Bayesian Sampling Approach Research Articles

Using the Bayesian sampling method to estimate corporate loss given default distribution

We use Markov chain Monte Carlo (MCMC) sampling to draw model coefficients to generate LGD distributions. We find that applying this Bayesian method on a sophisticated model, such as the zero-one-inflated beta (ZOIB) model, that accounts for the bi-modal distribution of the LGDs can generate LGD distributions that mimic the observed distributions well. By contrast, applying this Bayesian sampling approach on a simple model such as Tobit cannot capture the bi-modal LGD distributions accurately. Finally, we argue that this Bayesian sampling approach to generate LGD distributions is better fit for the stress testing purpose than the typical approach to estimate LGD model coefficients and then stress the macro variables. The latter approach yields stressed LGDs that may not be conservative enough, even if the macro variables are stressed to their worst historical values.

Particle filter‐based prognostics for composite curing process

AbstractProcess‐induced deformation (PID) arises in thermoset parts due to internal residual stress developed from their anisotropic properties, resulting in distortions. While passive numerical manufacturing control exists, active manufacturing control is crucial for enhancing the manufacturing process. The work focuses on diagnosing the polymerization reaction, known as the curing process, to consider the influence of uncertainties in thermal loading conditions on the behavior of cure kinetics. This is achieved using a Particle Filter approach, wherein a posterior distribution of cure evolution is recursively approximated based on observed measurements from characterization tests. The algorithm is designed to simultaneously perform the diagnosis and prognosis of the Degree of Cure and PID. This approach adopts the augmented cure formulation to address various scenarios with uncertainties in thermal loading conditions. It offers the advantage of providing comparable PID predictions with minimal computational costs. C‐shaped thermoset parts made of epoxy/carbon fibers with varying thicknesses are cured using the Manufacturing Recommended Curing Cycle, and the predictions with the developed algorithm are validated against experimental measures. Upon validation, the converged prognosis capability of the Particle Filter model is employed to assess the impact of thermal loading uncertainty on cure profiles, which, in turn, affects the final PIDs outcome.Highlights A Bayesian sampling approach enables the estimation of cure kinetics parameters. The estimated stochastic parameters forecast the process‐induced deformations. The augmented Degree of Cure accounts for uncertainties linked to thermal loadings. Analysis on AS4/8552 C‐shaped parts shows the cure kinetics impact. The framework reduces the computational costs required for active control.

Bayes-TrEx: a Bayesian Sampling Approach to Model Transparency by Example

Post-hoc explanation methods are gaining popularity for interpreting, understanding, and debugging neural networks. Most analyses using such methods explain decisions in response to inputs drawn from the test set. However, the test set may have few examples that trigger some model behaviors, such as high-confidence failures or ambiguous classifications. To address these challenges, we introduce a flexible model inspection framework: Bayes-TrEx. Given a data distribution, Bayes-TrEx finds in-distribution examples which trigger a specified prediction confidence. We demonstrate several use cases of Bayes-TrEx, including revealing highly confident (mis)classifications, visualizing class boundaries via ambiguous examples, understanding novel-class extrapolation behavior, and exposing neural network overconfidence. We use Bayes-TrEx to study classifiers trained on CLEVR, MNIST, and Fashion-MNIST, and we show that this framework enables more flexible holistic model analysis than just inspecting the test set. Code and supplemental material are available at https://github.com/serenabooth/Bayes-TrEx.

A Stochastic View of the 2020 Elazığ Mw 6.8 Earthquake (Turkey)

AbstractUntil the Mw 6.8 Elazığ earthquake ruptured the central portion of the East Anatolian Fault (EAF, Turkey) on January 24, 2020, the region had only experienced moderate magnitude (Mw < 6.2) earthquakes over the last century. We use geodetic data to constrain a model of subsurface fault slip. We adopt an unregularized Bayesian sampling approach relying solely on physically justifiable prior information and account for uncertainties in both the assumed elastic structure and fault geometry. The rupture of the Elazığ earthquake was mostly unilateral, with two primary disconnected regions of slip. This rupture pattern may be controlled by structural complexity. Both the Elazığ and 2010 Mw 6.1 Kovancılar events ruptured portions of the central EAF that are believed to be coupled during interseismic periods, and the Palu segment is the last portion of the EAF showing a large fault slip deficit which has not yet ruptured in the last 145 years.

