# Statistics

## quickNmix: Asymptotic N-mixture Models

Estimating population abundance for replicated counts data is a computationally intensive problem. N-mixture models are used extensively in ecology to estimate population sizes, and to ascertain under-detection rates. Here I will discuss my new R package: quickNmix, which implements asymptotic solutions to the N-mixture likelihood function. The asymptotic solutions admit faster computation of the likelihood function, and the addition of parallel computing to the package can further increase computing speeds.

## Functional Data Analysis: Discrete Observations to Functional Representations

Functional data can come from many different areas of study. Some of the most common examples come from finance (for example stock prices over time), or from health research (such as fMRI time series). Analyzing data of this form has been done traditionally using time series analysis techniques. However, viewing the data as functional, rather than individual observed points, can lead to more natural interpretations and analysis. Here we will be looking at a single example data set, and learning how to represent discrete data as functional data objects.

## Neural Networks for Clustering in Python

Neural Networks are an immensely useful class of machine learning model, with countless applications. Today we are going to analyze a data set and see if we can gain new insights by applying unsupervised clustering techniques to find patterns and hidden groupings within the data. Our goal is to produce a dimension reduction on complicated data, so that we can create unsupervised, interpretable clusters like this: Figure 1: Amazon cell phone data encoded in a 3 dimensional space, with K-means clustering defining eight clusters.

## Bootstrap Tutorial in R

Bootstrapping is a statistical technique for analyzing the distributional properties of sample data (such as variability and bias). It has many uses, and is generally quite easy to implement. Continue reading to learn how you can perform a bootstrap procedure in R! What is bootstrapping? The bootstrap essentially uses re-sampling of a set of sample data in order to observe properties of the distribution of the data. For each re-sampling of the data (each “bootstrap sample”), you sample with replacement from the sample data, and compute the statistic of interest on the bootstrap sample (the bootstrap statistic).