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Lectures 10: Maximum likelihood III. (nonlinear least square fits) 2 fitting procedure!

Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

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Page 1: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Lectures 10: Maximum likelihood III.(nonlinear least square fits)

𝜒2 fitting procedure!

Page 2: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

increasing temperature x in some arbitrary units

measured value of 2p-0.4 as a function of x

x

from Lecture 9:

Page 3: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood discussionfrom Lecture 9:

Page 4: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

increasing temperature x in some arbitrary units

from Lecture 9: Maximum Likelihood discussion

Page 5: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

𝜒2 distribution

Page 6: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

𝚪 function 1-pager

Page 7: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

𝜒2 distribution

Page 8: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

characteristic function by Fourier transformation:

(1-2i*t)-𝜈/2

𝜒2 distribution

Page 9: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood parameter errors?𝜒2 distribution

Page 10: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood parameter errors?𝜒2 distribution

Page 11: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood parameter errors?𝜒2 distribution

Page 12: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood parameter errors?𝜒2 distribution

Page 13: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood marginalized parameters𝜒2 distribution

Page 14: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

Maximum Likelihood marginalized parameters𝜒2 distribution

Page 15: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

generic idea of covariance matrix

Page 16: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

generic idea of covariance matrix

Page 17: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

correlated data - first glimpse

Page 18: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E

correlated data - first glimpse

Page 19: Lectures 10: Maximum likelihood III. (nonlinear least ... · bfit = 1.1235 3.2654 .4832 Suppose that what we really care about is the area of the bump, and that the other ... Ml-E