johnmyleswhite

"We are struck by the fact that in the social and behavioral sciences,
epidemiology, economics, market research, engineering, and even applied
physics, statistical methods are routinely used to justify causal inferences
from data not obtained from randomized experiments, and sample statistics are
used to predict the effects of policies, manipulations or experiments. Without
these uses the profession of statistics would be a far smaller business. It may
not strike many professional statisticians as particularly odd that the
discipline thriving from such uses assures its audience that they are
unwarranted, but it strikes us as very odd indeed."

johnmyleswhite

The sample mean is never exactly equal to the true mean when the true mean is irrational

Let D be any distribution over the integers. Suppose that the first moment exists for D and is an irrational number.

In this case, the sample mean is never exactly equal to the true mean because the sample mean is always a rational number.

This is simple to prove: the sample mean is always a sum of integers divided by the number of samples, which is always an integer.

johnmyleswhite

foo <- function(frame_number)
{
	assign("frame_number", -1, envir = sys.frame(frame_number))
}

bar <- function()
{
	frame_number <- sys.nframe()
	print(frame_number)
	foo(frame_number)

johnmyleswhite

a <- 1
b <- 2

ftw <- function()
{
	vars <- ls(envir = .GlobalEnv)
	rm(list = vars, envir = .GlobalEnv)
}

ftw()

johnmyleswhite

Julia and Statistical Computing

Julia is a new language for technical computing. The language is designed to solve the "two language problem", in which scientists prototype code in a higher-level language like R and then rewrite parts (or all) of their code in a lower-level language like C. Julia strives to expose a set of basic abstractions that allow programmers to transition easily between quick-and-dirty prototype code and production-quality code.

johnmyleswhite

using Distributions

const Ψ = digamma

# RNG
function generate(
    a::Real,
    b::Real,
    c::Real,
    d::Real,

johnmyleswhite

BinaryMF

Attempt to factor a binary matrix, $D$, under the assumption that entries are IID Bernoulli draws, conditional on the value of a link-transformed linear predictor, $\mathbb{E}[D_{i, j}] = I(\mu + a_i + b_j + X_{i}^{T} Y_{j})$, where $I$ is the inverse logit link function.

Because of non-identifiability problems, we use a consistent $\mathcal{N}(0, \sigma^2)$ prior over all parameters in the model

johnmyleswhite

# Ben Bitdiddle's demonstration that Julia uses applicative-order evaluation

p() = p()

# p (generic function with 1 method)

test(x, y) = x == 0 ? 0 : y

# test (generic function with 1 method)

johnmyleswhite

> x <- 1
> f <- factor(x)
> f[1] * f[1]
[1] NA
Warning message:
In Ops.factor(f[1], f[1]) : * not meaningful for factors
> p <- f[1] * f[1]
Warning message:
In Ops.factor(f[1], f[1]) : * not meaningful for factors
> class(p)

johnmyleswhite

julia> i = uint(0) - uint(1)
0xffffffffffffffff

julia> b = float64(i)
1.8446744073709552e19

julia> j = 0
0

julia> while float64(i) == b