Upper Limits from Counting Experiments with Multiple Pipelines

In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using different instruments, different event detection algorithms, or observations over multiple time intervals. We demonstrate how to generalize the classical frequentist upper limit calculation to the case where multiple counts of events are made over one or more time intervals using several (not necessarily independent) procedures. We show how different choices of the rank ordering of possible outcomes in the space of counts correspond to applying different levels of significance to the various measurements. We propose an ordering that is matched to the sensitivity of the different measurement procedures and show that in typical cases it gives stronger upper limits than other choices. As an example, we show how this method can be applied to searches for gravitational-wave bursts, where multiple burst-detection algorithms analyse the same data set, and demonstrate how a single combined upper limit can be set on the gravitational-wave burst rate.Comment: 26 pages (CQG style), 8 figures. Added study of robustness of limits

Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.Comment: 17 pages, 5 figure

The Loudest Event Statistic: General Formulation, Properties and Applications

The use of the loudest observed event to generate statistical statements about rate and strength has become standard in searches for gravitational waves from compact binaries and pulsars. The Bayesian formulation of the method is generalized in this paper to allow for uncertainties both in the background estimate and in the properties of the population being constrained. The method is also extended to allow rate interval construction. Finally, it is shown how to combine the results from multiple experiments and a comparison is drawn between the upper limit obtained in a single search and the upper limit obtained by combining the results of two experiments each of half the original duration. To illustrate this, we look at an example case, motivated by the search for gravitational waves from binary inspiral.Comment: 11 pages, 8 figure