Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in...

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Lecture 10: Maximum likelihood IV. (nonlinear least square fits) 2 fitting procedure!

Transcript of Lecture 10: Maximum likelihood IV. (nonlinear least square fits)...Fitting is usually presented in...

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

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

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: 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

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

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

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

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

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

𝜒2 distribution goodness of fit

Page 9: 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

𝜒2 distribution (from Lecture 9)

Page 10: 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

confidence intervals

Page 11: 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

𝜒2 distribution

Page 12: 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

confidence intervals

Page 13: 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

what is the Degree of Freedom?

Page 14: 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

what is the Degree of Freedom?

Page 15: 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

what is the Degree of Freedom?

Page 16: 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

what is the Degree of Freedom?

Page 17: 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

Goodness-of-fit

Page 18: 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

linear error propagation for arbitrary function of parameters

Page 19: 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

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

Sampling the posterior histogram

Page 21: 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

Sampling the posterior histogram