Graphical Models/Statistical Learning

A common practice in applied statistics is to determine the sample size under independence. When the available data have an obvious correlation structure the problem is how to determine  the decrease of sample size as a function of correlation. This problem is relevant when a pilot study has been carried out in a certain region and it is of interest to study a regionalized variable in the same area. Recently, some attention has been devoted in the literature to the determination of  geographical sample sizes (Griffith, 2005).

When one wants to perform digital processing of a signal, it must be sampled.  Classically one samples a continuous signal using the Nyquist theorem, that states that the sampling rate of a signal must be at least twice the largest frequency present in it. However, most signals are compressive, that is, their digital version can be alternatively represented with a much smaller number of bits than its original version, with very little information loss. This implies, in general, that they can be represented sparsely using some orthogonal bases.

The Internet has truly revolutionized the way information is gathered and disseminated globally. In the same direction, wireless sensor networks have opened a new lane that promises to extend the Internet's capabilities to include all physical objects and, potentially, all living things.