Bayesian bandwidth estimation for local linear fitting in nonparametric regression models

Abstract This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by a location-mixture density of Gaussian densities with means the individual errors and variance a constant parameter. This mixture density has the form of a kernel density estimator of errors and is referred to as the kernel-form error density (c.f. Zhang, X., M. L. King, and H. L. Shang. 2014. “A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density.” Computational Statistics & Data Analysis 78: 218–34.). While (Zhang, X., M. L. King, and H. L. Shang. 2014. “A Sampling Algorithm for Bandwidth Estimation in a Nonparametric Regression Model with a Flexible Error Density.” Computational Statistics & Data Analysis 78: 218–34) use the local constant (also known as the Nadaraya-Watson) estimator to estimate the regression function, we extend this to the local linear estimator, which produces more accurate estimation. The proposed investigation is motivated by the lack of data-driven methods for simultaneously choosing bandwidths in the local linear estimator of the regression function and kernel-form error density. Treating bandwidths as parameters, we derive an approximate (pseudo) likelihood and a posterior. A simulation study shows that the proposed bandwidth estimation outperforms the rule-of-thumb and cross-validation methods under the criterion of integrated squared errors. The proposed bandwidth estimation method is validated through a nonparametric regression model involving firm ownership concentration, and a model involving state-price density estimation.

Multivariate Shared-Parameter Mixed-Effects Location Scale Model for Analysis of Intensive Longitudinal Data

With the advancement of modern technologies, intensive longitudinal studies, where subjects get intensively measured in a relatively short period of time, have become popular in psychological and biomedical area. Challenges arise in better analyzing the rich amount of data and at the same time avoiding biased statistical inference introduced by potential informative missingness. Building upon previous studies by Lin et al. and Kapura et al., we aim to address the problem of informative missingness in the context of multivariate intensive longitudinal outcomes. In this article, we present a multivariate shared-parameter model, where the multivariate intensive longitudinal outcomes are modeled by a mixed-effects locations scale model and further linked with the corresponding missing mechanism by sharing the subject random effects. The proposed model is then estimated using Bayesian sampling approach. An adolescent mood study example is illustrated and results show that joint modeling of the mood assessments not only provide more accurate effect estimates, but also valuable information on the associations between multiple outcomes.

Mixed location scale hidden Markov model for the analysis of intensive longitudinal data

Hidden Markov models (HMM) presents an attractive analytical framework for capturing the state-switching process for auto-correlated data. These models have been extended to longitudinal data setting where simultaneous multiple processes are observed by including subject specific random effects. However, application of HMMs for intensive longitudinal data, where each subject gets measured intensively over relatively short period of time, has not been widely studied. In this paper, we extend the mixed hidden Markov model and allow subject heterogeneity with respect to the mean and within subject variance by including subject random effects in both perspectives. We focus on the application of this model to intensive longitudinal studies in psychological and behavioral research where individual’s latent states and state-switching process are of interest. Models are estimated using forward–backward algorithm via Bayesian sampling approach. Advantages over regular HMM and mixed HMM that only accounts for the subjects’ mean heterogeneity are illustrated through a series of simulation studies. Finally, models are applied to an adolescent mood study data set and results show that the proposed mixed location scale HMM achieves better model fit and more interpretative mood state identification in terms of state specific covariate effects compared to regular HMM and mixed HMM.

A Bayesian sampling approach to measuring the price responsiveness of gasoline demand using a constrained partially linear model

Partial linear models provide an intuitively appealing way to examine gasoline demand because one can examine how response to price varies according to the price level and people's income. However, despite their intuitive appeal, partial linear models have tended to produce implausible and/or erratic price effects. Blundell et al. (2012) propose a solution to this problem that involves using Slutsky shape restrictions to improve the precision of the nonparametric estimate of the demand function. They propose estimating a constrained partially linear model through three steps, where the weights are optimized by minimizing an objective function under the Slutsky constraint, bandwidths are selected through least squares cross-validation, and linear coefficients are estimated using profile least squares. A limitation of their three-step estimation method is that bandwidths are selected based on pre-estimated parameters. We improve on the Blundell et al. (2012) solution in that we derive a posterior and develop a posterior simulation algorithm to simultaneously estimate the linear coefficients, bandwidths in the kernel estimator and the weights imposed by the Slutsky condition. With our proposed sampling algorithm, we estimate a constrained partially linear model of household gasoline demand employing household survey data for the United States for 1991 and 2001 and for Canada for 2006–2009 and find plausible price effects.

