2005/08/02 by T. Podobnik, Tomaz Podobnik, Podobnik, Tomaz +3 · 1 citation
Mathematics · Neuroscience · Physics and Astronomy · #A priori and a posteriori #Artificial intelligence #Bayesian inference #Bayesian probability #Cognitive Science and Education Research #Computer science #Data Analysis #Econometrics #Epistemology #FOS: Physical sciences #Fiducial inference #Frequentist inference #High Energy Physics - Experiment (hep-ex) #Ignorance #Inductive reasoning #Inference #Limit (mathematics) #Mathematics #Philosophy #Sampling (signal processing) #Statistical Mechanics and Entropy #Statistical inference #Statistics #Statistics Education and Methodologies #Statistics and Probability (physics.data-an) #hep-ex #physics.data-an
paper · pdf · doi:10.48550/arxiv.physics/0508017
published in arXiv (Cornell University) (Cornell University) · 88 pages, 5 figures
arxiv created 2005/08/02 · openalex publication_date 2005/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The theory of probability, based on very general rules referred to as the Cox-Polya-Jaynes Desiderata, can be used both as a theory of random mass phenomena and as a quantitative theory of plausible inference about the parameters of sampling distributions. The existing applications of the Desiderata must be extended in order to allow for consistent inferences in the limit of complete a priori ignorance about the values of the parameters. Since the limits of consistent quantitative inference from incomplete information can clearly be established, the developed theory is necessarily an effective one. It is interesting to note that when applying the Desiderata strictly, we find no contradictions between the so-called Bayesian and frequentist schools of inductive reasoning.