Welcome to the co u rse ! FU N DAME N TAL S OF BAYE SIAN DATA AN - PowerPoint PPT Presentation

Welcome to the co u rse ! FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R Rasm u s Bååth Data Scientist

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

1 h � ps :// commons .w ikimedia . org /w iki / File : Enigma _08. jpg FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Ba y esian inference in a n u tshell A method for � g u ring o u t u nobser v able q u antities gi v en kno w n facts that u ses probabilit y to describe the u ncertaint y o v er w hat the v al u es of the u nkno w n q u antities co u ld be . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Ba y esian data anal y sis The u se of Ba y esian inference to learn from data . Can be u sed for h y pothesis testing , linear regression , etc . Is � e x ible and allo w s y o u to constr u ct problem - speci � c models . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Co u rse o v er v ie w Chapter 1 : A small Ba y esian anal y sis . Chapter 2 : Ho w Ba y esian inference w orks . Chapter 3 : Wh y y o u w o u ld w ant to u se Ba y esian data anal y sis ? Chapter 4 : Ba y esian inference w ith Ba y es theorem . Chapter 5 : Wrapping u p + a practical tool for Ba y esian Data Anal y sis in R . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Ba y esian Data anal y sis : a tool to make sense of y o u r data . FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R

A little bit of backgro u nd FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R Rasm u s Bååth Data Scientist

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Probabilit y A n u mber bet w een 0 and 1. A statement abo u t certaint y / u ncertaint y. 1 is complete certaint y something is the case . 0 is complete certaint y something is not the case . Not onl y abo u t y es / no e v ents . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

The role of probabilit y distrib u tions in Ba y esian data anal y sis is to represent u ncertaint y, and the role of Ba y esian inference is to u pdate probabilit y distrib u tions to re � ect w hat has been learned from data . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

A Ba y esian model for the proportion of s u ccess prop_model(data) The data is a v ector of s u ccesses and fail u res represented b y 1 s and 0 s . There is an u nkno w n u nderl y ing proportion of s u ccess . If data point is a s u ccess is onl y a � ected b y this proportion . Prior to seeing an y data , an y u nderl y ing proportion of s u ccess is eq u all y likel y. The res u lt is a probabilit y distrib u tion that represents w hat the model kno w s abo u t the u nderl y ing proportion of s u ccess . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c() prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c(0) prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c(0, 1) prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c(0, 1, 0) prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c(0, 1, 0, 0) prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c(0, 1, 0, 0, 0) prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Tr y ing o u t prop _ model data <- c(0, 1, 0, 0, 0, 1) prop_model(data) FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

No w, y o u tr y o u t prop _ model ! FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R

Yo u j u st did some Ba y esian data anal y sis ! FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R Rasm u s Bååth Data Scientist

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Priors & Posteriors A prior is a probabilit y distrib u tion that represents w hat the model kno w s before seeing the data . A posterior is a probabilit y distrib u tion that represents w hat the model kno w s a � er ha v ing seen the data . FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

The probabilit y distrib u tion o v er the n u mber of 6' s w hen rolling 5 dice 5 ) 6 1 x 1 ( x 5− x p(x) = ( ) (1 − ( )) 6 FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

number_of_sixes 1 1 0 0 1 0 1 2 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 2 0 0 1 0 0 1 0 0 1 0 1 2 0 1 0 0 0 1 2 1 2 0 0 1 1 3 3 0 0 1 1 1 1 1 0 0 1 2 0 1 3 1 1 1 0 1 0 1 2 0 1 1 0 1 1 1 0 2 1 0 4 0 1 2 1 1 1 2 0 1 0 1 1 0 0 2 0 0 0 0 0 1 1 0 1 0 0 0 0 2 0 0 0 0 0 1 1 0 0 2 1 1 1 0 2 1 1 1 0 0 1 1 1 ... mean(number_of_sixes) 0.83 FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

posterior <- prop_model(data) print(posterior) 0.23 0.36 0.20 0.21 0.12 0.10 0.03 0.16 0.09 0.14 0.23 0.05 0.15 0.26 0.22 ... FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Finish off the Zombie dr u g anal y sis ! FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R

Wrapping u p the z ombie anal y sis FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R Rasm u s Bååth Data Scientist

The res u lt of the z ombie anal y sis data = c(1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0) posterior <- prop_model(data) median(posterior) 0.19 quantile(posterior, c(0.05, 0.95)) 5% 95% 0.06 0.39 sum(posterior > 0.07) / length(posterior) 0.93 FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

The res u lt in a jo u rnal FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

FUNDAMENTALS OF BAYESIAN DATA ANALYSIS IN R

Ne x t u p : Ho w does Ba y es w ork ? FU N DAME N TAL S OF BAYE SIAN DATA AN ALYSIS IN R