Statistical Thinking for Data Science

PyTennessee 2015 Keynote Address

Transcript

1. Statistical Thinking for Data Science Chris Fonnesbeck Vanderbilt University
4. 21/22 falling 7+ stories survived
5. 2 fell together
6. 40% at night
7. “Even more surprising, the longer the fall, the greater the chance of survival.”
8. 2 to 32 stories (average = 5.5)
9. ?
10. "... 132 such victims were admitted to the Animal Medical Center on 62nd Street in Manhattan ..."
11. "Found" Data
12. convenience sample
13. Missing Data
14. Representative
15. Statistical Issues
16. Big Data
17. “With enough data, the numbers speak for themselves ” Chris Anderson, Wired
18. Alfred Landon
19. Literary Digest Straw Poll
20. "Next week, the first answers from these ten million will begin the incoming tide of marked ballots, to be triple-checked, verified, five-times cross-classified and totalled."
21. 2.4 million returns
22. 41 - 55
24. George Gallup
25. Sampled 50,000
26. 66%
27. Random Sampling
29. Bias
32. Self-selection Bias
34. For some estimate of unknown quantity ,
35. p = 0.5 sample_sizes = [10, 100, 1000, 10000, 100000] replicates = 1000 biases = [] for n in sample_sizes: bias = np.empty(replicates) for i in range(replicates): true_sample = np.random.normal(size=n) negative_values = true_sample<0 missing = np.random.binomial(1, p, n).astype(bool) observed_sample = true_sample[~(negative_values & missing)] bias[i] = observed_sample.mean() biases.append(bias)
37. Accuracy Mean Squared Error
38. “The numbers have no way of speaking for themselves” Nate Silver
39. White House Big Data Partners Workshop
40. White House Big Data Partners Workshop 19 Participants 0 Statisticians
41. NSF Working Group on Big Data
42. NSF Working Group on Big Data 100 experts convened 0 statisticians
43. Moore Foundation Data Science Environments
44. Moore Foundation Data Science Environments 0 directors with statistical expertise
45. NIH BD2K Executive Committee
46. NIH BD2K Executive Committee 17 committee members 0 statisticians
47. Feeling left out?
48. It's our own fault
49. “Almost everything you learned in your college statistics course was wrong”
50. Typical introductory statistics syllabus 1.Descriptive statistics and plotting
51. Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability
52. Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability 3.Hypothesis testing
53. Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability 3.Hypothesis testing 4.Experimental design
54. Typical introductory statistics syllabus 1.Descriptive statistics and plotting 2.Basic probability 3.Hypothesis testing 4.Experimental design 5.ANOVA
55. Statistical Hypothesis Testing
58. Test Statistic
59. T-statistic
63. p-value
66. false positive rate
67. "The value for which , or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation ought to be considered significant or not." R.A. Fisher
68. p-value
69. the probability that the observed differences are due to chance
70. the probability that the observed differences are due to chance
71. a measure of the reliability of the result
72. a measure of the reliability of the result
73. the probability that the null hypothesis is true
74. the probability that the null hypothesis is true
75. "If an experiment were repeated infinitely, p represents the proportion of values more extreme than the observed value, given that the null hypothesis is true."
76. H0 : Mean duckling body mass did not differ among years.
77. H0 : Mean duckling body mass did not differ among years.
78. H0 : The prevalence of autism spectrum disorder for males and females were equal.
79. H0 : The prevalence of autism spectrum disorder for males and females were equal.
80. H0 : The density of large trees in logged and unlogged forest stands were equal
81. H0 : The density of large trees in logged and unlogged forest stands were equal
82. Statistical Straw Man
83. Statistical hypotheses are not interesting
84. Hypothesis tests are not decision support tools
85. Multiple Comparisons
87. Family-wise Error Rate >>> 1. - (1. - 0.05) ** 20 0.6415140775914581
88. import seaborn as sb import pandas as pd n = 20 r = 36 df = pd.concat([pd.DataFrame({'y':np.random.normal(size=n), 'x':np.random.random(n), 'replicate':[i]*n}) for i in range(r)]) sb.lmplot('x', 'y', df, col='replicate', col_wrap=6)
90. Statistically Significant!
92. "Despite a large statistical literature for multiple testing corrections, usually it is impossible to decipher how much data dredging by the reporting authors or other research teams has preceded a reported research finding."
93. What's the Alternative?
94. Build models and use them to estimate things we care about
95. Effect size estimation
96. Data-generating Model
99. Florida manatee Trichechus manatus
103. occupied?
104. occupied? available?
105. occupied? available? seen?
107. Estimating visibility
115. Bayesian Statistics
118. Bayes' Formula
119. Probabilistic Modeling
120. Evidence-based Medicine
121. ASD Interventions Research 19 independent studies 27 different interventions
133. “While everyone is looking at the polls and the storm, Romney’s slipping into the presidency. ”
135. Heirarchical modeling
136. Pollster effects
141. Data Science
142. Data
143. Science
144. Those who ignore statistics are condemned to re-invent it. -- Brad Efron