Related papers: A Quantitative Occam's Razor
The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a…
We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
We investigate the evidence/flexibility (i.e., "Occam") paradigm and demonstrate the theoretical and empirical consistency of Bayesian evidence for the task of determining an appropriate generative model for network data. This model…
Prompted by misconceptions in the recent literature, we review the justifications for naturalness arguments and Occam's razor found in Bayesian statistics. We discuss the automatic Occam's razor that emerges in Bayesian formalism, bringing…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
We establish a generic theoretical tool to construct probabilistic bounds for algorithms where the output is a subset of objects from an initial pool of candidates (or more generally, a probability distribution on said pool). This general…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
User opinions expressed in the form of ratings can influence an individual's view of an item. However, the true quality of an item is often obfuscated by user biases, and it is not obvious from the observed ratings the importance different…
Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…
The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of low-temperature expansions, we arrive at a systematic series for the Bayesian posterior…
The present paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and…
Detecting quality in large unstructured datasets requires capacities far beyond the limits of human perception and communicability and, as a result, there is an emerging trend towards increasingly complex analytic solutions in data science…
Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum…
We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…
In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…
In this note we introduce linear regression with basis functions in order to apply Bayesian model selection. The goal is to incorporate Occam's razor as provided by Bayes analysis in order to automatically pick the model optimally able to…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
This paper applies the recently axiomatized Optimum Information Principle (minimize the Kullback-Leibler information subject to all relevant information) to nonparametric density estimation, which provides a theoretical foundation as well…