lecture 10: maximum likelihood iv. (nonlinear least square fits)...fitting is usually presented in...
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![Page 1: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/1.jpg)
Lecture 10: Maximum likelihood IV.(nonlinear least square fits)
𝜒2 fitting procedure!
![Page 2: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/2.jpg)
increasing temperature x in some arbitrary units
measured value of 2p-0.4 as a function of x
x
from Lecture 9:
= 2·p(x) - 0.4 = y(x|b)
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Maximum Likelihood discussionfrom Lecture 9:
frequentist: P(b) ~ δ(b-b0) b0?
Bayesian: P(b) ~ const simplest,leads to same b0 determination
repeating the experiment with yi and 𝜎i we also test f(x) as a hypothesis
![Page 4: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/4.jpg)
increasing temperature x in some arbitrary units
from Lecture 9: Maximum Likelihood discussion
![Page 5: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/5.jpg)
Maximum Likelihood parameter errors?from Lecture 9:
![Page 6: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/6.jpg)
Maximum Likelihood parameter errors?
![Page 7: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/7.jpg)
Maximum Likelihood parameter errors?
![Page 8: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/8.jpg)
𝜒2 distribution goodness of fit
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𝜒2 distribution (from Lecture 9)
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confidence intervals
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𝜒2 distribution
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confidence intervals
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what is the Degree of Freedom?
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what is the Degree of Freedom?
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what is the Degree of Freedom?
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what is the Degree of Freedom?
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Goodness-of-fit
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linear error propagation for arbitrary function of parameters
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linear error propagation for arbitrary function of parameters
![Page 20: Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in frequentist, Ml-E language. But one can equally well think of it as Bayesian: 1](https://reader033.vdocuments.site/reader033/viewer/2022050109/5f475852512ba0268b7edda7/html5/thumbnails/20.jpg)
Sampling the posterior histogram
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Sampling the posterior histogram