Related papers: Revisiting the Question of Information Content of …
In this study, we applied Bayesian inference for extended X-ray absorption fine structure (EXAFS) to select an appropriate basis from among Fourier, wavelet and advanced Fourier bases, and we extracted a radial distribution function (RDF)…
All measurements of continuous signals rely on taking discrete snapshots, with the Nyquist-Shannon theorem dictating sampling paradigms. We present a broader framework of information-optimal measurement, showing that traditional sampling is…
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…
In this paper, we present a new multi-scale information content calculation method based on Shannon information (and Shannon entropy). The original method described by Claude E. Shannon and based on the logarithm of the probability of…
A Bayesian method application to the deconvolution of EXAFS spectra is considered. It is shown that for purposes of EXAFS spectroscopy, from the infinitely large number of Bayesian solutions it is possible to determine an optimal range of…
Analysis of the extended X-ray absorption fine structure (EXAFS) can yield local structural information in magic size clusters even when other structural methods (such as X-ray diffraction) fail, but typically requires an initial guess --…
The necessary and sufficient conditions of optimality of the decoding of quantum signals minimizing the Bayesian risk are generalized for the Shannon mutual information criteria. It is shown that for a linear channel with Gaussian boson…
While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to asses the amount and quality of information inside a noisy optical channel. A number of theoretical…
Optical phase measurement is a simple example of a quantum--limited measurement problem with important applications in metrology such as gravitational wave detection. The formulation of optimal strategies for such measurements is an…
In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined…
We present a strategy for selecting the values of elasticity parameters by comparing walk-away vertical seismic profiling data with a multilayered model in the context of Bayesian Information Criterion. We consider $P$-wave traveltimes and…
In experiments searching for axionic dark matter, the use of the standard threshold-based data analysis discards valuable information. We present a Bayesian analysis framework that builds on an existing processing protocol to extract more…
In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…
The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve…
Neutron and X-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of a model-dependent methods. This…
Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data…
The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict…
We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes' theorem together with the principle of maximum…