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A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master…

Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The…

For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always…

We analyze how to parametrize general modifications of the dark matter perturbations equations in a model-independent way. We prove that a general model with an imperfect and non-conserved dark matter fluid with bulk and shear viscosities…

We describe a method for computing the biases that systematic signals introduce in parameter estimation using a simple extension of the Fisher matrix formalism. This allows us to calculate the offset of the best fit parameters relative to…

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…

Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…

Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…

The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…

Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

In a Bayesian context, theoretical parameters are correlated random variables. Then, the constraints on one parameter can be improved by either measuring this parameter more precisely - or by measuring the other parameters more precisely.…

In future gravitational-wave (GW) detections, a large number of overlapping GW signals will appear in the data stream of detectors. When extracting information from one signal, the presence of other signals can cause large parameter…

An important step in the planning of future gravitational-wave (GW) detectors and of the networks they will form is the estimation of their detection and parameter-estimation capabilities, which is the basis of science-case studies. Several…

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach…

Fisher developed his geometric model to support the micro-mutationalism hypothesis which claims that small mutations are more likely to be beneficial and therefore to contribute to evolution and adaptation. While others have provided a…

The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape-measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing…

High-dimensional data clustering has become and remains a challenging task for modern statistics and machine learning, with a wide range of applications. We consider in this work the powerful discriminative latent mixture model, and we…

We forecast the sensitivity of thirty-five different combinations of future Cosmic Microwave Background and Large Scale Structure data sets to cosmological parameters and to the total neutrino mass. We work under conservative assumptions…