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)

johnmyleswhite

# Ground rules:
#
# (1) Must collect at least 10 observations
# (2) After that, keep collecting observations until
#     we satisfy condition: s / sqrt(n) < tolerance
# (3) Then output a tuple of s and n.

using Distributions

function run_simulation()

johnmyleswhite

> binom.test(2, 12)

	Exact binomial test

data:  2 and 12
number of successes = 2, number of trials = 12, p-value = 0.03857
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
 0.02086253 0.48413775
sample estimates:

johnmyleswhite

julia> function foo(x; y = 0)
           return x + y
       end
foo (generic function with 1 method)

julia> foo(0, y = 1)
1

julia> foo(0, y = 1.0)
1.0

johnmyleswhite

import Distributions: Binomial

function clt_ci(x)
    m = mean(x)
    s = std(x)
    n = length(x)
    se = s / sqrt(n)
    return max(0.0, m - 1.96 * se), min(1.0, m + 1.96 * se)
end

johnmyleswhite

Using a 64-bit floating point number (AKA a double), what is the smallest integer n such that?

• 0.1^n == 0.0
• 10.0^n == Inf
• exp(-n) == 0.0
• exp(n) == Inf

I frequently forget these numbers, so here they are:

• 0.1^n == 0.0: n = 324

johnmyleswhite

import Distributions: LogNormal, Normal, cdf, cquantile

function coverage(cis, truth)
    s = 0
    n = length(cis)
    for ci in cis
        s += ci[1] <= truth <= ci[2]
    end
    return s / n
end

johnmyleswhite

Univariate API

A new univariate distribution type should implement all of the following methods:

• Core constructors
  • MyDistribution{T}(args[...])
  • We need to clarify whether constructors should handle input validation or not. There are use cases in which people want to avoid input validation.
• params(d::MyDistribution{T})::Tuple: A tuple of the distribution's parameters in our canonical order.
• minimum(d::MyDistribution{T})::T: The lowest value in the support of MyDistribution.
• maximum(d::MyDistribution{T})::T: The highest value in the support of MyDistribution.