Principle of Urban Informatics CUSP 2015 Lecture 5

2a1046385e6cf8e4d07d590f9821ece5?s=47 federica
October 08, 2015

Principle of Urban Informatics CUSP 2015 Lecture 5

2a1046385e6cf8e4d07d590f9821ece5?s=128

federica

October 08, 2015
Tweet

Transcript

  1. Urban Informatics Fall 2015 dr. federica bianco fb55@nyu.edu @fedhere

  2. V: Likelihood and Regression Models ASK QUESTIONS!!

  3. 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:
  4. 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
  5. V: Likelihood and Regression Models Likelihood

  6. V: Likelihood and Regression Models Probability Likelihood

  7. V: Likelihood and Regression Models Probability Likelihood

  8. V: Likelihood and Regression Models Probability Likelihood μ σ

  9. V: Likelihood and Regression Models Probability Likelihood

  10. V: Likelihood and Regression Models Probability Likelihood

  11. V: Likelihood and Regression Models Probability Likelihood

  12. V: Likelihood and Regression Models Probability Likelihood

  13. V: Likelihood and Regression Models Probability Likelihood

  14. V: Likelihood and Regression Models Probability Likelihood

  15. V: Likelihood and Regression Models Probability Likelihood

  16. V: Likelihood and Regression Models Probability Likelihood

  17. V: Likelihood and Regression Models Probability Likelihood

  18. V: Likelihood and Regression Models Probability Likelihood

  19. V: Likelihood and Regression Models Likelihood-ratio tests

  20. V: Likelihood and Regression Models LR = _______________________________ False Negative

    True Negative
  21. 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)
  22. 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)
  23. V: Likelihood and Regression Models https://github.com/fedhere/UInotebooks/blob/master/ line_fit_and_residuals.ipynb

  24. V: Likelihood and Regression Models Maximizing Likelihood

  25. 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.
  26. 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
  27. V: Likelihood and Regression Models Probability Likelihood FIND µ*, σ*

    | = max( )
  28. V: Likelihood and Regression Models Logarithm:

  29. V: Likelihood and Regression Models Logarithm: MONOTONICALLY INCREASING

  30. 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!
  31. V: Likelihood and Regression Models Logarithm: MONOTONICALLY INCREASING SUPPORT :

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

    (0: ] Not a problem cause L like P is positive defined
  33. V: Likelihood and Regression Models Probability log Likelihood

  34. V: Likelihood and Regression Models Probability log Likelihood

  35. V: Likelihood and Regression Models Probability log Likelihood

  36. V: Likelihood and Regression Models Probability log Likelihood

  37. V: Likelihood and Regression Models Probability log Likelihood

  38. V: Likelihood and Regression Models Probability log Likelihood

  39. V: Likelihood and Regression Models Probability max log Likelihood

  40. V: Likelihood and Regression Models Probability max log Likelihood

  41. V: Likelihood and Regression Models Probability max log Likelihood

  42. 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)
  43. 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)
  44. V: Likelihood and Regression Models J. Leek & P. Rodgers

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

  46. V: Likelihood and Regression Models

  47. V: Likelihood and Regression Models

  48. V: Likelihood and Regression Models Predictive

  49. V: Likelihood and Regression Models

  50. V: Likelihood and Regression Models

  51. V: Likelihood and Regression Models

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

  53. V: Likelihood and Regression Models Why?

  54. V: Likelihood and Regression Models git status

  55. V: Likelihood and Regression Models How?

  56. V: Likelihood and Regression Models

  57. V: Likelihood and Regression Models

  58. V: Likelihood and Regression Models

  59. V: Likelihood and Regression Models

  60. V: Likelihood and Regression Models

  61. V: Likelihood and Regression Models

  62. V: Likelihood and Regression Models 11655.34 12155.24 Sum of residuals

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

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

  65. IV: Statistical analysis MUST KNOWS: • What is the likelihood

    • Likelihood ratio test • Minimization concepts • Least square fits (OLS, WLS)
  66. 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