---
title: "Entropy and Testing with np"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Entropy and Testing with np}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
options(np.messages = FALSE)
```

This vignette is meant to be a small package-side introduction to the
entropy-based testing tools in `np`. It is intentionally much shorter than the
legacy article-style document and focuses on what the functions are for and one
small runnable example.

The fuller narrative treatment now belongs on the gallery site rather than in a
shipped package vignette:

- <https://jeffreyracine.github.io/gallery/entropy_tests.html>

## Main functions

The main entropy-based testing functions are:

- `npdeneqtest`: equality of multivariate densities
- `npunitest`: equality of univariate densities
- `npsymtest`: asymmetry in a univariate variable or series
- `npdeptest`: nonlinear pairwise dependence
- `npsdeptest`: nonlinear serial dependence

These functions can be computationally demanding, especially when integration
and bootstrap resampling are involved.

## A small example

For a first run, it is reasonable to begin with a simple univariate comparison
and keep the example small enough that bootstrapping remains practical.

```{r}
library(np)
set.seed(42)

n <- 250
x <- rnorm(n)
y <- rnorm(n)

npunitest(x, y, bootstrap = TRUE)
```

## Practical guidance

- start with the smallest example that answers your question,
- use the default integral-based versions for serious work unless you have a
  reason not to,
- expect runtime to grow quickly when bootstrap resampling is involved,
- if the testing workflow is correct but the runtime becomes burdensome, move to
  `npRmpi` rather than rewriting the statistical problem.

## Where to go next

- `?npunitest`, `?npdeneqtest`, `?npdeptest`, `?npsdeptest`, `?npsymtest`
- <https://jeffreyracine.github.io/gallery/entropy_tests.html> for the longer
  website article
- <https://jeffreyracine.github.io/gallery/mpi_large_data.html> if the testing
  workflow is correct but runtime now points to `npRmpi`