Improved estimators for dispersion models with dispersion covariates

In this paper we discuss improved estimators for the regression and the dispersion parameters in an extended class of dispersion models (J{\o}rgensen, 1996). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the second-order bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the second-order biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the second-order biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to the second-order that are based on bootstrap methods. These estimators are compared by simulation

Assessment of uncertainties in hot-wire anemometry and oil-film interferometry measurements for wall-bounded turbulent flows

In this study, the sources of uncertainty of hot-wire anemometry (HWA) and oil-film interferometry (OFI) measurements are assessed. Both statistical and classical methods are used for the forward and inverse problems, so that the contributions to the overall uncertainty of the measured quantities can be evaluated. The correlations between the parameters are taken into account through the Bayesian inference with error-in-variable (EiV) model. In the forward problem, very small differences were found when using Monte Carlo (MC), Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow velocity measurements with HWA, the results indicate that the estimated uncertainty is lower when the correlations among parameters are considered, than when they are not taken into account. Moreover, global sensitivity analyses with Sobol indices showed that the HWA measurements are most sensitive to the wire voltage, and in the case of OFI the most sensitive factor is the calculation of fringe velocity. The relative errors in wall-shear stress, friction velocity and viscous length are 0.44%, 0.23% and 0.22%, respectively. Note that these values are lower than the ones reported in other wall-bounded turbulence studies. Note that in most studies of wall-bounded turbulence the correlations among parameters are not considered, and the uncertainties from the various parameters are directly added when determining the overall uncertainty of the measured quantity. In the present analysis we account for these correlations, which may lead to a lower overall uncertainty estimate due to error cancellation. Furthermore, our results also indicate that the crucial aspect when obtaining accurate inner-scaled velocity measurements is the wind-tunnel flow quality, which is more critical than the accuracy in wall-shear stress measurements

Structured count data regression

Overdispersion in count data regression is often caused by neglection or inappropriate modelling of individual heterogeneity, temporal or spatial correlation, and nonlinear covariate effects. In this paper, we develop and study semiparametric count data models which can deal with these issues by incorporating corresponding components in structured additive form into the predictor. The models are fully Bayesian and inference is carried out by computationally efficient MCMC techniques. In a simulation study, we investigate how well the different components can be identified with the data at hand. The approach is applied to a large data set of claim frequencies from car insurance

Nearly optimal Bayesian Shrinkage for High Dimensional Regression

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. In this paper, we study the problem for high-dimensional linear regression models. We show that if the shrinkage prior has a heavy and flat tail, and allocates a sufficiently large probability mass in a very small neighborhood of zero, then its posterior properties are as good as those of the spike-and-slab prior. While enjoying its efficiency in Bayesian computation, the shrinkage prior can lead to a nearly optimal contraction rate and selection consistency as the spike-and-slab prior. Our numerical results show that under posterior consistency, Bayesian methods can yield much better results in variable selection than the regularization methods, such as Lasso and SCAD. We also establish a Bernstein von-Mises type results comparable to Castillo et al (2015), this result leads to a convenient way to quantify uncertainties of the regression coefficient estimates, which has been beyond the ability of regularization methods

Confidence Intervals for the Coefficient of Quartile Variation of a Zero-inflated Lognormal Distribution

There are many types of skewed distribution, one of which is the lognormal distribution that is positively skewed and may contain true zero values. The coefficient of quartile variation is a statistical tool used to measure the dispersion of skewed and kurtosis data. The purpose of this study is to establish confidence and credible intervals for the coefficient of quartile variation of a zero-inflated lognormal distribution. The proposed approaches are based on the concepts of the fiducial generalized confidence interval, and the Bayesian method. Coverage probabilities and expected lengths were used to evaluate the performance of the proposed approaches via Monte Carlo simulation. The results of the simulation studies show that the fiducial generalized confidence interval and the Bayesian based on uniform and normal inverse Chi-squared priors were appropriate in terms of the coverage probability and expected length, while the Bayesian approach based on Jeffreys' rule prior can be used as alternatives. In addition, real data based on the red cod density from a trawl survey in New Zealand is used to illustrate the performances of the proposed approaches. Doi: 10.28991/esj-2021-01289 Full Text: PD

Bayesian Estimation of The Impacts of Food Safety Information on Household Demand for Meat and Poultry

Consumer reaction to changes in the amount of food safety information on beef, pork, and poultry available in the media is the focus of this study. Specifically, any differences in consumer reactions due to heterogeneous household characteristics are investigated. The data used in this study are monthly data from the Nielsen Homescan panel and cover the time period January 1998 to December 2005. These panel data contain information on household purchases of fresh meat and poultry as well as demographic characteristics of the participating households. The data used to describe food safety information were obtained from searches of newspapers using the Lexis-Nexis academic search engine. Consumer reactions are modeled in this study using a demand system that allows for both discrete and continuous choice situations. A seemingly unrelated regression (SUR) tobit model is estimated using a Gibbs sampler with data augmentation. A component error structure (random effects model) is incorporated into the SUR tobit model to account for unobserved heterogeneity of households making repeated purchases over time. Estimates of food safety elasticities calculated from the random effects SUR tobit model suggest that food safety information does not have a statistically or economically significant effect on household purchases of meat and poultry.food safety, panel data, Gibbs sampler, component error, Agricultural and Food Policy, Consumer/Household Economics, Food Consumption/Nutrition/Food Safety,

A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in PDE-based models and correspond to quantities such as density or pressure fields, elasto-plastic moduli and internal variables in solid mechanics, conductivity fields in heat diffusion problems, permeability fields in fluid flow through porous media etc. The proposed model has all the advantages of traditional Bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty. In contrast to existing approaches it utilizes a parsimonious, non-parametric formulation that favors sparse representations and whose complexity can be determined from the data. The proposed framework in non-intrusive and makes use of a sequence of forward solvers operating at various resolutions. As a result, inexpensive, coarse solvers are used to identify the most salient features of the unknown field(s) which are subsequently enriched by invoking solvers operating at finer resolutions. This leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy. It is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in Markov Chain Monte Carlo schemes