Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

The Golden Rule Ethic, its Measurement, and Relationships with Well-Being and Prosocial Values Across Four Religions in India

As a psychological principle, the golden rule represents an ethic of universal empathic concern. It is, surprisingly, present in the sacred texts of virtually all religions, and in philosophical works across eras and continents. Building on the literature demonstrating a positive impact of prosocial behavior on well-being, the present study investigates the psychological function of universal empathic concern in Indian Hindus, Christians, Muslims and Sikhs.

I develop a measure of the centrality of the golden rule-based ethic, within an individual’s understanding of his or her religion, that is applicable to all theistic religions. I then explore the consistency of its relationships with psychological well-being and other variables across religious groups.

Results indicate that this construct, named Moral Concern Religious Focus, can be reliably measured in disparate religious groups, and consistently predicts well-being across them. With measures of Intrinsic, Extrinsic and Quest religious orientations in the model, only Moral Concern and religiosity predict well-being. Moral Concern alone mediates the relationship between religiosity and well-being, and explains more variance in well-being than religiosity alone. The relationship between Moral Concern and well-being is mediated by increased preference for prosocial values, more satisfying interpersonal relationships, and greater meaning in life. In addition, across religious groups Moral Concern is associated with better self-reported physical and mental health, and more compassionate attitudes toward oneself and others.

Two additional types of religious focus are identified: Personal Gain, representing the motive to use religion to improve one’s life, and Relationship with God. Personal Gain is found to predict reduced preference for prosocial values, less meaning in life, and lower quality of relationships. It is associated with greater interference of pain and physical or mental health problems with daily activities, and lower self-compassion. Relationship with God is found to be associated primarily with religious variables and greater meaning in life.

I conclude that individual differences in the centrality of the golden rule and its associated ethic of universal empathic concern may play an important role in explaining the variability in associations between religion, prosocial behavior and well-being noted in the literature.