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Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling...

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Lectures 12: Bootstrap II. bootstrap and its statistics reviewed

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Page 1: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

Lectures 12: Bootstrap II.

bootstrap and its statistics reviewed

Page 2: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

error on nonlinear function of fitted parameters?

I. Linearized error propagation

Page 3: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

Linearized error propagation

Page 4: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

Sampling the posterior histogram

Page 5: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

Sampling the posterior histogram

Page 6: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

comparison of linear propagation and posterior sampling:

Page 7: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 8: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 9: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 10: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 11: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

statistics reviewed

Page 12: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

statistics reviewed

α=3 β=1 a parameter θ on F: θ=mean/median

Page 13: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

F distributions

statistics reviewed

α=3 β=1 a parameter θ on F: θ=mean/median

Page 14: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

F distributionF distribution^

θ=

➙θ parameterθ statistic^

Page 15: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

statistics reviewed

Page 16: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

statistics reviewed

Page 17: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

statistics reviewed

Page 18: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 19: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 20: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 21: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 22: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 23: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 24: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 25: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 26: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 27: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 28: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap review and bias

Page 29: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 30: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 31: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

bootstrap sampling

Page 32: Lectures 12: Bootstrap II. bootstrap and its statistics ...€¦ · Method 3: Bootstrap resampling of the data We applied some end-to-end process to a data set and got a number f

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