Related papers: Priors in quantum Bayesian inference
A satisfactory resolution of the persistent quantum measurement problem remains stubbornly unresolved in spite of an overabundance of efforts of many prominent scientists over the decades. Among others, one key element is considered yet to…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…
Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when…
Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…
Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the…
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…
Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under…
Incompatibility of certain measurements -- impossibility of obtaining deterministic outcomes simultaneously -- is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to…
Every physical measuring needs a finite, different from zero measurement time and provides information in form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results…