Fast Fisher Matrices and Lazy Likelihoods

Beyond Fisher: exact sampling distributions of the maximum-likelihood estimator in gravitational-wave parameter estimation

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise realizations, as well as the leading-order width of the posterior probability, but it is limited to high signal strengths often not realized in practice. By contrast, Monte Carlo Bayesian inference provides the full posterior for any signal strength, but it is too expensive to repeat for a representative set of noises. Here I describe an efficient semianalytical techni…

GWDALI：一种基于Fisher矩阵的引力波参数估计软件，超越高斯近似

GWDALI: A Fisher-matrix based software for gravitational wave parameter-estimation beyond Gaussian approximation

GWDALI是一种基于Fisher矩阵的Python软件，利用似然导数近似（DALI）超越高斯近似，预测地面引力波探测器网络的参数估计精度，并在Fisher矩阵不可逆时提供有效估计。

Geometrical Aspects on Parameter estimation of stochastic gravitational wave background: beyond the Fisher analysis

The maximum likelihood method is often used for parameter estimation in gravitational wave astronomy. Recently, an interesting approach was proposed by Vallisneri to evaluate the distributions of parameter estimation errors expected for the method. This approach is to statistically analyze the local peaks of the likelihood surface, and works efficiently even for signals with low signal-to-noise ratios. Focusing special attention to geometric structure of the likelihood surface, we follow the proposed approach and derive formulae for a simplified model of data analysis where the target signal h…

Parameter estimation from Gravitational waves generated by non-spinning binary black holes with laser interferometers: beyond the Fisher information

In this paper we apply to gravitational waves from non-spinning binary systems a recently intro- duced frequentist methodology to calculate analytically the error for a maximum likelihood estimate (MLE) of physical parameters. While existing literature focuses on using the Cramer Rao Lower bound (CRLB) and Monte Carlo simulations, we use a power expansion of the bias and covariance in inverse powers of the signal to noise ratio. The use of higher order derivatives of the likelihood function in the expansions makes the prediction also sensitive to the secondary lobes of the MLE probability dist…

Extending the Fisher Information Matrix in Gravitational-wave Data Analysis

The Fisher information matrix (FM) plays an important role in forecasts and inferences in many areas of physics. While giving fast parameter estimation with the Gaussian likelihood approximation in the parameter space, the FM can only give the ellipsoidal posterior contours of parameters and lose the higher-order information beyond Gaussianity. We extend the FM in gravitational-wave (GW) data analysis using the Derivative Approximation for LIkelihoods (DALI), a method to expand the likelihood while keeping it positive definite and normalizable at every order, for more accurate forecasts and in…

验证基于先验信息的Fisher矩阵分析与GWTC数据

Validating Prior-informed Fisher-matrix Analyses against GWTC Data

本文通过比较Fisher代码GWFish与GWTC数据，探讨先验信息对Fisher近似准确性的影响，发现高退化性参数化下先验信息的重要性，表明Fisher方法适用于爱因斯坦望远镜科学案例研究。