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In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of…
Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…
We perform a quantitative analysis of the gain/loss asymmetry for financial time series by using a Bayesian approach. In particular, we focus on some selected indices and analyze the statistical significance of the asymmetry amount through…
Organisms are nonequilibrium, stationary systems self-organized via spontaneous symmetry breaking and undergoing metabolic cycles with broken detailed balance in the environment. The thermodynamic free-energy principle describes an…
The problem of hypothesis testing is examined from both the historical and Bayesian points of view in the case that sampling is from an underlying joint probability distribution and the hypotheses tested for are those of independence and…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…
In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study,…
We study the statistical properties of the variation of the kinetic energy of a spherical Brownian particle that freely moves in an incompressible fluid at constant temperature. Based on the underdamped version of the generalized Langevin…
An understanding of how input parameter uncertainty in the numerical simulation of physical models leads to simulation output uncertainty is a challenging task. Common methods for quantifying output uncertainty, such as performing a grid or…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
The paper considers the problem of distributed adaptive linear parameter estimation in multi-agent inference networks. Local sensing model information is only partially available at the agents and inter-agent communication is assumed to be…
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible,…
An analyst observes an agent take a sequence of actions. The analyst does not have access to the agent's information and ponders whether the observed actions could be justified through a rational Bayesian model with a known utility…
Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…
Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations…
Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics have traditionally dominated empirical data analysis, and certainly remain prevalent in empirical software…