A spatial Bayesian semiparametric mixture model for positive definite matrices with applications in diffusion tensor imaging

Studies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.     

Testing equality of survival distributions when the population marks are missing

This paper introduces a nonparametric approach for testing the equality of two or more survival distributions based on right censored failure times with missing population marks for the censored observations. The standard log-rank test is not applicable here because the population membership information is not available for the right censored individuals. We propose to use the imputed population marks for the censored observations leading to fractional at-risk sets that can be used in a two sample censored data log-rank test. We demonstrate with a simple example that there could be a gain in power by imputing population marks (the proposed method) for the right censored individuals compared to simply removing them (which also would maintain the right size). Performance of the imputed log-rank tests obtained this way is studied through simulation. We also obtain an asymptotic linear representation of our test statistic. Our testing methodology is illustrated using a real data set.     

Risk Attitude,Ambiguity Intolerance and Decision Making: An Exploratory Investigation*

Although recent research has identified attitudes towards ambiguity and risk to be important determinants of choice behavior [8] [18], no prior work jointly assessed the roles of both attitudes. We conducted a laboratory experiment using a real decision scenario and conducted exploratory analyses of the relationship between attitudes towards risk and ambiguity and the decision taken by the subjects. The results support the prediction that attitudes towards both risk and ambiguity affect choice behavior. Our exploratory analyses indicate interesting avenues for future research, including an examination of the decision process itself.     

NONPARAMETRIC ESTIMATION OF CONDITIONAL CUMULATIVE HAZARDS FOR MISSING POPULATION MARKS

A new function for the competing risks model, the conditional cumulative hazard function, is introduced, from which the conditional distribution of failure times of individuals failing due to cause  j  can be studied. The standard Nelson–Aalen estimator is not appropriate in this setting, as population membership (mark) information may be missing for some individuals owing to random right-censoring. We propose the use of imputed population marks for the censored individuals through fractional risk sets. Some asymptotic properties, including uniform strong consistency, are established. We study the practical performance of this estimator through simulation studies and apply it to a real data set for illustration.     

A class of tests for exponentiality against decreasing mean residual life alternatives

A class of tests is proposed for testing Exponentiality against the Decreasing Mean Residual Life (DMRL) class of non-exponential probability distributions. These tests are consistent and asymptotically unbiased against all continuous DMRL alternatives. They are U - statistics and hence asymptotically normally distributed. The asymptotic relative efficiency (ARE) with respect to other tests for DMRL are quite high. Small sample powers are also comparable with small sample powers of the competitors.     

Sustainability of community-based organizations of the rural poor: Learning from Concern's rural development projects, Bangladesh

Based on two decades of grassroots experiences, Concern Bangladeshhas developed a federation structure to ensure the sustainabilityof community-based organizations (CBO). Despite capacity-buildinginputs to all federations, only a few of them have been ableto operate without substantial external aid. This lack of progressrelates to a ‘one size fits all’ capacity-buildingstrategy and other sociopolitical issues such as the alienationof federations from the wider community and to political manipulation.Successful federations demonstrate that a committed leader whoensures participation, respects transparency and accountability,and promotes second line leadership can contribute positivelyto sustainability, even in an adverse sociopolitical context,and with limited capacity-building support.     

Structure of Uncertainty and Decision Making: An Experimental Investigation*

Decisions in the real world usually involve imprecise information or uncertainty about the precesses by which outcomes may be determined. This research reports the results of a laboratory experiment which examined whether the structure of uncertainty, namely, both the center and the range of the probability distribution describing the uncertainty, is an important determinant of choice. Specifically, it examines how the uncertainty of audit by the Internal Revenue Service of income tax returns affects taxpayers' decisions about intentional noncompliance. The context is relevant as almost nothing is known about how taxpayers assess detection risks using the probability information they have. The study focuses on intentional noncompliance. The factors affecting it are distinct and separate from those affecting unintentional noncompliance. Other factors that affect intentional tax noncompliance, such as risk, tax rates, and penalty rates, were controlled in the experiment. It was hypothesized that the lower the mean and the lesser the range (ambiguity) of the perceived audit probability, the greater the international noncompliance. As hypothesized, the analysis indicates that both the mean and the range of the perceived audit probability rate affect intentional noncompliance, though the effect of ambiguity is greater at a relatively higher level of mean. This result suggests that the strength of the information describing an uncertain event is captured better by both the mean and the range of the uncertainty than either of those components singly.     

Risk,Ambiguity, and Decision Choice: Some Additional Evidence*

This paper extends prior research by jointly assessing the roles of risk attitude and tolerance for ambiguity in predicting choice. An experiment examined the effects of these variables on decisions made in four different scenarios. The four scenarios (treatment combinations) were generated by manipulating risk and ambiguity into two levels (high and low). The context was defined in terms of a sample size selection problem. The second issue explored was the effect of attitudes toward risk and ambiguity on decision confidence. The results indicate that (1) both risk attitude and ambiguity intolerance determined choice behavior, (2) the roles of these individual attitudes depend on the levels of the two treatment variables of risk and ambiguity, (3) the presence of ambiguity accentuates the perception of risk in individual subjects, and (4) decision makers who are less risk averse, and have more tolerance for ambiguity, display greater confidence in their choice. The paper discusses some of the managerial implications of the results.