Bayesian Analysis

After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue of Bayesian analysis: the assignment of prior probabilities. The other example illustrates the use of Bayesian ideas in the real world of experimental physics.Comment: 14 pages, 5 figures, Workshop on Confidence Limits, CERN, 17-18 January, 200

Strategy for discovering a low-mass Higgs boson at the Fermilab Tevatron

We have studied the potential of the CDF and DZero experiments to discover a low-mass Standard Model Higgs boson, during Run II, via the processes $p\bar{p}$ -> WH -> $\ell\nu b\bar{b}$, $p\bar{p}$ -> ZH -> $\ell^{+}\ell^{-}b\bar{b}$ and $p\bar{p}$ -> ZH ->$\nu \bar{\nu} b\bar{b}$. We show that a multivariate analysis using neural networks, that exploits all the information contained within a set of event variables, leads to a significant reduction, with respect to {\em any} equivalent conventional analysis, in the integrated luminosity required to find a Standard Model Higgs boson in the mass range 90 GeV/c**2 < M_H < 130 GeV/c**2. The luminosity reduction is sufficient to bring the discovery of the Higgs boson within reach of the Tevatron experiments, given the anticipated integrated luminosities of Run II, whose scope has recently been expanded.Comment: 26 pages, 8 figures, 7 tables, to appear in Physical Review D, Minor fixes and revision

Optimizing Event Selection with the Random Grid Search

The random grid search (RGS) is a simple, but efficient, stochastic algorithm to find optimal cuts that was developed in the context of the search for the top quark at Fermilab in the mid-1990s. The algorithm, and associated code, have been enhanced recently with the introduction of two new cut types, one of which has been successfully used in searches for supersymmetry at the Large Hadron Collider. The RGS optimization algorithm is described along with the recent developments, which are illustrated with two examples from particle physics. One explores the optimization of the selection of vector boson fusion events in the four-lepton decay mode of the Higgs boson and the other optimizes SUSY searches using boosted objects and the razor variables.Comment: 26 pages, 9 figure

Simulation-Based Frequentist Inference with Tractable and Intractable Likelihoods

High-fidelity simulators that connect theoretical models with observations are indispensable tools in many sciences. When coupled with machine learning, a simulator makes it possible to infer the parameters of a theoretical model directly from real and simulated observations without explicit use of the likelihood function. This is of particular interest when the latter is intractable. We introduce a simple modification of the recently proposed likelihood-free frequentist inference (LF2I) approach that has some computational advantages. The utility of our algorithm is illustrated by applying it to three pedagogically interesting examples: the first is from cosmology, the second from high-energy physics and astronomy, both with tractable likelihoods, while the third, with an intractable likelihood, is from epidemiology

Reference priors for high energy physics

Bayesian inferences in high energy physics often use uniform prior distributions for parameters about which little or no information is available before data are collected. The resulting posterior distributions are therefore sensitive to the choice of parametrization for the problem and may even be improper if this choice is not carefully considered. Here we describe an extensively tested methodology, known as reference analysis, which allows one to construct parametrization-invariant priors that embody the notion of minimal informativeness in a mathematically well-defined sense. We apply this methodology to general cross section measurements and show that it yields sensible results. A recent measurement of the single top quark cross section illustrates the relevant techniques in a realistic situation