Inferring the intensity of Poisson processes at the limit of the detector sensitivity (with a case study on gravitational wave burst search)

We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters believe or not to having found the searched-for effect. Since this work uses the language of Bayesian theory, to which most physicists are not used, we find that it could be useful to practitioners to have in a single paper a simple presentation of Bayesian inference, together with an example of application of it in search of rare processes.Comment: 36 pages, 11 figures, Latex files using cernart.cls (included). This paper and related work are also available at http://www-zeus.roma1.infn.it/~agostini/prob+stat.htm

Bayesian Quadrature for Multiple Related Integrals

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to incomplete/finite information about the continuous mathematical problem being approximated. In this paper, we demonstrate that this paradigm can provide additional advantages, such as the possibility of transferring information between several numerical methods. This allows users to represent uncertainty in a more faithful manner and, as a by-product, provide increased numerical efficiency. We propose the first such numerical method by extending the well-known Bayesian quadrature algorithm to the case where we are interested in computing the integral of several related functions. We then prove convergence rates for the method in the well-specified and misspecified cases, and demonstrate its efficiency in the context of multi-fidelity models for complex engineering systems and a problem of global illumination in computer graphics.Comment: Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:5369-5378, 201

Confidence limits: what is the problem? Is there the solution?

This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in general, not possible, still a search result can be reported in a mostly unbiased and efficient way, which satisfies some desiderata which I believe are shared by the people interested in the subject. The simpler case of `closed likelihood' will also be treated, and I will discuss why a uniform prior on a sensible quantity is a very reasonable choice for most applications. In both cases, I think that much clarity will be achieved if we remove from scientific parlance the misleading expressions `confidence intervals' and `confidence levels'.Comment: 20 pages, 6 figures, using cernrepp.cls (included). Contribution to the Workshop on Confidence Limits, CERN, Geneva, 17-18 January 2000. This paper and related work are also available at http://www-zeus.roma1.infn.it/~agostini/prob+stat.htm