Optimal parameters

Statistical Thinking in Python (Part 2)

Justin Bois

Lecturer at the California Institute of Technology

Histogram of Michelson's measurements

ch1-1.002.png

¹ Data: Michelson, 1880

CDF of Michelson's measurements

ch1-1.004.png

¹ Data: Michelson, 1880

Checking Normality of Michelson data

import numpy as np
import matplotlib.pyplot as plt

mean = np.mean(michelson_speed_of_light)
std = np.std(michelson_speed_of_light)
samples = np.random.normal(mean, std, size=10000)

CDF of Michelson's measurements

ch1-1.010.png

¹ Data: Michelson, 1880

CDF with bad estimate of st. dev.

ch1-1.012.png

¹ Data: Michelson, 1880

CDF with bad estimate of mean

ch1-1.014.png

¹ Data: Michelson, 1880

Optimal parameters

Parameter values that bring the model in closest agreement with the data

Mass of MA large mouth bass

ch1-1.017.png

¹ Source: Mass. Dept. of Environmental Protection

Packages to do statistical inference

ch1-1.020.png

Packages to do statistical inference

ch1-1.021.png

Packages to do statistical inference

ch1-1.022.png

¹ Knife image: D-M Commons, CC BY-SA 3.0

Let's practice!

Statistical Thinking in Python (Part 2)