Principle of Urban Informatics CUSP 2015 Lecture 5

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