Physical Sciences Forum, Volume 3, Issue 1

The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids in thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when information abou...

The mathematical formalism of quantum mechanics is derived or “reconstructed” from more basic considerations of the probability theory and information geometry. The starting point is the recognition that probabilities are central to QM; t...

We present an approach to enhance the performance and flexibility of the Bayesian inference of model parameters based on observations of the measured data. Going beyond the usual surrogate-enhanced Monte-Carlo or optimization methods that focus on a...

The Full Bayesian Significance Test (FBST) has been proposed as a convenient method to replace frequentist p-values for testing a precise hypothesis. Although the FBST enjoys various appealing properties, the purpose of this paper is to investigate t...

Why quantum? Why spacetime? We find that the key idea underlying both is uncertainty. In a world lacking probes of unlimited delicacy, our knowledge of quantities is necessarily accompanied by uncertainty. Consequently, physics requires a calculus of...

Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an uncon...

Earth’s gravitational field provides invaluable insights into the changing nature of our planet. It reflects mass change caused by geophysical processes like continental hydrology, changes in the cryosphere or mass flux in the ocean. Satellite...

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model’s credibility. For computationally expensive simulations, this is often feasible only via surrogate models that are learne...

In previously published articles, our research group has developed the Haphazard Intentional Sampling method and compared it to the Rerandomization method proposed by K.Morgan and D.Rubin. In this article, we compare both methods to the pure randomiz...

A Gaussian-process surrogate model based on already acquired data is employed to approximate an unknown target surface. In order to optimally locate the next function evaluations in parameter space a whole variety of utility functions are at one’s di...

Dynamics of many classical physics systems are described in terms of Hamilton’s equations. Commonly, initial conditions are only imperfectly known. The associated volume in phase space is preserved over time due to the symplecticity of the Hami...

We derive a weakly informative prior for a set of ordered resonance frequencies from Jaynes’ principle of maximum entropy. The prior facilitates model selection problems in which both the number and the values of the resonance frequencies are unknown...

Here I investigate some mathematical aspects of the maximum entropy theory of ecology (METE). In particular I address the geometrical structure of METE endowed by information geometry. As novel results, the macrostate entropy is calculated analytical...