Bayesian inference for the mixed conditional heteroskedasticity model

Summary We estimate by Bayesian inference the mixed conditional heteroskedasticity model of Haas et al. (2004a Journal of Financial Econometrics 2, 211–50). We construct a Gibbs sampler algorithm to compute posterior and predictive densities. The number of mixture components is selected by the marginal likelihood criterion. We apply the model to the SP500 daily returns.     

Bayesian statistics in medical research: an intuitive alternative to conventional data analysis

Statistical analysis of both experimental and observational data is central to medical research. Unfortunately, the process of conventional statistical analysis is poorly understood by many medical scientists. This is due, in part, to the counter-intuitive nature of the basic tools of traditional (frequency-based) statistical inference. For example, the proper definition of a conventional 95% confidence interval is quite confusing. It is based upon the imaginary results of a series of hypothetical repetitions of the data generation process and subsequent analysis. Not surprisingly, this formal definition is often ignored and a 95% confidence interval is widely taken to represent a range of values that is associated with a 95% probability of containing the true value of the parameter being estimated. Working within the traditional framework of frequency-based statistics, this interpretation is fundamentally incorrect. It is perfectly valid, however, if one works within the framework of Bayesian statistics and assumes a 'prior distribution' that is uniform on the scale of the main outcome variable. This reflects a limited equivalence between conventional and Bayesian statistics that can be used to facilitate a simple Bayesian interpretation based on the results of a standard analysis. Such inferences provide direct and understandable answers to many important types of question in medical research. For example, they can be used to assist decision making based upon studies with unavoidably low statistical power, where non-significant results are all too often, and wrongly, interpreted as implying 'no effect'. They can also be used to overcome the confusion that can result when statistically significant effects are too small to be clinically relevant. This paper describes the theoretical basis of the Bayesian-based approach and illustrates its application with a practical example that investigates the prevalence of major cardiac defects in a cohort of children born using the assisted reproduction technique known as ICSI (intracytoplasmic sperm injection).     

Estimating efficacy in clinical trials with clustered binary responses

When non-compliance occurs in a clinical trial, it may be of interest to supplement the intent-to-treat analysis with an analysis of the efficacy (or biological effect) of therapy. Sommer and Zeger (1991) developed a method for estimating efficacy applicable to the case of a binary response variable and all-or-none compliance that assumes independent subject responses. We extend this approach to accommodate within-cluster correlations as may be expected in a cluster-randomized design. The method is illustrated using data from a controlled village-randomized clinical trial conducted in Indonesia to investigate the effect of vitamin A supplementation on mortality in children. We find that within-cluster correlations for these data are very small and that taking into account the clustering does not substantially affect inferences in this case. Additional calculations show that small within-cluster correlations (though larger than those found in the vitamin A data) may have a large impact on efficacy inferences. We also present the results of a simulation study that demonstrates the validness of the proposed approach for finite sample sizes.     

激活 联想 逻辑推理 模块组合——解决歧义的认知过程

本文从认知心理学的角度对歧义的认知心理过程作尝试性分析，并认为激活，联想，逻辑推理和模块组合这四个步骤构成一个完整的，能解决歧义的认知心理模式。     

Small-sample performance of the robust score test and its modifications in generalized estimating equations

The sandwich variance estimator of generalized estimating equations (GEE) may not perform well when the number of independent clusters is small. This could jeopardize the validity of the robust Wald test by causing inflated type I error and lower coverage probability of the corresponding confidence interval than the nominal level. Here, we investigate the small-sample performance of the robust score test for correlated data and propose several modifications to improve the performance. In a simulation study, we compare the robust score test to the robust Wald test for correlated Bernoulli and Poisson data, respectively. It is confirmed that the robust Wald test is too liberal whereas the robust score test is too conservative for small samples. To explain this puzzling operating difference between the two tests, we consider their applications to two special cases, one-sample and two-sample comparisons, thus motivating some modifications to the robust score test. A modification based on a simple adjustment to the usual robust score statistic by a factor of J/(J - 1) (where J is the number of clusters) reduces the conservativeness of the generalized score test. Simulation studies mimicking group-randomized clinical trials with binary and count responses indicated that it may improve the small-sample performance over that of the generalized score and Wald tests with test size closer to the nominal level. Finally, we demonstrate the utility of our proposal by applying it to a group-randomized clinical trial, trying alternative cafeteria options in schools (TACOS).     

