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1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

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Earth and Space Sciences · 术语表

什么是 Model resolution matrix？

Definition 1.13 University Earth and Space Sciences — Year 3 · 第 1 章 — Seismology and Earth Imaging

For a linear estimate $\mathbf m_\varepsilon = \mathsf H_\varepsilon \mathbf d$ of the model $\mathbf m$ from data $\mathbf d = \mathsf G\mathbf m + \mathbf e$ , the model resolution matrix is $\mathsf R = \mathsf H_\varepsilon\mathsf G$ , so that

\mathbf m_\varepsilon = \mathsf R\,\mathbf m + \mathsf H_\varepsilon\mathbf e .

For damped least squares, $\mathsf R = (\mathsf N + \varepsilon^2\mathsf I)^{-1} \mathsf N$ . Row $j$ of $\mathsf R$ shows how the estimate of parameter $j$ averages the true parameters; $\mathsf R = \mathsf I$ means perfect resolution.

The linear inverse problem as a loop (schematic). The forward problem predicts data from a model; the misfit, weighted by the data errors, measures the disagreement; the regularisation term keeps the model small; minimising their sum gives the estimate, which is only interpretable together with its resolution matrix and covariance.

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