic corrosion under dynamic thin film electrolyte by incorporating data derived from real-world weather conditions and finite element simulations. The presented model successfully captures the trend of galvanic corrosion rate for a given atmospheric environmental condition. The model predictions are compared with experimental data in the literature. Good agreements are observed. The model is further used for prediction of galvanic corrosion of two identical vehicles located in two different geographic locations (i.e., Miami Beach in Florida and Wendover in Nevada) in the year 2021 leveraging weather station data. Additionally, a Bayesian estimation method is used to account for uncertainties in the model parameters and estimation of the probability of failure.

The Crosswise Model for Surveys on Sensitive Topics: A General Framework for Item Selection and Statistical Analysis

When surveys contain direct questions about sensitive topics, participants may not provide their true answers. Indirect question techniques incentivize truthful answers by concealing participants’ responses in various ways. The Crosswise Model aims to do this by pairing a sensitive target item with a non-sensitive baseline item, and only asking participants to indicate whether their responses to the two items are the same or different. Selection of the baseline item is crucial to guarantee participants’ perceived and actual privacy and to enable reliable estimates of the sensitive trait. This research makes the following contributions. First, it describes an integrated methodology to select the baseline item, based on conceptual and statistical considerations. The resulting methodology distinguishes four statistical models. Second, it proposes novel Bayesian estimation methods to implement these models. Third, it shows that the new models introduced here improve efficiency over common applications of the Crosswise Model and may relax the required statistical assumptions. These three contributions facilitate applying the methodology in a variety of settings. An empirical application on attitudes toward LGBT issues shows the potential of the Crosswise Model. An interactive app, Python and MATLAB codes support broader adoption of the model.

A new extended Pham distribution for modelling cancer data

In this study, a novel extended Pham model is offered and examined. This model can fit positive, negative, and approximately symmetric data. In addition, it features four alternative hazard rate shapes, namely increasing, decreasing, bathtub, and upside-down bathtub shapes. The new model's main properties, such as quantiles, moments, and mean deviations, are derived. To evaluate the estimation of distribution parameters, two approaches are studied. From a classical standpoint, the maximum likelihood technique is used to determine the point and approximate confidence intervals of all unknown parameters. The Bayesian estimation method, on the other hand, is considered via the Markov chain Monte Carlo technique for obtaining Bayes point estimates alongside Bayes credible intervals. We present various Monte Carlo simulation studies to investigate the efficacy of maximum likelihood and Bayes estimation findings for the model's parameters. Numerical investigations showed that the offered Bayes estimates outperformed those derived using the conventional method. We also analyzed two sets of real data taken from the medical sector; the first represents survival rates for cancer patients who received a combination of radiotherapy and chemotherapy, and the second consists of remission times for bladder cancer patients. These clinical scenarios reveal that the new model outperforms other important competing models based on specific statistical criteria. Ultimately, for both clinical data applications, the proposed extended Pham distribution is the best choice compared to the traditional Pham and the other well-known eight lifetime models.

Reflecting on the contributions of Professor Tsionas in time series analysis, asset price modelling, and forecasting

While Professor Tsionas is widely acclaimed for his ground-breaking works in Bayesian panel econometrics and frontier analysis models, his substantial impact in time series analysis in finance remains relatively less known. Nonetheless, the doctoral thesis of Professor Tsionas focussed on asset pricing models, serving as a foundation for his subsequent research pursuits in time series analysis and forecasting. Characterised by elegance and simplicity, Professor Tsionas conceptualised econometric models and Bayesian estimation methods that have been applied to fields such as banking, finance, macro-finance, and tourism. In addition, his insights into time series analysis have informed decision-making processes in these fields.

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

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