The Efficacy of a Decision Support System in Enhancing Risk Assessment Performance

A pervasive challenge for decision‐makers is evaluating data of varying form (e.g., quantitative vs. qualitative) and credibility in arriving at an overall risk assessment judgment. The current study tests the efficacy of a Decision Support System (DSS) for facilitating auditors’ evaluation and assimilation of financial and nonfinancial information in accurately assessing the risk of material misstatements (RMM) in financial information. Utilizing the proximity compatibility principle, the DSS manipulates the display of cues either in an integral (where pieces of information are displayed on one computer screen) or separable (where pieces of information are displayed on different computer screens) format. Based on cognitive fit theory, we expect that the integral (separable) display best supports financial (nonfinancial) information processing, leading to enhanced risk assessment performance. In addition, we predict that consistent DSS display of financial and nonfinancial information facilitates risk assessment performance. Further, this study accentuates the importance of auditors’ preference for presentation of financial and nonfinancial information and consistent presentation of all the information in strengthening the effect of DSS display format on risk assessment performance. We design a case which includes a seeded high fraud risk. A total of 112 audit seniors participated in the experiment where the DSS display format was manipulated and the auditors’ RMM assessments and display preferences were measured. The results support the hypotheses and highlight the value of the DSS in enhancing risk assessment performance.     

Change point analysis of a Gaussian model

In this paper, the testing and estimation of a single change point in means and variances of a sequence of independent Gaussian normal random variables are studied. The Schwarz Information Criterion, SIC, is used to search for the change point. The unbiased version of the SIC for this change point problem is also derived for the finite sample case. Other properties of the SIC test statistic are given as well. Finally, two examples are given at the end of this paper to illustrate the method proposed, and changes are successfully detected.     

Exponential progressive step-stress life-testing with link function based on Box–Cox transformation

In order to quickly extract information on the life of a product, accelerated life-tests are usually employed. In this article, we discuss a k-stage step-stress accelerated life-test with M-stress variables when the underlying data are progressively Type-I group censored. The life-testing model assumed is an exponential distribution with a link function that relates the failure rate and the stress variables in a linear way under the Box–Cox transformation, and a cumulative exposure model for modelling the effect of stress changes. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique is developed for inference on all the parameters of this model. Numerical examples are presented to illustrate all the methods of inference developed here, and a comparison of the ML and Bayesian methods is also carried out.     

Bayesian analysis of mark‐recapture data with travel time‐dependent survival probabilities

The authors extend the classical Cormack‐Jolly‐Seber mark‐recapture model to account for both temporal and spatial movement through a series of markers (e.g., dams). Survival rates are modeled as a function of (possibly) unobserved travel times. Because of the complex nature of the likelihood, they use a Bayesian approach based on the complete data likelihood, and integrate the posterior through Markov chain Monte Carlo methods. They test the model through simulations and apply it also to actual salmon data arising from the Columbia river system. The methodology was developed for use by the Pacific Ocean Shelf Tracking (POST) project.     

A Bayesian model for multinomial sampling with misclassified data

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented.     

Bayesian assessment of times to diagnosis in breast cancer screening

Breast cancer is one of the diseases with the most profound impact on health in developed countries and mammography is the most popular method for detecting breast cancer at a very early stage. This paper focuses on the waiting period from a positive mammogram until a confirmatory diagnosis is carried out in hospital. Generalized linear mixed models are used to perform the statistical analysis, always within the Bayesian reasoning. Markov chain Monte Carlo algorithms are applied for estimation by simulating the posterior distribution of the parameters and hyperparameters of the model through the free software WinBUGS.     

Model Selection and Regression t-Statistics

It is shown that dropping quantitative variables from a linear regression, based on t-statistics, is mathematically equivalent to dropping variables based on commonly used information criteria.     

Bayesian estimation of quantile distributions

Use of Bayesian modelling and analysis has become commonplace in many disciplines (finance, genetics and image analysis, for example). Many complex data sets are collected which do not readily admit standard distributions, and often comprise skew and kurtotic data. Such data is well-modelled by the very flexibly-shaped distributions of the quantile distribution family, whose members are defined by the inverse of their cumulative distribution functions and rarely have analytical likelihood functions defined. Without explicit likelihood functions, Bayesian methodologies such as Gibbs sampling cannot be applied to parameter estimation for this valuable class of distributions without resorting to numerical inversion. Approximate Bayesian computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier use of quantile distributions under the Bayesian framework. Parameter estimates for simulated and experimental data are presented.     

Bayesian meta-analysis using skewed elliptical distributions

Meta-analysis refers to a quantitative method for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution proposed originally by Chen, Dey, and Shao [M. H. Chen, D. K. Dey, Q. M. Shao, A new skewed link model for dichotomous quantal response data, J. Amer. Statist. Assoc. 94 (1983), pp. 1172–1186.] and Branco and Dey [D. Branco and D.K. Dey, A general class of multivariate skew-elliptical distributions, J. Multivariate Anal. 79, pp. 99–113.]. These rich classes of models combine the information of independent studies, allowing investigation of variability both between and within studies and incorporating weight functions. We constructed a detailed computational scheme under skewed normal and skewed Student's t distribution using the MCMC method. Bayesian model selection was conducted by Bayes factor under a different skewed error. Finally, we illustrated our methodology using a real data example taken from Johnson [M.F. Johnson, Comparative efficacy of Naf and SMFP dentifrices in caries prevention: a meta-analysis overview, J Eur. Organ. Caries Res. 27 (1993), pp. 328–336.].     

Nonparametric survival regression using the beta-Stacy process

A novel class of hierarchical nonparametric Bayesian survival regression models for time-to-event data with uninformative right censoring is introduced. The survival curve is modeled as a random function whose prior distribution is defined using the beta-Stacy (BS) process. The prior mean of each survival probability and its prior variance are linked to a standard parametric survival regression model. This nonparametric survival regression can thus be anchored to any reference parametric form, such as a proportional hazards or an accelerated failure time model, allowing substantial departures of the predictive survival probabilities when the reference model is not supported by the data. Also, under this formulation the predictive survival probabilities will be close to the empirical survival distribution near the mode of the reference model and they will be shrunken towards its probability density in the tails of the empirical distribution.