Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

An Introduction to Behaviour Analysis

Behaviour Analysis is a distinct philospophy of science. Individuals new to the approach often find difficulty in understanding the basic principles involved. This presentation, aimed at Final Year undergraduates, is designed to provide an introduction to the principles of operant conditioning (e.g., reinforcement, punishment, and extinction), making clear that these words describe functional, rather than structural, relations.

An Introduction to Verbal Behaviour

Skinner's approach to verbal behaviour (language) is central to behaviour analysis, as a philosophy of science, and, increasingly in application, including interventions for autism and challenging behaviour. This PowerPoint show provides an advanced undergraduate level introduction to the basic concepts of Skinner's functional approach to understanding verbal behaviour.

Introduction to Network Mathematics

Introduction to Network Mathematics provides college students with basic graph theory to better understand the Internet

Introduction to JavaScript Programming

These are the resources for an introductory lecture in JavaScript programming. Exercises are provided to practice simple JavaScript programming, including a template for a DHTML implementation of Conway's Game of Life (with encrypted solution).

Introduction to Matlab - a self-study tutorial

Matlab is a high level language that is very easy to use and very powerful. It comes with a wealth of libraries and toolboxes, that you can use directly, so that you don't need to program low level functions. It enables you to display results very easily on graphs and images. To get started with it, you need to understand how to manipulate and represent data, and how to find information about the available functions. During this self-study tutorial, you will learn: 1- How to start Matlab. 2- How you can find out all the information you need. 3- How to create simple vectors and matrices. 4- What functions are available and how to find them. 5- How to plot graphs of functions. 6- How to write a script. After this (should take about an hour), you will know most of what you need to know about Matlab and should definitely know how to go on learning about it on your own…

Introduction to Group Theory

Exam questions and solutions for a second year group theory course.

Introduction to estuaries and Southampton Water

A resource which answers the question "Why bother to study estuaries?" for SOES 6018. This module aims to ensure that MSc Oceanography, MSc Marine Science, Policy & Law and MSc Marine Resource Management students are equipped with the skills they need to function as professional marine scientists, in addition to / in conjuction with the skills training in other MSc modules. The module covers training in fieldwork techniques, communication & research skills, IT & data analysis and professional development.

Introduction to 'Surfer'

'Surfer' is a computer package used to produce contour plots. Its marine applications therefore include production of bathymetric maps from measurements of depth, as well as contour plots of how oceanographic parameters vary in space and time in the water column.

An Introduction to Adobe Connect

This 7-minute video shows you how to create a web-conferenced meeting using Adobe Connect, welcome the participants, communicate using sound and video, and share resources.

Introduction to IT and basic facilites at WSA (Winchester School of Art)

Week 0 induction for all new WSA students. Includes Details on iSolutions, WSA Technical Services, Workshop and Studio Professional practice and some basic Health and Safety guidance.

INFO 1010 Introduction and An Introduction to Learning at University

Describes course objectives and looks at what it takes to be successful in learning at University

Introduction to the Careers Service for ECS

Discusses the services that the Careers service provides for ECS students - and some that ECS provides too. The importance of developing a CV over time.

An introduction to video podcasts

This PowerPoint slideshow covers the educational uses of video podcasts, describes how RSS feeds work and shows how they can be created using Blackboard.

An introduction to lecture capture

This short PowerPoint presentation shows how the Echo360 lecture capture systems works