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Lecture 12: Maximum likelihood (continued) 2 ﬁtting procedure! Midterm tools reviewed

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Page 1: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Lecture 12: Maximum likelihood (continued)

𝜒2 fitting procedure!

Midterm tools reviewed

Page 2: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

increasing temperature x in some arbitrary units

from Lecture 10: Maximum Likelihood discussion

Page 3: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Maximum Likelihood parameter errors?from Lecture 10:

Page 4: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Maximum Likelihood parameter errors?

Page 5: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Maximum Likelihood parameter errors?

Page 6: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

multivariate normal distribution

Page 7: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

linear error propagation for arbitrary function of parameters

Page 8: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

linear error propagation for arbitrary function of parameters

Page 9: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Sampling the posterior histogram

Page 10: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Sampling the posterior histogram

Page 11: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

𝜒2 distribution goodness of fit

Page 12: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

𝜒2 distribution (from Lecture 10)

Page 13: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

confidence intervals

Page 14: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

𝜒2 distribution

Page 15: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

confidence intervals

Page 16: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

confidence intervals

Monte Carlo to generate parameters (non-linear models):

Page 17: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

confidence intervals

Monte Carlo distribution of the non-linear parameters:

Page 18: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

what is the Degree of Freedom?

Page 19: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

what is the Degree of Freedom?

Page 20: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

what is the Degree of Freedom?

Page 21: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

what is the Degree of Freedom?

Page 22: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

Goodness-of-fit

Page 23: Lecture 12: Maximum likelihood (continued) · This is the covariance structure of all the parameters, and indeed ... the magic word is: ... 5.89 9.24 15.1

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