# Statistics

## Focus on statistical applications, techniques, tutorials, and general resources. Some overlap with the tools involved (e.g. the R language) but they are not the main focus.Covers topics such as numerical ecology, bioinformatics, regression, multivariate ordination, machine learning etc.

Analysis of community ecology data in R [Analysis of community ecology data in R] Introduction This website is focused on multivariate analysis of community ecology data.

Since I am vegetation ecologist, the website descriptions and elaborated examples are heavily biased toward analysis of vegetation data; still, I think that also other ecological fields (e.g. zoologists or microbiologists) may find the website useful. The aim is NOT a comprehensive on-line source of information about multivariate analysis (there are much more useful websites for this, see links).

I focus mostly on preparing useful working examples of analyses with real datasets and elaborated solutions of individual exercises. The secondary aim of the website is to provide brief summaries of established multivariate methods and links to recent developments in the field of multivariate analysis. Time to time, this website is used as teaching material for class Analysis of community ecology data in R program or some of the R workshops.

How to use this website Export button creating pdf of the website. Markov Chains explained visually. Explained Visually By Victor Powell with text by Lewis Lehe Markov chains, named after Andrey Markov, are mathematical systems that hop from one "state" (a situation or set of values) to another.

For example, if you made a Markov chain model of a baby's behavior, you might include "playing," "eating", "sleeping," and "crying" as states, which together with other behaviors could form a 'state space': a list of all possible states. In addition, on top of the state space, a Markov chain tells you the probabilitiy of hopping, or "transitioning," from one state to any other state---e.g., the chance that a baby currently playing will fall asleep in the next five minutes without crying first.

A simple, two-state Markov chain is shown below. Eigenvectors and Eigenvalues explained visually. Explained Visually By Victor Powell and Lewis Lehe Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's PageRank algorithm.

Let's see if visualization can make these ideas more intuitive. To begin, let v be a vector (shown as a point) and A be a matrix with columns a1 and a2 (shown as arrows). If we multiply v by A, then A sends v to a new vector Av. If you can draw a line through the three points (0,0), v and Av, then Av is just v multiplied by a number λ; that is, Av=λv. Av=(1281)⋅(12)=5(12)=λv. Below, change the columns of A and drag v to be an eigenvector.

What are eigenvalues/vectors good for? If you keep multiplying v by A, you get a sequence v,Av,A2v, etc. Let's explore some applications and properties of these sequences. Fibonacci Sequence Suppose you have some amoebas in a petri dish. Adultst+1=adultst+childrentchildrent+1=adultst which we can rewrite in matrix form like.

## Multivariate ordination

Regression. Machine learning. Computational Cognitive Science Lab. In late 2013 I gave a one-day workshop out at CSIRO that aimed to provide a brief introduction to R for an audience who knew statistics but not R.

The workshop consisted of two distinct parts, an introduction to the basic mechanics of R, followed by a fairly rapid coverage of a lot of core statistical tools in R. (There's also a bonus "Part 3" that covers a few additional topics that I'm fond of). Anyway, given that the University owns the IP associated with the workshop, and with the agreement of both CSIRO and the University, I've posted copies of all the slides, the exercises and the solution sets to the exercises. I also had the presence of mind to record screencasts of my practice talk, so there's about 5 hours of me talking about statistics linked to below! Two warnings about the videos. Part 1: Introducing R Getting Started. Part 2: Introductory Statistics in R Descriptive Statistics. Part 3: Extras Additional Statistical Tools. OpenIntro. Simple tools for simpler modelling.