An Adaptive Bayesian Sequential Sampling Approach for Global Metamodeling

Computer simulations have been increasingly used to study physical problems in various fields. To relieve computational budgets, the cheap-to-run metamodels, constructed from finite experiment points in the design space using the design of computer experiments (DOE), are employed to replace the costly simulation models. A key issue related to DOE is designing sequential computer experiments to achieve an accurate metamodel with as few points as possible. This article investigates the performance of current Bayesian sampling approaches and proposes an adaptive maximum entropy (AME) approach. In the proposed approach, the leave-one-out (LOO) cross-validation error estimates the error information in an easy way, the local space-filling exploration strategy avoids the clustering problem, and the search pattern from global to local improves the sampling efficiency. A comparison study of six examples with different types of initial points demonstrated that the AME approach is very promising for global metamodeling.

Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome

Diarrhoea-associated Haemolytic Uraemic syndrome (HUS) is a disease that affects the kidneys and other organs. Motivated by the annual number of cases of HUS collected in Birmingham and Newcastle of England, respectively, from 1970 to 1989, we consider Bayesian changepoint analysis with specific attention to Poisson changepoint models. For changepoint models with unknown number of changepoints, we propose a new non-iterative Bayesian sampling approach (called exact IBF sampling), which completely avoids the problem of convergence and slow convergence associated with iterative Markov chain Monte Carlo (MCMC) methods. The idea is to first utilize the sampling inverse Bayes formula (IBF) to derive the conditional distribution of the latent data given the observed data, and then to draw iid samples from the complete-data posterior distribution. For the purpose of selecting the appropriate model (or determining the number of changepoints), we develop two alternative formulae to exactly calculate marginal likelihood (or Bayes factor) by using the exact IBF output and the point-wise IBF, respectively. The HUS data are re-analyzed using the proposed methods. Simulations are implemented to validate the performance of the proposed methods.

New Calibration Methodology for Microscopic Traffic Simulation Using Enhanced Simultaneous Perturbation Stochastic Approximation Approach

Traffic simulation models can represent real-world conditions such as delays, travel times, queues, and flows. However, accurate evaluation of these traffic conditions depends on the selection of model parameters and the calibration methodology. Most previous calibration studies have focused on minimizing the sum of the differences between the observed data and simulation output during a certain time period on a typical day. However, to capture a realistic distribution of all possible traffic conditions, a more general calibration methodology that can be used with any traffic condition is required. This paper proposes a new calibration methodology–-the Bayesian sampling approach in conjunction with the application of the simultaneous perturbation stochastic approximation (SPSA) optimization method [enhanced SPSA (E-SPSA)]–-that enables the modeler to enhance calibration by considering statistical data distribution. Instead of calibrating with input data for certain time periods, calibration is performed with data obtained from a complete input distribution. Mean square variation (MSV) was used to evaluate the accuracy of the proposed E-SPSA calibration approach. On the basis of the MSV of flows, the MSV value of the E-SPSA methodology was found to be 0.940, which was greater than the variation of speed obtained from SPSA-only (0.897) or from a variation approach (0.888). Thus, this proposed methodology not only makes it possible to overcome some of the limitations of previous calibration approaches, but also improves the results of simulation model calibration by accurately capturing a wide range of real-world conditions. Future work will focus on testing the proposed calibration methodology using more extensive data sets and models developed using simulation tools other than PARAMICS.

Joint Segmentation of Piecewise Constant Autoregressive Processes by Using a Hierarchical Model and a Bayesian Sampling Approach

We propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow us to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However, an extension to models with unknown model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals

A Bayesian sampling approach to decision fusion using hierarchical models

Data fusion and distributed detection have been studied extensively, and numerous results have been obtained in the literature. In this paper, the design of a fusion rule for distributed detection problems is re-examined, and a novel approach using Bayesian inference tools is proposed. Specifically, the decision fusion problem is reformulated using hierarchical models, and a Gibbs sampler is proposed to perform posterior probability-based fusion. Performance-wise, it is essentially identical to the optimal likelihood-based fusion rule whenever it exists. The true merit of this approach is its applicability to various complex situations, e.g., in dealing with unknown signal/noise statistics where the likelihood-based fusion rule may not be easy to obtain or may not even exist.

A Bayesian Sampling Approach to Regression Model Checking

A necessary step in any regression analysis is checking the fit of the model to the data. Graphical methods are often employed to allow visualization of features that the data should exhibit if the model holds. Judging whether such features are present or absent in any particular diagnostic plot can be problematic. In this article I take a Bayesian approach to aid in this task. The “unusualness” of some data with respect to a model can be assessed using the predictive distribution of the data under the model; an alternative is to use the posterior predictive distribution. Both approaches can be given a sampling interpretation that can then be used to enhance regression diagnostic plots such as marginal model plots.