Particle filters provide Monte Carlo approximations of intractable quantities, such as likelihood evaluations in state-space models. In many cases, the interest does not lie in the values of the estimates themselves, but in the comparison of these values for various parameters. For instance, we might want to compare the likelihood at two parameter values. Such…

In this talk, I will discuss the prediction properties of techniques commonly used to scale up kernel methods and Gaussian processes. In particular, I will focus on data dependent and independent sub-sampling methods, namely Nystrom and random features, and study their generalization properties within a statistical learning theory framework. On the one hand I will…

Henry L. Rietz, the first president of IMS, published his book “Mathematical Statistics” in 1927. One review wrote in 1928: “Professor Rietz has developed this theory so skillfully that the ’workers in other fields’, provided only that they have a passing familiarity with the grammar of mathematics, can secure a satisfactory understanding of the points…