Related papers: Beyond Fisher Forecasting for Cosmology
Statistical methods for automatically identifying dependent word pairs (i.e. dependent bigrams) in a corpus of natural language text have traditionally been performed using asymptotic tests of significance. This paper suggests that Fisher's…
Galaxy surveys that map multiple species of tracers of large-scale structure can improve the constraints on some cosmological parameters far beyond the limits imposed by a simplistic interpretation of cosmic variance. This enhancement…
The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap…
How to design a Markov Decision Process (MDP) based radar controller that makes small sacrifices in performance to mask its sensing plan from an adversary? The radar controller purposefully minimizes the Fisher information of its emissions…
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…
In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
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…
Maximum likelihood estimation is a popular method in statistical inference. As a way of assessing the accuracy of the maximum likelihood estimate (MLE), the calculation of the covariance matrix of the MLE is of great interest in practice.…
Key science questions, such as galaxy distance estimation and weather forecasting, often require knowing the full predictive distribution of a target variable $y$ given complex inputs $\mathbf{x}$. Despite recent advances in machine…
Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
We introduce a method---called Fisher exact scanning (FES)---for testing and identifying variable dependency that generalizes Fisher's exact test on $2\times 2$ contingency tables to $R\times C$ contingency tables and continuous sample…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
Standard cosmological analysis, which relies on two-point statistics, fails to extract the full information of the data. This limits our ability to constrain with precision cosmological parameters. Thus, recent years have seen a paradigm…
In the context of the usual calibration model, we consider the case in which the independent variable is unobservable, but a pre-fixed value on its surrogate is available. Thus, considering controlled variables and assuming that the…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
Using the Fisher matrix formalism, we quantitatively investigate the constraints on a 10 dimensional space of cosmological parameters which may be obtained with future cluster surveys. We explore the dependence of the Omega_m constraint on…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
Making inferences about physical properties of the Universe requires knowledge of the data likelihood. A Gaussian distribution is commonly assumed for the uncertainties with a covariance matrix estimated from a set of simulations. The noise…