Toward an integrated Bayesian network approach to measurement error detection and correction

In this article, the quality of data produced by national statistical institutes and by governmental institutions is considered. In particular, the problem of measurement error is analyzed and an integrated Bayesian network decision support system based on non-parametric Bayesian networks is proposed for its detection and correction. Non-parametric Bayesian networks are graphical models expressing dependence structure via bivariate copulas associated to the edges of the graph. The network structure and the misreport probability are estimated using a validation sample. The Bayesian network model is proposed to decide: (i) which records have to be corrected; (ii) the kind and amount of correction to be adopted. The proposed correction procedure is applied to the Banca d’Italia Survey on Household Income and Wealth and, specifically, the bond amounts are analyzed. Finally, the sensitivity of the conditional distribution of the true value random variable given the observed one to different evidence configurations is studied.     

Pre-decisional information acquisition: Why do we pay too much for information? Brief report

People tend to acquire more information while making their decisions than a rational and risk-neutral benchmark would predict. We conduct a carefully designed experiment to derive five plausible reasons for pre-decision information overpurchasing. The results show that overpurchasing of information can be almost entirely explained by systematic information processing errors (misestimation or incorrect Bayesian updating), possibly caused by biased intuitive decision processes. Other factors, such as overoptimism about the validity of the new information, risk aversion, ambiguity aversion, and curiosity about (irrelevant) information, play at most a minor role. Our results imply that information overacquisitions are mainly driven by the overestimation of the usefulness of additional information.     

Estimating the effects of network covariates on subgroup insularity with a hierarchical mixed membership stochastic blockmodel

Social networks describe the relationships and interactions among a group of individuals. In many peer relationships, individuals tend to associate more often with some members than others, forming subgroups or clusters. Subgroup structure varies across networks; subgroups may be insular, appearing distinct and isolated from one another, or subgroups may be so integrated that subgroup structure is not visually apparent, and there are numerous ways of quantifying these types of structures. We propose a new model that relates the amount of subgroup integration to network attributes, building on the mixed membership stochastic blockmodel (Airoldi et al., 2008) and subsequent work by Sweet and Zheng (2017) and Sweet et al. (2014). We explore some of the operating characteristics of this model with simulated data and apply this model to determine the relationship between teachers’ instructional practices and their classrooms’ peer network subgroup structure.     

Bayesian partial likelihood approach for tied observations

The Bayesian analysis based on the partial likelihood for Cox's proportional hazards model is frequently used because of its simplicity. The Bayesian partial likelihood approach is often justified by showing that it approximates the full Bayesian posterior of the regression coefficients with a diffuse prior on the baseline hazard function. This, however, may not be appropriate when ties exist among uncensored observations. In that case, the full Bayesian and Bayesian partial likelihood posteriors can be much different. In this paper, we propose a new Bayesian partial likelihood approach for many tied observations and justify its use.     

On reliability estimation based on fuzzy lifetime data

Real lifetime data are never precise numbers but more or less non-precise, also called fuzzy. This kind of imprecision is connected with all measurement results of continuous variables, therefore also with time observations. Imprecision is different from errors and variability. Therefore estimation methods for reliability characteristics have to be adapted to the situation of fuzzy lifetimes in order to obtain realistic results.     

A Bayesian Approach for Analyzing Results of Vehicle Collision Tests

Certain motor vehicle safety standards stipulate a collision test speed and a set of performance criteria that vehicles must satisfy during or after the collision test. For example, Federal Motor Vehicle Safety Standard 301 requires a 30 mile per hour (mph) barrier collision and specifies a certain maximum allowable limit on the total spillage of fuel. Vehicle designs are required to meet this standard; however, when collision tests are conducted at speeds higher than the standard, vehicles do not always satisfy the performance criteria. This paper develops a mathematical model for estimating the probability of meeting the standard by using a Bayesian framework to incorporate engineering judgment with collision test results. The model is based on the idea that there are random features to a vehicle's ability to meet performance standards in a collision, especially at such elevated speeds. Example calculations are included to illustrate the estimation of the probability of meeting the standard and to compare it with a maximum likelihood approach.     

An intuitive risk factors search algorithm: usage of the Bayesian network technique in personalized medicine

The article focuses on the application of the Bayesian networks (BN) technique to problems of personalized medicine. The simple (intuitive) algorithm of BN optimization with respect to the number of nodes using naive network topology is developed. This algorithm allows to increase the BN prediction quality and to identify the most important variables of the network. The parallel program implementing the algorithm has demonstrated good scalability with an increase in the computational cores number, and it can be applied to the large patients database containing thousands of variables. This program is applied for the prediction for the unfavorable outcome of coronary artery disease (CAD) for patients who survived the acute coronary syndrome (ACS). As a result, the quality of the predictions of the investigated networks was significantly improved and the most important risk factors were detected. The significance of the tumor necrosis factor-alpha gene polymorphism for the prediction of the unfavorable outcome of CAD for patients survived after ACS was revealed for the first time.     

Interquantile shrinkage in additive models

In this paper, we investigate the commonality of nonparametric component functions among different quantile levels in additive regression models. We propose two fused adaptive group Least Absolute Shrinkage and Selection Operator penalties to shrink the difference of functions between neighbouring quantile levels. The proposed methodology is able to simultaneously estimate the nonparametric functions and identify the quantile regions where functions are unvarying, and thus is expected to perform better than standard additive quantile regression when there exists a region of quantile levels on which the functions are unvarying. Under some regularity conditions, the proposed penalised estimators can theoretically achieve the optimal rate of convergence and identify the true varying/unvarying regions consistently. Simulation studies and a real data application show that the proposed methods yield good numerical results.     

Objective Bayesian analysis based on upper record values from two-parameter Rayleigh distribution with partial information

In the life test, predicting higher failure times than the largest failure time of the observed is an important issue. Although the Rayleigh distribution is a suitable model for analyzing the lifetime of components that age rapidly over time because its failure rate function is an increasing linear function of time, the inference for a two-parameter Rayleigh distribution based on upper record values has not been addressed from the Bayesian perspective. This paper provides Bayesian analysis methods by proposing a noninformative prior distribution to analyze survival data, using a two-parameter Rayleigh distribution based on record values. In addition, we provide a pivotal quantity and an algorithm based on the pivotal quantity to predict the behavior of future survival records. We show that the proposed method is superior to the frequentist counterpart in terms of the mean-squared error and bias through Monte carlo simulations. For illustrative purposes, survival data on lung cancer patients are analyzed, and it is proved that the proposed model can be a good alternative when prior information is not given.     

Comparison of dichotomized and distributional approaches in rare event clinical trial design: a fixed Bayesian design

This research was motivated by our goal to design an efficient clinical trial to compare two doses of docosahexaenoic acid supplementation for reducing the rate of earliest preterm births (ePTB) and/or preterm births (PTB). Dichotomizing continuous gestational age (GA) data using a classic binomial distribution will result in a loss of information and reduced power. A distributional approach is an improved strategy to retain statistical power from the continuous distribution. However, appropriate distributions that fit the data properly, particularly in the tails, must be chosen, especially when the data are skewed. A recent study proposed a skew-normal method. We propose a three-component normal mixture model and introduce separate treatment effects at different components of GA. We evaluate operating characteristics of mixture model, beta-binomial model, and skew-normal model through simulation. We also apply these three methods to data from two completed clinical trials from the USA and Australia. Finite mixture models are shown to have favorable properties in PTB analysis but minimal benefit for ePTB analysis. Normal models on log-transformed data have the largest bias. Therefore we recommend finite mixture model for PTB study. Either finite mixture model or beta-binomial model is acceptable for ePTB study.