Sparsely Sampling the Sky: A Bayesian Experimental Design Approach

The next generation of galaxy surveys will observe millions of galaxies over large volumes of the universe. These surveys are expensive both in time and cost, raising questions regarding the optimal investment of this time and money. In this work we investigate criteria for selecting amongst observing strategies for constraining the galaxy power spectrum and a set of cosmological parameters. Depending on the parameters of interest, it may be more efficient to observe a larger, but sparsely sampled, area of sky instead of a smaller contiguous area. In this work, by making use of the principles of Bayesian Experimental Design, we will investigate the advantages and disadvantages of the sparse sampling of the sky and discuss the circumstances in which a sparse survey is indeed the most efficient strategy. For the Dark Energy Survey (DES), we find that by sparsely observing the same area in a smaller amount of time, we only increase the errors on the parameters by a maximum of 0.45%. Conversely, investing the same amount of time as the original DES to observe a sparser but larger area of sky we can in fact constrain the parameters with errors reduced by 28%

Symmetry, regression design, and sampling distributions

When values of regressors are symmetrically disposed, many M-estimators in a wide class of models have a reflection property, namely, that as the signs of the coefficients on regressors are reversed, their estimators' sampling distribution is reflected about the origin. When the coefficients are zero, sign reversal can have no effect. So in this case, the sampling distribution of regression coefficient estimators is symmetric about zero, the estimators are median unbiased and, when moments exist, the estimators are exactly uncorrelated with estimators of other parameters. The result is unusual in that it does not require response variates to have symmetric conditional distributions. It demonstrates the potential importance of covariate design in determining the distributions of estimators, and it is useful in designing and interpreting Monte Carlo experiments. The result is illustrated by a Monte Carlo experiment in which maximum likelihood and symmetrically censored least-squares estimators are calculated for small samples from a censored normal linear regression, Tobit, model. © 1994, Cambridge University Press. All rights reserved

Design of general-purpose sampling strategies for geometric shape measurement

Quality inspection is a preliminary step for different further analyses (process monitoring, control and optimisation) and requires one to select a measuring strategy, i.e., number and location of measurement points. This phase of data gathering usually impacts on inspection times and costs (via sample size) but it also affects the performance of the following tasks (process monitoring, control and optimisation). While most of the approaches for sampling design are specifically presented with reference to a target application (namely, monitoring, control or optimisation), this paper presents a general-purpose procedure, where the number and location of measurement points are selected in order to retain most of the information related to the feature under study. The procedure is based on principal component analysis and its application is shown with reference to a real case study concerning the left front window of a car. A different approach based on multidimensional scaling is further applied as validation tool, in order to show the effectiveness of the PCA solution