johnmyleswhite

using Distributions
for sigma in -1:-1:-12
    p = 2 * cdf(Normal(0.0, 1.0), sigma)
    n = round(BigInt, big(10)^(-log10(p)))
    @printf("%d\t%s\n", -sigma, n)
end

johnmyleswhite

Some Operations on Standard Normal Variables

Assume that:

• x[i] ~ Normal(0, 1) for all i
• c is a constant

Then the following operations have analytic results:

• x[1] + c ~ Normal(c, 1)

johnmyleswhite

@doc """
Search through all pairs of primes below n, then compute a table R[i, j] which
indicates the numbers of pairs (p, q) such that mod1(p, b) == i and
mod(q, b) + 1.
""" ->
function prime_pairs_mod_b(n, b, debug::Bool = false)
    ps = primes(n)
    R = zeros(Int, b, b)
    for i in 1:(length(ps) - 1)
        p, q = ps[i], ps[i + 1]

johnmyleswhite

In relation to the test of significance, we may say that a phenomenon is experimentally demonstrable when we know how to conduct an experiment which will rarely fail to give us a statistically significant result.

(Fisher 1947, p. 14)

From "Don't throw out the error control baby with the bad statistics bathwater: a commentary" by Deborah G. Mayo

johnmyleswhite

• Correlation is not causation (???)
• No causation without manipulation. (Holland)
• All models are wrong, some are useful. (Box)
• Statistics is the science of uncertainty. (arguably Tukey)
• Statistics is the science of learning from experience, especially experience that arrives a little bit at a time. (Efron)

johnmyleswhite

# Generate a closure that computes the unnormalized negative log-posterior at
# any set of parameters.
function make_nlp(
    n_legislators,
    n_bills,
    legislators,
    bills,
    votes,
)
    function nlp(θ)

johnmyleswhite

Introduction

To understand the design of the new Nullable type in Julia 0.4, let's review how Julia worked in 0.3.

For the purpose of this discussion, there are only three things that matter in the Julia language: values, types and functions. 1 is a value; its type is Int; and one(x::Int) = 1 is a function that maps any value of type Int to the value 1.

For the purposes of this note, we'll make the simplifying assumption that types are simply sets of values. For example, the type Int is the set containing all of the valid Int values: it is effectively equivalent to the set of values {..., -1, 0, 1, ...}. In Julia, a type is uniquely defined by the set of values that it contains. At the same time, any value in Julia also has a unique concrete type, which is the smallest set that contains that value.

Given these three parts of the language, we want to introduce a new parametric class of values to represent the concept of nullness found in other languages. To help out type inference by pr

johnmyleswhite

> library("dplyr")

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

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

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

packageVersion("dplyr")
packageVersion("ggplot2")

foo <- iris %>% group_by(Species) %>% summarize(m = mean(Sepal.Length))

ggplot(foo, aes(x = 1, y = m)) +
  stat_summary(fun.data = "mean_cl_boot", geom = "errorbar")