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Fitting (special modeling)

Fitting (special modeling). 预习 BR2003, Chap. 6. 董小波 2009.11.18. Schematic. The role of data analysis. On the learning of curve fitting. 分清三种性质的学习内容： 原理性 技术性 / 方法性 操作性 由于选课同学层次弥散极大，请各人根据不同的阶段、个人不同的需求等，给予不同的学习时间权重。 在 独观大略 与 惟务精纯 之间平衡. 3. 想象力 与 数据分析 之间的平衡.

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Fitting (special modeling)

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  1. Fitting (special modeling) 预习BR2003, Chap. 6 董小波 2009.11.18

  2. Schematic The role of data analysis

  3. On the learning of curve fitting 分清三种性质的学习内容： • 原理性 • 技术性/方法性 • 操作性 • 由于选课同学层次弥散极大，请各人根据不同的阶段、个人不同的需求等，给予不同的学习时间权重。 • 在独观大略 与 惟务精纯 之间平衡

  4. 3. 想象力 与 数据分析 之间的平衡

  5. Anyway, data are necessary. Data! Data! He cried impatiently, I can’t make bricks without clay. --- <The Copper Beeches>, Conan Doyle Then, The science and art of data handling and decision making: Data Analysis

  6. 数学与统计 统计的理论基础： 现代科学视野下的偶然性与因果律 量子力学的几率解释，不确定性原理； 物理定律（如相对论、量子力学等）的变换不变性 [若干例子。人（观察者）有一定的自由，然而不昧因果。] 变量vs.随机变量 知识：对不确定性的量度 —— “给出概率！” 。 一种（新的）思维方法：基于概率的推理方法。 BTW, even a possibility：因果律是一定初始条件（或选择）下的 大数极限(统计学近似)。

  7. 进一步的问题 偶然性（随机、不确定性等）的起源？ E.g., 测量误差中，量子涨落（then, what is the origin of the quantum uncertainty? Unknown to us still.） 另一种可能：随机性来源于底层的确定论系统，是一种（极好的）统计近似性质。比如布朗运动: Anyway, what we concern in this course: 应用随机性，应用统计学理论与方法，从而解决天体物理中的问题。

  8. Curve fitting • Step 1: 选定函数模型（假设/假说） • Step 2: 模型是否正确？（假说检验） 【e.g., 参数个数是否足够？】 • Step 3: 拟合得到的最佳参数值，及其置信区间 Our goal: Grasp and practice general data analysis in one semester (60hrs).

  9. Overview of Chap.6 • Focused on Subsection 6.2 specifically, careful only for ``Method of Maximum Likelihood’’. • To glance over Subsection 6.3 • To read ``Chisq Probability’’ (p.108) and ``Uncertanties in the Parameters’’ (p.109) [Note: actually, nobody bothers to estimate the Uncertanties in the Parameters using the formal error propagation equation.] • To skip other sections if you have no time/interest.

  10. Only one thing in this Chapter you should understand z Maximizing the likelyhood  minimizing 统计量z (在最佳参数值a,b附近，z符合chi^2分布。后面讲述。)

  11. For the next class • Read in advance chapter 7. • Pay much time to finish the case, see: ftp://210.45.66.48/teaching/methods09/Course_Notes_and_Homeworks/fitting/ or http://ustcastroph.blog.sohu.com/#tp_95a1b1f5a7a Advice: practice is more important than reading.

  12. Case discussion Today 现有一个类星体光谱观测样本，红移在0.45—0.8之间，共2092个源。根据光谱，我们可以测得MgII λ2800A发射线的半高全宽（FWHM）和等值宽度（EW）；可以测得类星体连续谱在3000A处的光度[ L3000= 3000A * L_lambda(3000) ]。根据以上参数我们还可以计算出类星体中心黑洞的质量（M）和Eddington ratio（L/Ledd）。数据及其简要说明见data_for_spearman.txt文件。 我们要研究：EW(MgII)大小是否由以上某一个参量主要决定（L3000, FWHM, M, L/Ledd），为此我们开展相关与偏相关分析。最后，根据Spearman相关与偏相关分析的结果，给出你的结论。

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