On Hotelling’s T2 test in a special paired sample case

In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given.     

Beliefs about overconfidence

This experiment elicits beliefs about other people’s overconfidence and abilities. We find that most people believe that others are unbiased, and only few think that others are overconfident. There is a remarkable heterogeneity between these groups. Those people who think others are underconfident or unbiased are overconfident themselves. Those who think others are overconfident are underconfident themselves. Despite this heterogeneity, people overestimate on average the abilities of others as they do their own ability. One driving force behind this result is the refusal to process information about oneself: not only does this lead to overestimation of one’s own ability, but by means of social projection also to overestimation of others’ abilities.     

Mortality, fertility, education and capital accumulation in a simple OLG economy

We develop a simple OLG model to analytically show that aging leads to increased educational efforts through a general equilibrium effect. The mechanism is that scarcity of raw labor increases the return of human relative to physical capital. While a reduction in the birth rate is shown to unambiguously increase educational efforts, increases in the survival rate have ambiguous effects. Falling birth rates also increase capital per worker, but the effects of rising survival rates are again ambiguous. We conclude that our model is a useful laboratory to highlight potentially offsetting effects in models with endogenous education and overlapping generations.     

Habitat equivalency in urban estuaries: An analytical hierarchy process for planning ecological restoration

Ecosystem restoration is critically important in urbanized landscapes because habitat degradation is severe and ubiquitous in such areas. Because successful restoration requires specification of desired environmental endpoints, a generally applicable method for valuing and comparing possible restoration endpoints is needed. One method available for comparative valuation is the Analytical Hierarchy Process (AHP). AHP allows a suite of alternatives to be valued on a rank scale based on simple, tractable, paired comparisons among all alternatives. Given a sound technical foundation for the paired comparisons, the method yields an objective set of rank values. By incorporating the relative values of various restoration alternatives in a restoration scaling evaluation such as a Habitat Equivalency Analysis (HEA), restoration programs can be designed effectively both qualitatively (in terms of the kinds of resources or habitats desired) and quantitatively (in terms of the amounts or areas of each). In this study, we develop and apply AHP in the context of a specimen HEA for US Mid-Atlantic coast estuaries. By ranking various habitat types as potential restoration targets based on their value for a suite of key natural resources, a series of restoration ratios is produced, relating relative habitat areas of each type needed to offset specific impairment levels. These ratios provide a basic tool for restoration planning in urbanized estuaries, as these comprise nearly entirely built environments with little or no natural habitat. Under these conditions, restoration planners must specify desired states of the ecosystem, and the restoration ratios allow various permutations of presumed post-restoration environments to be valued and compared.     

Adaptive Gaussian Markov random fields with applications in human brain mapping

Summary.  Functional magnetic resonance imaging has become a standard technology in human brain mapping. Analyses of the massive spatiotemporal functional magnetic resonance imaging data sets often focus on parametric or non-parametric modelling of the temporal component, whereas spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high curvature transitions between activated and non-activated regions of the brain. To improve spatial adaptivity, we introduce a class of inhomogeneous Markov random fields with stochastic interaction weights in a space-varying coefficient model. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, can be carried out through efficient Markov chain Monte Carlo simulation. Although motivated by the analysis of functional magnetic resonance imaging data, the methodological development is general and can also be used for spatial smoothing and regression analysis of areal data on irregular lattices. An application to stylized artificial data and to real functional magnetic resonance imaging data from a visual stimulation experiment demonstrates the performance of our approach in comparison with Gaussian and robustified non-Gaussian Markov random-field models.     

The Perceived Threat of Nuclear War, Salience, and Open Questions

The most serious problem facing the United States, accordingto many scientific and political leaders, is the threat of nuclearwar. Yet the standard survey question on the most importantproblem facing the country has often shown little public concurrencewith this assumption. Our article uses experimentation in nationalsamples to test whether this difference can be traced to limitationsin either the form or the wording of the standard question.The results indicate that there are some important systematicdifferences between open and closed versions of the question,and also differences that result from reference to the nationas distinct from the world, but neither type of difference accountsfor the infrequent mention of nuclear war on the standard question.Instead, other evidence indicates that most Americans believethat nuclear war is not going to happen at all, or that if itdoes happen it will be too far in the distant future to be ofpressing concern to them personally.