物理模型构造中的似然法和Fisher信息

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…

DerivKit: 稳定的数值导数连接Fisher预测与MCMC

DerivKit: stable numerical derivatives bridging Fisher forecasts and MCMC

DerivKit通过稳定数值导数连接Fisher预测与MCMC，提供高阶似然近似和非高斯展开方法。

非高斯似然的配分函数方法：用于函数推断与 Fisher 泛函的配分

Partition function approach to non-Gaussian likelihoods: partitions for the inference of functions and the Fisher-functional

该研究基于 Kullback-Leibler 泛函散度构建路径积分形式的配分泛函与 Fisher 泛函，用于超新星约束暗能量状态方程的贝叶斯函数推断，并分析离散化复杂度与外推误差。

Fisher information vs. signal-to-noise ratio for a split detector

We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information. Although the signal-to-noise ratio is known to be simply related to the Fisher information under idealised detection, we find the two measures of precision differ markedly for a split detector. We show that a greater signal-to-noise ratio 'before' the detector leads to a greater information penalty, unless adaptive realignment is used. We find that with an …

关于使用导数近似似然进行引力波推断的研究

On the use of the Derivative Approximation for Likelihoods for Gravitational Wave Inference

本文比较了Fisher矩阵、导数近似似然(DALI)和传统MCMC方法在引力波后验推断中的精度和计算成本，发现DALI能以55倍更低的计算成本良好近似后验，并介绍了公共代码GWDALI 1.0版本。