johnmyleswhite

using Distributions
using HypothesisTests

n_sims = 100_000
n = 25
x = Array{Float64}(n)
y = Array{Float64}(n)
p_x = Array{Float64}(n_sims)
p_y = Array{Float64}(n_sims)
p_d = Array{Float64}(n_sims)

johnmyleswhite

function construct_x(x9)
    x = fill(0, 9)
    r = fill(0, 9)
    x[9], r[9] = x9, 0
    x[8], r[8] = fld(7 * x[9], 6), rem(7 * x[9], 6)
    x[7], r[7] = fld(7 * x[8] + 1, 6), rem(7 * x[8] + 1, 6)
    for i in 7:-1:2
        x[i], r[i] = fld(7 * x[i + 1] + 1, 6), rem(7 * x[i + 1] + 1, 6)
    end

johnmyleswhite

> x <- 1:8
> y <- c(1, 1, 2, 3, 5, 8, 13, 21)
> summary(lm(y ~ x - 1))

Call:
lm(formula = y ~ x - 1)

Residuals:
   Min     1Q Median     3Q    Max
-3.922 -3.306 -2.422 -0.326  7.157

johnmyleswhite

library("ggplot2")
library("dplyr")

# Population size
n <- 2500

# Sessions per user if assigned to test
sessions_test <- as.integer(exp(rnorm(n, 0.5, 1)))

# Sessions per user if assigned to control

johnmyleswhite

using Distributions

function simulate_coupled(v0, n, t_max, allow_debt)
    cur = fill(v0, n)
    nxt = copy(cur)

    for t in 1:t_max
        for i in 1:n
            j = rand(1:n)
            if allow_debt

johnmyleswhite

n <- 100000L

x <- rnorm(n, 0, 1)
y <- -x

cor(x, y)

for (z in c(10, 100, 1000, 10000, 100000)) {
    rho <- cor(c(-z, x, z), c(-z, y, z))
    print(paste0("z = ", z, "; rho = ", rho))

johnmyleswhite

library("ggplot2")

n <- 10000
s_e <- 0.01

x1 <- runif(n, -10, 10)
x2 <- runif(n, -10, 10)
y <- sin(x1 * x2) + rnorm(n, 0, s_e)

df <- data.frame(y = y, x1 = x1, x2 = x2, z = x1 * x2)

johnmyleswhite

> median(FALSE)
[1] FALSE

> median(c(TRUE, FALSE))
[1] 0.5

> median(c(TRUE, FALSE, TRUE))
[1] TRUE

> f <- factor(c('a', 'b', 'c'), levels = c('a', 'b', 'c'), ordered = TRUE)

johnmyleswhite

Handling Nulls in Julia

There are several core cases that need to be handled to ensure that all operations on non-nullable data can be lifted to work on nullable data.

• The scalar case: lift f(x::T) to f(x::?T).
• Tuple case: lift f(xs::Tuple{T1, ..., TN}) to f(x::Tuple{?T1, ..., ?Tn}).
• Single array case: lift f(xs::Array{T}) to f(xs::Array{?T}).
• Multiple array case: lift f(xs::Tuple{Array{T1}, ..., Array{Tn}}) to f(xs::Tuple{Array{?T1}, ..., Array{?Tn}})

Others may exist, but these are the obvious cases that we absolutely must resolve.

johnmyleswhite

using Distributions

p = 100

d_x = MultivariateNormal(zeros(p), eye(p, p))
d_y = MultivariateNormal(100 * ones(p), 2 * eye(p, p))

n_sims = 10_000

mean_x = Array(Float64, n_sims)