Related papers: On possible issues of Backus average
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of…
Ground motion scenarios exists for most of the seismically active areas around the globe. They essentially correspond to shaking level maps at given earthquake return times which are used as reference for the likely areas under threat from…
Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and…
The conditional value of a stationary random process, given the level-upcrossing of another dependent stationary random process, is considered. Assuming that both processes are weakly non-Gaussian, an analytical approximation for the…
In this work the issue of Bayesian inference for stationary data is addressed. Therefor a parametrization of a statistically suitable subspace of the the shift-ergodic probability measures on a Cartesian product of some finite state space…
Analog forecasting has been applied in a variety of fields for predicting future states of complex nonlinear systems that require flexible forecasting methods. Past analog methods have almost exclu- sively been used in an empirical…
We employ Bayesian Model Averaging (BMA) as a powerful statistical framework to address key cosmological questions about the universe's fundamental properties. We explore extensions beyond the standard $\Lambda$CDM model, considering a…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
The two fundamental assumptions in cosmology are that the Universe is statistically homogeneous and isotropic when averaged on large scales. Given the big implication of these assumptions, there has been a lot of statistical tests carried…
Major issues arising in the theory of Bose-Einstein condensation are reviewed. These issues, although being principally important, are very often misunderstood, which results in wrong conclusions. The basic point is global gauge symmetry…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
Coastal flooding drives considerable risks to many communities, but projections of future flood risks are deeply uncertain. The paucity of observations of extreme events often motivates the use of statistical approaches to model the…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states.…
Backus (1962) developed his technique for homogenization of a layered structure solely within the context of linear elastic theory. In this paper we propose an extended use of Backus average for finitely deformed materials of a layered…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…