R Code rethinking statistics ch4

library(rethinking)

load the rethinking library in

data(Howell)

load data howell from a library

d ← Howell

put Howell data into a variable

str(d)

inspect structure of data d

d$height

extract data in data frame d for height

d2 <- d[d$age >= 18,]

extract data from data frame d where the age is greater than or equal to 18 and assign to variable d2

curve(dnorm( x, 178, 20), from=100, to=250)

make a prior for a normal distribution of x with mean 178 and 95% CI of 80, plot from 100 to 250

dunif(x, 0, 50)

make a prior with a uniform distribution from 0 to 50

sample <- rnorm(1e4, 178, 20)

take 10,000 samples from a normal distribution with mean 178 and standard deviation 20 and assign them to a sample variable

sample ← runif(1e4, 0, 50)

take 10,000 samples from a uniform distibution from 0 to 50

sum(sample) / 1e4

take the average of a sample variable with 10,000 entries

prior_h <- rnorm(1e4, sample_mu, sample_sigma)

sample 10,000 values from a set of sample_mu and sample_sigma

dens(sample)

create a density plot of sample values

sample a row then take samples from that row

how to sample a posterior that contains multiple values

alist (
height ~ dnorm(mu , sigma),

mu ~ dnorm(178 , 20),

sigma ~ dunif(0 , 50)

)

how to create a list with variable relations, height follows a normal distribution, mu follows normal distribution 178 average, with stdev 20, sigma follows uniform from 0 to 50

m4.1 <- map (flist , data=d2)

Create a maximum a posteri model from d2 onto a quadratic function using the variables described in flist and their

precis(m4.1)

find the mean and stdev, and 89% confidence interval of m4.1

vcov(m4.1)

how to find the covariance of MAP model m4.1

cov2cor(vcov(m4.1))

how to find the relationship between mu and sigma of MAP m4.1

extract.samples(m4.1, n=1e4)

how to sample 10,000 times multi-dimensional posterioir from a MAP value m4.1, output is a data frame

rm(list = ls())

how to clear environment in R

plot(d2$height ~ d2$weight)

plot height (y) over weight (x)

precis(m4.3, corr=TRUE)

find a precis model with correlation matrix for map m4.3

rethinking link function

take all values of x for the model, sample from the posterior

str(x)

how to find the structure (N rows and cols) for x

link functuon

creates a sample of dist values for 1000 values of mu

standardizing data

puts the mean at 0 and makes the points clump around it better, done by subtracting everything by the mean then dividing by a standard deviation