1996/07/25 by William Bialek, Curtis G. Callan, Steven Strong +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Gaussian Processes and Bayesian Inference #Mathematical and Theoretical Analysis #Statistics Education and Methodologies #adap-org #cond-mat #hep-th #nlin.AO
paper · pdf · doi:10.1103/physrevlett.77.4693
published as Phys.Rev.Lett. 77 (1996) 4693-4697 · 12 pages, REVTEX
arxiv created 1996/07/25 · openalex publication_date 1996/12/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Imagine being shown N samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless you have some prior notions about what to expect. From a Bayesian point of view one needs an a priori distribution on the space of possible probability distributions, which defines a scalar field theory. In one dimension, free field theory with a normalization constraint provides a tractable formulation of the problem, and we discuss generalizations to higher dimensions.