Variance estimation for clustered recurrent event data with a small number of clusters

Often in biomedical studies, the event of interest is recurrent and within-subject events cannot usually be assumed independent. In semi-parametric estimation of the proportional rates model, a working independence assumption leads to an estimating equation for the regression parameter vector, with within-subject correlation accounted for through a robust (sandwich) variance estimator; these methods have been extended to the case of clustered subjects. We consider variance estimation in the setting where subjects are clustered and the study consists of a small number of moderate-to-large-sized clusters. We demonstrate through simulation that the robust estimator is quite inaccurate in this setting. We propose a corrected version of the robust variance estimator, as well as jackknife and bootstrap estimators. Simulation studies reveal that the corrected variance is considerably more accurate than the robust estimator, and slightly more accurate than the jackknife and bootstrap variance. The proposed methods are used to compare hospitalization rates between Canada and the U.S. in a multi-centre dialysis study. Copyright (c) 2005 John Wiley & Sons, Ltd.     

Bayesian inference on the patient population size given list mismatches

In applying capture-recapture methods for closed populations to epidemiology, one needs to estimate the total number of people with a certain disease in a certain research area by using several lists with information of patients. Problems of lists error often arise due to mistyping or misinformation. Adopting the concept of tag-loss methodology in animal populations, Seber et al. (Biometrics 2000; 56:1227-1232) proposed solutions to a two-list problem. This article reports an interesting simulation study, where Bayesian point estimates based on improper constant and Jeffreys prior for unknown population size N could have smaller frequentist standard errors and MSEs compared to the estimates proposed in Seber et al. (2000). The Bayesian credible intervals based on the same priors also have super frequentist coverage probabilities while some of the frequentist confidence intervals procedures have drastically poor coverage. Seber's real data set on gestational diabetics is analysed with the proposed new methods.     

Effects on orientation perception of manipulating the spatio-temporal prior probability of stimuli

Spatial and temporal regularities commonly exist in natural visual scenes. The knowledge of the probability structure of these regularities is likely to be informative for an efficient visual system. Here we explored how manipulating the spatio-temporal prior probability of stimuli affects human orientation perception. Stimulus sequences comprised four collinear bars (predictors) which appeared successively towards the foveal region, followed by a target bar with the same or different orientation. Subjects' orientation perception of the foveal target was biased towards the orientation of the predictors when presented in a highly ordered and predictable sequence. The discrimination thresholds were significantly elevated in proportion to increasing prior probabilities of the predictors. Breaking this sequence, by randomising presentation order or presentation duration, decreased the thresholds. These psychophysical observations are consistent with a Bayesian model, suggesting that a predictable spatio-temporal stimulus structure and an increased probability of collinear trials are associated with the increasing prior expectation of collinear events. Our results suggest that statistical spatio-temporal stimulus regularities are effectively integrated by human visual cortex over a range of spatial and temporal positions, thereby systematically affecting perception.     

Robust Bayesian prediction of subject disease status and population prevalence using several similar diagnostic tests

Sometimes several diagnostic tests are performed on the same population of subjects with the aim of assessing disease status of individuals and the prevalence of the disease in the population, but no test is a reference test. Although the diagnostic tests may have the same biological underpinnings, test results may disagree for some specific animals. In that case, it may be difficult to determine disease status for individual subjects, and consequently population prevalence estimation becomes difficult. In this paper, we propose a robust method of estimating disease status and prevalence that uses heavy-tailed sampling distributions in a hierarchical model to protect against the influence of conflicting observations on inferences. If a subject has a test outcome that is discordant with the other test results then it is downweighted in diagnosing a subject's disease status, and for estimating disease prevalence. The amount of downweighting depends on the degree of conflict among the test results for the subject.     

On the analysis of viral load endpoints in HIV vaccine trials

First generation HIV vaccines are not likely to provide complete protection from HIV-1 infection. Therefore, it is important to assess a vaccine's effect on disease progression and infectiousness of infected vaccinees in an efficacy trial; however, direct assessment of such vaccine effects is not feasible within current trial designs. Viral load in HIV-infected individuals correlates with infectiousness and disease progression in a natural history setting, and thus is a reasonable candidate for a surrogate outcome in vaccine efficacy trials. We consider comparisons of viral load of infected vaccinees to that of infected trial participants in the control group. Dramatic differences in viral loads between these groups would suggest a vaccine effect on disease progression. However, modest differences, even if statistically significant, could be consistent with an imperfect vaccine effect on susceptibility to infection and not an effect on disease progression, that is, a selection effect of the vaccine. Thus, the usual statistical tests for no difference between groups do not test the biologically and clinically relevant hypothesis. We propose a model for the possible selective effects of a vaccine and develop several test statistics for assessing a direct effect of the vaccine on viral load given this selection model. Finite sample properties of these tests are evaluated using computer simulations.