Power Spectrum Estimation I. Basics

This paper and its companion form an extended version of notes provided to participants in the Valencia September 2004 summer school on Data Analysis in Cosmology. The papers offer a pedagogical introduction to the problem of estimating the power spectrum from galaxy surveys. The intention is to focus on concepts rather than on technical detail, but enough mathematics is provided to point the student in the right direction. This first paper presents background material. It collects some essential definitions, discusses traditional methods for measuring power, notably the Feldman-Kaiser-Peacock (1994) [2] method, and introduces Bayesian analysis, Fisher matrices, and maximum likelihood. For pedagogy and brevity, several derivations are set as exercises for the reader. At the summer school, multiple choice questions, included herein, were used to convey some didactic ideas, and provoked a little lively debate.