Cosmological Parameter Estimation: Method

CMB anisotropy data could put powerful constraints on theories of the evolution of our Universe. Using the observations of the large number of CMB experiments, many studies have put constraints on cosmological parameters assuming different frameworks. Assuming for example inflationary paradigm, one can compute the confidence intervals on the different components of the energy densities, or the age of the Universe, inferred by the current set of CMB observations. The aim of this note is to present some of the available methods to derive the cosmological parameters with their confidence intervals from the CMB data, as well as some practical issues to investigate large number of parameters

Recursive Parameter Estimation: Convergence

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general statistical model and study convergence.Comment: 25 pages with 1 postscript figur

Estimation of Collision Impact Parameter

We demonstrate that the nuclear collision geometry (i.e. impact parameter) can be determined with 1.5 fm accuracy in an event-by-event analysis by measuring the transverse energy flow in the pseudorapidity region $3 \le |\eta| \le 5$ with a minimal dependence on collision dynamics details at the LHC energy scale. Using the HIJING model we have illustrated our calculation by a simulation of events of nucleus-nucleus interactions at the c.m.s energy from 1 up to 5.5 TeV per nucleon and various type of nuclei.Comment: 6 pages, 3 figure

Parameter Estimation from an Optimal Projection in a Local Environment

The parameter fit from a model grid is limited by our capability to reduce the number of models, taking into account the number of parameters and the non linear variation of the models with the parameters. The Local MultiLinear Regression (LMLR) algorithms allow one to fit linearly the data in a local environment. The MATISSE algorithm, developed in the context of the estimation of stellar parameters from the Gaia RVS spectra, is connected to this class of estimators. A two-steps procedure was introduced. A raw parameter estimation is first done in order to localize the parameter environment. The parameters are then estimated by projection on specific vectors computed for an optimal estimation. The MATISSE method is compared to the estimation using the objective analysis. In this framework, the kernel choice plays an important role. The environment needed for the parameter estimation can result from it. The determination of a first parameter set can be also avoided for this analysis. These procedures based on a local projection can be fruitfully applied to non linear parameter estimation if the number of data sets to be fitted is greater than the number of models

Unifying parameter estimation and the Deutsch-Jozsa algorithm for continuous variables

We reveal a close relationship between quantum metrology and the Deutsch-Jozsa algorithm on continuous-variable quantum systems. We develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter-estimation protocol or the Deutsch-Jozsa algorithm. The parameter-estimation part of the procedure attains the Heisenberg limit and is therefore optimal. Due to the use of approximate normalizable continuous-variable eigenstates, the Deutsch-Jozsa algorithm is probabilistic. The procedure estimates a value of an unknown parameter and solves the Deutsch-Jozsa problem without the use of any entanglement

Multimessenger Parameter Estimation of GW170817

We combine gravitational wave (GW) and electromagnetic (EM) data to perform a Bayesian parameter estimation of the binary neutron star (NS) merger GW170817. The EM likelihood is constructed from a fit to a large number of numerical relativity simulations which we combine with a lower bound on the mass of the remnant's accretion disk inferred from the modeling of the EM light curve. In comparison with previous works, our analysis yields a more precise determination of the tidal deformability of the binary, for which the EM data provide a lower bound, and of the mass ratio of the binary, with the EM data favoring a smaller mass asymmetry. The 90\% credible interval for the areal radius of a $1.4\ M_\odot$ NS is found to be $12.2^{+1.0}_{-0.8} \pm 0.2\ {\rm km}$ (statistical and systematic uncertainties).Comment: 7 pages, 3 figures, accepted to the EPJA Topical Issue: The first Neutron Star Merger Observation - Implications for Nuclear Physic

Parameter estimation for boundary value problems by integral equations of the second kind

This paper is concerned with the parameter estimation for boundary integral equations of the second kind. The parameter estimation technique through use of the spline collocation method is proposed. Based on the compactness assumption imposed on the parameter space, the convergence analysis for the numerical method of parameter estimation is discussed. The results obtained here are applied to a boundary parameter estimation for 2-D elliptic systems

An architecture for efficient gravitational wave parameter estimation with multimodal linear surrogate models

The recent direct observation of gravitational waves has further emphasized the desire for fast, low-cost, and accurate methods to infer the parameters of gravitational wave sources. Due to expense in waveform generation and data handling, the cost of evaluating the likelihood function limits the computational performance of these calculations. Building on recently developed surrogate models and a novel parameter estimation pipeline, we show how to quickly generate the likelihood function as an analytic, closed-form expression. Using a straightforward variant of a production-scale parameter estimation code, we demonstrate our method using surrogate models of effective-one-body and numerical relativity waveforms. Our study is the first time these models have been used for parameter estimation and one of the first ever parameter estimation calculations with multi-modal numerical relativity waveforms, which include all l <= 4 modes. Our grid-free method enables rapid parameter estimation for any waveform with a suitable reduced-order model. The methods described in this paper may also find use in other data analysis studies, such as vetting coincident events or the computation of the coalescing-compact-binary detection statistic.Comment: 10 pages, 3 figures, and 1 tabl