Lectures 11: Maximum likelihood IV. (nonlinear least...

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Lectures 11: Maximum likelihood IV. (nonlinear least square fits) 2 fitting procedure!

Transcript of Lectures 11: Maximum likelihood IV. (nonlinear least...

Page 1: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

Lectures 11: Maximum likelihood IV.(nonlinear least square fits)

𝜒2 fitting procedure!

Page 2: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

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)

Page 3: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

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: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

increasing temperature x in some arbitrary units

from Lecture 9: Maximum Likelihood discussion

Page 5: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

Maximum Likelihood parameter errors?from Lecture 9:

Page 6: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

Maximum Likelihood parameter errors?

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Maximum Likelihood parameter errors?

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𝜒2 distribution goodness of fit

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confidence intervals

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𝜒2 distribution (from Lecture 10)

Page 11: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

𝜒2 distribution

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confidence intervals

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what is the Degree of Freedom?

Page 14: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

what is the Degree of Freedom?

Page 15: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

what is the Degree of Freedom?

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what is the Degree of Freedom?

Page 17: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,

Goodness-of-fit

Page 18: Lectures 11: Maximum likelihood IV. (nonlinear least ...courses.physics.ucsd.edu/2016/Fall/physics139/Lectures/Lecture11/... · This is the covariance structure of all the parameters,