Data envelopment analysis in the presence of measurement error: case study from the National Database of Nursing Quality Indicators® (NDNQI®)

Data envelopment analysis (DEA) is the most commonly used approach for evaluating healthcare efficiency [B. Hollingsworth, The measurement of efficiency and productivity of health care delivery. Health Economics 17(10) (2008), pp. 1107–1128], but a long-standing concern is that DEA assumes that data are measured without error. This is quite unlikely, and DEA and other efficiency analysis techniques may yield biased efficiency estimates if it is not realized [B.J. Gajewski, R. Lee, M. Bott, U. Piamjariyakul, and R.L. Taunton, On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process. Journal of Applied Statistics 36(9) (2009), pp. 933–944; J. Ruggiero, Data envelopment analysis with stochastic data. Journal of the Operational Research Society 55 (2004), pp. 1008–1012]. We propose to address measurement error systematically using a Bayesian method (Bayesian DEA). We will apply Bayesian DEA to data from the National Database of Nursing Quality Indicators^® to estimate nursing units’ efficiency. Several external reliability studies inform the posterior distribution of the measurement error on the DEA variables. We will discuss the case of generalizing the approach to situations where an external reliability study is not feasible.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

A Hellinger distance approach to MCMC diagnostics

Bayesian analysis often requires the researcher to employ Markov Chain Monte Carlo (MCMC) techniques to draw samples from a posterior distribution which in turn is used to make inferences. Currently, several approaches to determine convergence of the chain as well as sensitivities of the resulting inferences have been developed. This work develops a Hellinger distance approach to MCMC diagnostics. An approximation to the Hellinger distance between two distributions f and g based on sampling is introduced. This approximation is studied via simulation to determine the accuracy. A criterion for using this Hellinger distance for determining chain convergence is proposed as well as a criterion for sensitivity studies. These criteria are illustrated using a dataset concerning the Anguilla australis, an eel native to New Zealand.     

统计显著性:一个被误读的P值——基于美国统计学会的声明

美国统计学会"关于统计显著性与P值"的官方声明发布之后,再次引发国内外研究学者对P值的广泛关注。在介绍国内统计教材中假设检验的基本内容和步骤的基础上,以"硬币投掷"与"背影识人"为例直观性解释P值、统计显著性与统计功效等相关概念,并引用心理学统计经典调查案例分析P值被误读的原因。同时,基于美国统计学会的声明,给出正确使用P值的建议。     

Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data

The benchmark dose (BMD) approach has gained acceptance as a valuable risk assessment tool, but risk assessors still face significant challenges associated with selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose‐response models. Current approaches do not explicitly address model uncertainty, and there is an existing need to more fully inform health risk assessors in this regard. In this study, a Bayesian model averaging (BMA) BMD estimation method taking model uncertainty into account is proposed as an alternative to current BMD estimation approaches for continuous data. Using the “hybrid” method proposed by Crump, two strategies of BMA, including both “maximum likelihood estimation based” and “Markov Chain Monte Carlo based” methods, are first applied as a demonstration to calculate model averaged BMD estimates from real continuous dose‐response data. The outcomes from the example data sets examined suggest that the BMA BMD estimates have higher reliability than the estimates from the individual models with highest posterior weight in terms of higher BMDL and smaller 90th percentile intervals. In addition, a simulation study is performed to evaluate the accuracy of the BMA BMD estimator. The results from the simulation study recommend that the BMA BMD estimates have smaller bias than the BMDs selected using other criteria. To further validate the BMA method, some technical issues, including the selection of models and the use of bootstrap methods for BMDL derivation, need further investigation over a more extensive, representative set of dose‐response data.     

Complex Latent Variable Modeling in Educational Assessment

Bayesian item response theory models have been widely used in different research fields. They support measuring constructs and modeling relationships between constructs, while accounting for complex test situations (e.g., complex sampling designs, missing data, heterogenous population). Advantages of this flexible modeling framework together with powerful simulation-based estimation techniques are discussed. Furthermore, it is shown how the Bayes factor can be used to test relevant hypotheses in assessment using the College Basic Academic Subjects Examination (CBASE) data.     

Inferences on functions of Pareto parameters with application to income inequality measures

The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the Pareto distribution function are expressed in terms of parameters defining the Pareto distribution. Inference procedures based on the generalized variable method, the large sample method, and the Bayesian method for testing of, and constructing confidence interval for, these measures are discussed. The results of Monte Carlo study are used to compare the performance of the suggested inference procedures from a population characterized by a Pareto distribution.     

Bayesian Network Structure Learning with Permutation Tests

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e., the maximization algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this article, we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.     

金融资产的动态非线性相关:一个新的模型

基于Kendall’sτ秩相关系数的优越性和定义,本文提出了新的具有明确经济意义的动态条件相关copula模型,将常用的Gaussian、Clayton和Gumbel函数统一根据该演化方程实现动态化,构造出三种Kendall’sτ动态条件相关copula模型,可用于刻画不同的相关模式。这些模型不仅参数少、容易估计,避免了现有动态条件相关copula模型构建方法各异导致的在实证中不利于比较的缺点,而且能够进行多步向前预测,有效地减少了进行样本外预测时的计算量,从而为刻画时变、非线性、非对称性和尾部相关等复杂的动态相关模式提供了新方法。     

Choosing Prior Hyperparameters: With Applications to Time-Varying Parameter Models

Time-varying parameter models with stochastic volatility are widely used to study macroeconomic and financial data. These models are almost exclusively estimated using Bayesian methods. A common practice is to focus on prior distributions that themselves depend on relatively few hyperparameters such as the scaling factor for the prior covariance matrix of the residuals governing time variation in the parameters. The choice of these hyperparameters is crucial because their influence is sizeable for standard sample sizes. In this article, we treat the hyperparameters as part of a hierarchical model and propose a fast, tractable, easy-to-implement, and fully Bayesian approach to estimate those hyperparameters jointly with all other parameters in the model. We show via Monte Carlo simulations that, in this class of models, our approach can drastically improve on using fixed hyperparameters previously proposed in the literature. Supplementary materials for this article are available online.