Related papers: Asymptotic Behavior of Free Energy When Optimal Pr…
A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In…
Within the framework of likelihood-based statistical tests for high energy physics measurements, we derive generalized expressions for estimating the statistical significance of discovery using the asymptotic approximations of Wilks and…
Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…
The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to non-equilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics…
In this paper we study the Random energy model - so called toy model of the spin glass theory - where the underlying distributions are compactly supported. We prove a general theorem on the asymptotics of free energy and obtain formulae in…
Many learning machines that have hierarchical structure or hidden variables are now being used in information science, artificial intelligence, and bioinformatics. However, several learning machines used in such fields are not regular but…
Recent results concerning asymptotic Bayes-optimality under sparsity (ABOS) of multiple testing procedures are extended to fairly generally distributed effect sizes under the alternative. An asymptotic framework is considered where both the…
Biological synaptic transmission is unreliable, and this unreliability likely degrades neural circuit performance. While there are biophysical mechanisms that can increase reliability, for instance by increasing vesicle release probability,…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…
Bayesian optimal design is a well-established approach to planning experiments. A distribution for the responses, i.e. a statistical model, is assumed which is dependent on unknown parameters. A utility function is then specified giving…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
We exhibit optimal control strategies for a simple toy problem in which the underlying dynamics depend on a parameter that is initially unknown and must be learned. We consider a cost function posed over a finite time interval, in contrast…
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:…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
In regular statistical models, the leave-one-out cross-validation is asymptotically equivalent to the Akaike information criterion. However, since many learning machines are singular statistical models, the asymptotic behavior of the…
Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…
The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…