Related papers: Priors in quantum Bayesian inference
Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models…
Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…
We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…
We consider the apparatus in a quantum measurement process to be in a mixed state. We propose a simple upper bound on the probability of correctly distinguishing any number of mixed states. We use this to derive fundamental bounds on the…
The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…
Quantum measurements with feed-forward are crucial components of fault-tolerant quantum computers. We show how the error rate of such a measurement can be directly estimated by fitting the probability that successive randomly compiled…
Order effects occur when judgments about a hypothesis's probability given a sequence of information do not equal the probability of the same hypothesis when the information is reversed. Different experiments have been performed in the…
Prior probabilities of clinical hypotheses are not systematically used for clinical trial design yet, due to a concern that poor priors may lead to poor decisions. To address this concern, a conservative approach to Bayesian trial design is…
We present the amounts of information, fidelity, and reversibility obtained by arbitrary quantum measurements on completely unknown states. These quantities are expressed as functions of the singular values of a measurement operator…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
In this paper we investigate the potential for persuasion linked to the quantum indeterminacy of beliefs. We first formulate the persuasion problem in the context of quantum-like beliefs. We provide an economic example of belief…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
In this note we consider the stability of posterior measures occuring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function. This extends the well-posedness analysis of Bayesian inverse problems. In…
Informally, "Information Inconsistency" is the property that has been observed in many Bayesian hypothesis testing and model selection procedures whereby the Bayesian conclusion does not become definitive when the data seems to become…
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…