Related papers: The diachronic Bayesian
Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…
Concerning systematic effects, the recommendation given in the GUM is to correct for them, but unfortunately no detailed information is available, how to do this. This publication will show, how systematic measurement deviations can be…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…
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…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…
Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…
In this paper we propose a procedure to evaluate Bayesian confidence intervals in counting experiments where both signal and background fluctuations are described by the Poisson statistics. The results obtained when the method is applied to…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
This paper reviews the growing field of Bayesian prediction. Bayes point and interval prediction are defined and exemplified and situated in statistical prediction more generally. Then, four general approaches to Bayes prediction are…
It is often the case that risk assessment and prognostics are viewed as related but separate tasks. This chapter describes a risk-based approach to prognostics that seeks to provide a tighter coupling between risk assessment and fault…
In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and…
People naturally bring their prior beliefs to bear on how they interpret the new information, yet few formal models exist for accounting for the influence of users' prior beliefs in interactions with data presentations like visualizations.…
Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…
Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations…
Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or…
Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event given observed evidence. Since exact inference…