a brief tour of statistics - noisebridge · 1/61 a brief tour of statistics this work by thomas...

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A Brief Tour of Statistics

This work by Thomas Lotze is licensed under a Creative Commons

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

9/61Creative Commons licensed, from Jason Tromm on flickr

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

21/61Creative Commons licensed, from gr0don on flickr

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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31/610.10.44

0.050.41

0.010.34

0.0010.30

Probability of 21 or

more successes

Actual

Field

Goal Rate

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?• Bootstrapping• Multiple Testing

• Useful Tools

47/61Creative Commons licensed, from Alan Vernon on flickr

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing• Useful Tools

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0.991000.05

0.40100.05

0.0510.05

0.631000.01

0.10100.01

0.0110.01

Probability of

False Detection (in at least 1 test)Number of Tests

Probability of

False Detection (per test)

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• What are Distributions?• Models

– Binomial– Poisson– Uniform– Gaussian (normal)

• Using Distributions to Answer Questions

• Distribution Parameters• Estimating Parameters

• Confidence Intervals and P-values• Why Gaussian?

• Regression

• Logistic Regression• Why Not Gaussian?

• Bootstrapping• Multiple Testing

• Useful Tools

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• R: http://cran.r-project.org/

• Casella & Berger, Statistical Inference

• Wikipedia: http://en.wikipedia.org/wiki/List_of_probability_distributions

• Salsburg, The Lady Tasting Tea

• thomas.lotze@thomaslotze.com

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1. Everything is a Distribution

2. Many Kinds of “Random” (many Distributions)

3. Estimated Parameters are RandomThey have Distributions!

4. Statistical Decisions come from Distribution Estimates

5. Be Skeptical of NormalityMean and Variance are not sufficient!

6. Be Skeptical of Multiple Testing

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• Practical Take-home– Normality test– T-test– Wilcoxon rank-sum test

• Other Distributions– Student’s T– F– Lognormal– Geometric– Levy– Weibull– Benford

• Goodness of fit– Chi-squared test– Q-Q plots

• Distribution Connections• Multivariate Distributions

• Bias/Variance Tradeoff

•Nonparametric Distributions•Model Comparison:

Parameters and Fit (AIC, BIC)

•Bayesian Statistics•Bayes’ Law

•Cognitive Biases•Time series

•Counterintuitive Probability•Monty Haul

•Two Aces

•Poisson Waiting Times•Markov Chain Monte Carlo

•Extreme Value Statistics