Probabilit y densit y f u nctions STATISTIC AL TH IN K IN G IN P - PowerPoint PPT Presentation

Probabilit y densit y f u nctions STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 ) J u stin Bois Lect u rer at the California Instit u te of Technolog y

Contin u o u s v ariables Q u antities that can take an y v al u e , not j u st discrete v al u es STATISTICAL THINKING IN PYTHON ( PART 1)

Michelson ' s speed of light e x periment STATISTICAL THINKING IN PYTHON ( PART 1)

Michelson ' s speed of light e x periment STATISTICAL THINKING IN PYTHON ( PART 1)

Probabilit y densit y f u nction ( PDF ) Contin u o u s analog to the PMF Mathematical description of the relati v e likelihood of obser v ing a v al u e of a contin u o u s v ariable STATISTICAL THINKING IN PYTHON ( PART 1)

Normal PDF STATISTICAL THINKING IN PYTHON ( PART 1)

Normal PDF STATISTICAL THINKING IN PYTHON ( PART 1)

Normal CDF STATISTICAL THINKING IN PYTHON ( PART 1)

Normal CDF STATISTICAL THINKING IN PYTHON ( PART 1)

Let ' s practice ! STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 )

Introd u ction to the Normal distrib u tion STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 ) J u stin Bois Lect u rer at the California Instit u te of Technolog y

Normal distrib u tion Describes a contin u o u s v ariable w hose PDF has a single s y mmetric peak . STATISTICAL THINKING IN PYTHON ( PART 1)

Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

STATISTICAL THINKING IN PYTHON ( PART 1)

STATISTICAL THINKING IN PYTHON ( PART 1)

Comparing data to a Normal PDF STATISTICAL THINKING IN PYTHON ( PART 1)

Checking Normalit y of Michelson data import numpy as np mean = np.mean(michelson_speed_of_light) std = np.std(michelson_speed_of_light) samples = np.random.normal(mean, std, size=10000) x, y = ecdf(michelson_speed_of_light) x_theor, y_theor = ecdf(samples) STATISTICAL THINKING IN PYTHON ( PART 1)

Checking Normalit y of Michelson data import matplotlib.pyplot as plt import seaborn as sns sns.set() _ = plt.plot(x_theor, y_theor) _ = plt.plot(x, y, marker='.', linestyle='none') _ = plt.xlabel('speed of light (km/s)') _ = plt.ylabel('CDF') plt.show() STATISTICAL THINKING IN PYTHON ( PART 1)

Checking Normalit y of Michelson data STATISTICAL THINKING IN PYTHON ( PART 1)

Let ' s practice ! STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 )

The Normal distrib u tion : Properties and w arnings STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 ) J u stin Bois Lect u rer at the California Instit u te of Technolog y

Image : De u tsche B u ndesbank STATISTICAL THINKING IN PYTHON ( PART 1)

The Ga u ssian distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Length of MA large mo u th bass STATISTICAL THINKING IN PYTHON ( PART 1)

Length of MA large mo u th bass STATISTICAL THINKING IN PYTHON ( PART 1)

Length of MA large mo u th bass STATISTICAL THINKING IN PYTHON ( PART 1)

Mass of MA large mo u th bass STATISTICAL THINKING IN PYTHON ( PART 1)

Light tails of the Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Light tails of the Normal distrib u tion STATISTICAL THINKING IN PYTHON ( PART 1)

Let ' s practice ! STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 )

The E x ponential distrib u tion STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 ) J u stin Bois Lect u rer at the California Instit u te of Technolog y

The E x ponential distrib u tion The w aiting time bet w een arri v als of a Poisson process is E x ponentiall y distrib u ted STATISTICAL THINKING IN PYTHON ( PART 1)

The E x ponential PDF STATISTICAL THINKING IN PYTHON ( PART 1)

Possible Poisson process N u clear incidents : Timing of one is independent of all others STATISTICAL THINKING IN PYTHON ( PART 1)

E x ponential inter - incident times mean = np.mean(inter_times) samples = np.random.exponential(mean, size=10000) x, y = ecdf(inter_times) x_theor, y_theor = ecdf(samples) _ = plt.plot(x_theor, y_theor) _ = plt.plot(x, y, marker='.', linestyle='none') _ = plt.xlabel('time (days)') _ = plt.ylabel('CDF') plt.show() STATISTICAL THINKING IN PYTHON ( PART 1)

E x ponential inter - incident times STATISTICAL THINKING IN PYTHON ( PART 1)

Let ' s practice ! STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 )

Final tho u ghts STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 ) J u stin Bois Lect u rer at the California Instit u te of Technolog y

Yo u no w can … Constr u ct ( bea u tif u l ) instr u cti v e plots Comp u te informati v e s u mmar y statistics Use hacker statistics Think probabilisticall y STATISTICAL THINKING IN PYTHON ( PART 1)

In the seq u el , y o u w ill … Estimate parameter v al u es Perform linear regressions Comp u te con � dence inter v als Perform h y pothesis tests STATISTICAL THINKING IN PYTHON ( PART 1)

Let ' s practice ! STATISTIC AL TH IN K IN G IN P YTH ON ( PAR T 1 )