The Hitchhiker's Guide to Nonlinear Filtering

Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We start our review of the theory on nonlinear filtering from the simplest `filtering' task we can think of, namely static Bayesian inference. From there we continue our journey through discrete-time models, which is usually encountered in machine learning, and generalize to and further emphasize continuous-time filtering theory. The idea of changing the probability measure connects and elucidates several aspects of the theory, such as the parallels between the discrete- and continuous-time problems and between different observation models. Furthermore, it gives insight into the construction of particle filtering algorithms. This tutorial is targeted at scientists and engineers and should serve as an introduction to the main ideas of nonlinear filtering, and as a segway to more advanced and specialized literature.Comment: 64 page

Hitchhiker's guide to the fractional Sobolev spaces

This paper deals with the fractional Sobolev spaces W^[s,p]. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains

A hitchhiker's guide to understanding exchange rates

A nontechnical guide to exchange rates that discusses the role of inflation and monetary policy in determining exchange rate movements, uses balance-of-payments concepts to illustrate the economic role of the real exchange rate, and examines the crucial role of expectations.Foreign exchange rates

A Hitchhiker's Guide to Statistical Comparisons of Reinforcement Learning Algorithms

Consistently checking the statistical significance of experimental results is the first mandatory step towards reproducible science. This paper presents a hitchhiker's guide to rigorous comparisons of reinforcement learning algorithms. After introducing the concepts of statistical testing, we review the relevant statistical tests and compare them empirically in terms of false positive rate and statistical power as a function of the sample size (number of seeds) and effect size. We further investigate the robustness of these tests to violations of the most common hypotheses (normal distributions, same distributions, equal variances). Beside simulations, we compare empirical distributions obtained by running Soft-Actor Critic and Twin-Delayed Deep Deterministic Policy Gradient on Half-Cheetah. We conclude by providing guidelines and code to perform rigorous comparisons of RL algorithm performances.Comment: 8 pages + supplementary materia

The hitchhiker's guide to avian malaria

The ecological mechanisms underlying the dispersal of parasites are poorly understood, which is of particular concern in view of currently emerging infectious diseases. In a new study, Pérez-Tris and Bensch examined the distribution and prevalence of avian malaria in a migratory bird across Western Europe. They concluded that repeated independent evolution of year-round transmission has enabled some avian malaria lineages to become more widespread, and more prevalent, than lineages that are transmitted only during the summer. This study blurs the boundaries of evolutionary ecology, epidemiology and macroecology with great potential for cross-disciplinary research