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Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
We present a novel Bayesian model and a corresponding robust, probabilistic calibration procedure for the CORSAIR polarimeter that can be applied to other polarimeters. Our calibration procedure combines existing Mueller matrix…
We propose a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this article is restricted to…
Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…
The Fisher Information Matrix formalism is extended to cases where the data is divided into two parts (X,Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary…
In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold $\mathrm{SO}(3)\times\mathbb{R}^n$. It is constructed by conditioning a (9+n)-variate…
We study the sample variance of the matter power spectrum for the standard Lambda Cold Dark Matter universe. We use a total of 5000 cosmological N-body simulations to study in detail the distribution of best-fit cosmological parameters and…
In this paper we extent the previously published DALI-approximation for likelihoods to cases in which the parameter dependency is in the covariance matrix. The approximation recovers non-Gaussian likelihoods, and reduces to the Fisher…
Fisher-matrix methods are widely used to predict how accurately parameters can be estimated. Being computationally efficient, this approach is prompted by the large number of signals simulated in forecast studies for future…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
The cosmological information encapsulated within a weak lensing signal can be accessed via the power spectrum of the so called convergence. We use the Fisher information matrix formalism with the convergence power spectrum as the observable…
Fisher forecasts are a common tool in cosmology with applications ranging from survey planning to the development of new cosmological probes. While frequently adopted, they are subject to numerical instabilities that need to be carefully…
Standard chance constrained control algorithms typically rely on the assumption that uncertainties in vehicle states obey Gaussian statistics. Highly nonlinear systems tend to disrupt Gaussianity, challenging standard chance-constrained…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
We use Fisher Matrix analysis techniques to forecast the cosmological impact of astrophysical tests of the stability of the fine-structure constant to be carried out by the forthcoming ESPRESSO spectrograph at the VLT (due for commissioning…
Weak gravitational lensing has become a common tool to constrain the cosmological model. The majority of the methods to derive constraints on cosmological parameters use second-order statistics of the cosmic shear. Despite their success,…
We describe a method for forecasting errors in interferometric measurements of polarization of the cosmic microwave background (CMB) radiation, based on the use of the Fisher matrix calculated from the visibility covariance and relation…
We derive a Fisher matrix for the parameters characterising a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes…
Assuming a Euclid-like weak lensing data set, we compare different methods of dealing with its inherent parameter degeneracies. Including priors into a data analysis can mask the information content of a given data set alone. However, since…