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Urban Informatics Fall 2015 dr. federica bianco [email protected] @fedhere

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V: Likelihood and Regression Models ASK QUESTIONS!!

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V: Likelihood and Regression Models • Good practices with data: falsifiability, reproducibility • Basic data retrieving and munging: APIs, Data formats • Basic statistics: distributions and their moments • Hypothesis testing: p-value, statistical significance • Statistical and Systematic errors • Goodness of fit tests Recap:

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V: Likelihood and Regression Models • Good practices with data: falsifiability, reproducibility • Basic data retrieving and munging: APIs, Data formats • Basic statistics: distributions and their moments • Hypothesis testing: p-value, statistical significance • Statistical and Systematic errors • Goodness of fit tests Recap: Today: • Likelihood • Linear Regression • Predictive models

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V: Likelihood and Regression Models Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood μ σ

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Probability Likelihood

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V: Likelihood and Regression Models Likelihood-ratio tests

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V: Likelihood and Regression Models LR = _______________________________ False Negative True Negative

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V: Likelihood and Regression Models This statistic is chi-squared distributed with degrees of freedom equal to the difference in the number of degrees of freedom between the two models (i.e., the number of variables added to the model). LR = -2 loge ____________ L(model 1) L(model 2)

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V: Likelihood and Regression Models This statistic is chi-squared distributed with degrees of freedom equal to the difference in the number of degrees of freedom between the two models (i.e., the number of variables added to the model). LR = -2 loge ____________ L(model 1) L(model 2)

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V: Likelihood and Regression Models https://github.com/fedhere/UInotebooks/blob/master/ line_fit_and_residuals.ipynb

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V: Likelihood and Regression Models Maximizing Likelihood

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V: Likelihood and Regression Models Probability Likelihood Given some observations x we want to model them with the best function: the one that is MAXIMALLY LIKELY.

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V: Likelihood and Regression Models Probability Likelihood Given some observations x we want to model them with the best function: the one that is MAXIMALLY LIKELY. After we choose a functional form (N) for the model we want to choose the parameters that maximize

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V: Likelihood and Regression Models Probability Likelihood FIND µ*, σ* | = max( )

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V: Likelihood and Regression Models Logarithm:

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V: Likelihood and Regression Models Logarithm: MONOTONICALLY INCREASING

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V: Likelihood and Regression Models Logarithm: MONOTONICALLY INCREASING if x grows, log(x) grows, if x decreases, log(x) decreases the location of the maximum is the same!

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V: Likelihood and Regression Models Logarithm: MONOTONICALLY INCREASING SUPPORT : (0: ]

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V: Likelihood and Regression Models Logarithm: MONOTONICALLY INCREASING SUPPORT : (0: ] Not a problem cause L like P is positive defined

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V: Likelihood and Regression Models Probability log Likelihood

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V: Likelihood and Regression Models Probability log Likelihood

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V: Likelihood and Regression Models Probability log Likelihood

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V: Likelihood and Regression Models Probability log Likelihood

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V: Likelihood and Regression Models Probability log Likelihood

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V: Likelihood and Regression Models Probability log Likelihood

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V: Likelihood and Regression Models Probability max log Likelihood

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V: Likelihood and Regression Models Probability max log Likelihood

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V: Likelihood and Regression Models Probability max log Likelihood

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V: Likelihood and Regression Models This statistic is chi-squared distributed with degrees of freedom equal to the difference in the number of degrees of freedom between the two models (i.e., the number of variables added to the model). LR = -2 loge ________________ max L(model 1) max L(model 2)

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V: Likelihood and Regression Models This statistic is chi-squared distributed with degrees of freedom equal to the difference in the number of degrees of freedom between the two models (i.e., the number of variables added to the model). LR = -2 loge ________________ max L(model 1) max L(model 2)

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V: Likelihood and Regression Models J. Leek & P. Rodgers Leek&Rodgers 2015 in Science http://www.sciencemag.org/content/347/6228/1314.full.pdf

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V: Likelihood and Regression Models Causal / Mechanicistic

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models Predictive

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models http://www.sciencemag.org/content/349/6251/aac4716.full.pdf

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V: Likelihood and Regression Models Why?

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V: Likelihood and Regression Models git status

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V: Likelihood and Regression Models How?

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models

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V: Likelihood and Regression Models 11655.34 12155.24 Sum of residuals squared

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V: Likelihood and Regression Models https://github.com/fedhere/UInotebooks/blob/master/ Anscombe's%20Quartet.ipynb

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V: Likelihood and Regression Models https://github.com/fedhere/ PUI2015_fbianco/blob/master/HW5/ building_nrg.ipynb

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IV: Statistical analysis MUST KNOWS: • What is the likelihood • Likelihood ratio test • Minimization concepts • Least square fits (OLS, WLS)

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V: Likelihood and Regression Models Resources: Sarah Boslaugh, Dr. Paul Andrew Watters, 2008 Statistics in a Nutshell (Chapters 3,4,5) https://books.google.com/books/about/Statistics_in_a_Nutshell.html?id=ZnhgO65Pyl4C David M. Lane et al. Introduction to Statistics (XVIII) http://onlinestatbook.com/Online_Statistics_Education.epub http://onlinestatbook.com/2/index.html