A method for choosing the smoothing parameter in a semi-parametric model for detecting change-points in blood flow

In a smoothing spline model with unknown change-points, the choice of the smoothing parameter strongly influences the estimation of the change-point locations and the function at the change-points. In a tumor biology example, where change-points in blood flow in response to treatment were of interest, choosing the smoothing parameter based on minimizing generalized cross-validation (GCV) gave unsatisfactory estimates of the change-points. We propose a new method, aGCV, that re-weights the residual sum of squares and generalized degrees of freedom terms from GCV. The weight is chosen to maximize the decrease in the generalized degrees of freedom as a function of the weight value, while simultaneously minimizing aGCV as a function of the smoothing parameter and the change-points. Compared with GCV, simulation studies suggest that the aGCV method yields improved estimates of the change-point and the value of the function at the change-point.     

Multiple testing using the posterior probabilities of directional alternatives,with application to genomic studies

This paper aims to connect Bayesian analysis and frequentist theory in the context of multiple comparisons. The authors show that when testing the equality of two sample means, the posterior probability of the one‐sided alternative hypothesis, defined as a half‐space, shares with the frequentist P‐value the property of uniformity under the null hypothesis. Ultimately, the posterior probability may thus be used in the same spirit as a P‐value in the Benjamini‐Hochberg procedure, or in any of its extensions.     

Numerical experiments with the thin plate histospline

The thin plate volume matching and volume smoothing histosplines are described. These histosplines are suitable for estimating densities or incidence rates as a function of position on the plane when data is aggregated by area, for example by county. We give a numerical algorithm for the volume matching histospline and for the volume smoothing histospline using generalized cross validation to estimate the smoothing parameter. Some numerical experiments were performed using synthetic data, population data and SMR's (standardized mortality ratios) aggregated by county over the state of Wisconsin. The method turns out to be not particularly suited for obtaining population density maps where the population density can vary by two orders of magnitude, because the histospline can be negative in