Related papers: XAFS spectroscopy. II. Statistical evaluations in …
We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…
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.…
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
This study aims to investigate the utilization of Bayesian techniques for the calibration of micro-electro-mechanical systems (MEMS) accelerometers. These devices have garnered substantial interest in various practical applications and…
We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -- geometric fit, Kasa fit, Pratt fit, and Taubin fit -- is…
When teaching and discussing statistical assumptions, our focus is oftentimes placed on how to test and address potential violations rather than the effects of violating assumptions on the estimates produced by our statistical models. The…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical…
Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…
Astronomers often deal with data where the covariates and the dependent variable are measured with heteroscedastic non-Gaussian error. For instance, while TESS and Kepler datasets provide a wealth of information, addressing the challenges…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
In observational causal inference, exact covariate matching plays two statistical roles: (i) it effectively controls for bias due to measured confounding; (ii) it justifies assumption-free inference based on randomization tests. This paper…
In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the…