The Mathematics of Duelling

Duelling with pistols. If you were the one issuing the challenge, your dilemma was that custom dictated that your adversary be allowed to shoot first. Only then, if you were still able to shoot, would you be permitted to seek “satisfaction”.

How much of an advantage does the first shooter really have? In this article, we build a simple probability model, and implement a numerical model in a few lines of R code.

Two gentleman face off in the snow.  Convention dictates the challenged shoots first.

Two gentleman face off in the snow. Convention dictates the challenged shoots first.

Continue reading this article…

Software: A Force-Multiplier for R&D

Your computer, kitted out with specialised software (mostly free) and configured for efficiency of use, is perhaps the single greatest ‘force multiplier’ that you can have as a Scientist, R&D Engineer, or Mathematician — unless of course you have a large budget and a team of bright minds at your disposal.

With good tools, a bit of creative joinery, and a good dose of persistence, you can become an army of one…

Continue reading this article…

A Radar Tracking Approach to Data Mining

(Statistics and Data Mining II)

Automated decision problems are frequently encountered in statistical data processing and data mining. An heuristic filter or heuristic classifier typically has a limited set of input data from which to arrive at a set of conclusions and make a decision: REJECT, ACCEPT, or UNDETERMINED. In such cases, pre-processing the input data before applying the heuristic classifier can substantially enhance the performance of the decision system.

In this article, I’ll motivate the use of a radar-tracking algorithm to improve the performance of automated decision making and statistical estimation in data processing. I will illustrate using the website visitation statistics problem.

Continue reading this article…

Disaster Management for Web-Hosted Data

(Technology Infrastructure Series)

In case you’re taking seriously guarantees about uptime, reliability, or backups advertised by website hosting companies, you should know that most guarantees of service are an idealized concept, especially if you use a low-cost web hosting service. Now, this doesn’t mean you should avoid low-cost web hosts. What you should do is give a little thought to the “what if’s” that may arise, and what you can do before they arise to minimize the pain when they do.

In this article, I’ll go through a few situations you might want to consider, and some options you can use to reduce your risk.

Continue reading this article…

Analysis of Visitor Statistics: Data Mining in-the-Small

(Statistics and Data Mining I)

For a variety of reasons, meaningful website visitation and visitor behavior statistics are an elusive data set to generate. This article introduces the visitor statistics problem, and describes seven challenges that must be overcome by statistical and data analysis techniques aiming for accurate estimates. Along the way, we’ll encounter the “Good News Cheap, Bad News Expensive” Paradox of Data Mining — or, why information is often used “as-is”.

This article is the first in a series on algorithms, statistics and data analysis techniques (using free and open source tools) using the visitor statistics problem as a vehicle for illustration.

Continue reading this article…

Mathematical Finance and The Rise of the Modern Financial Marketplace

Abstract

One of the fascinating areas to arise recently in applied mathematics has been Mathematical Finance. From a technical point of view, Mathematical Finance uses a broad range of sophisticated mathematics for its financial models, and relies on state-of-the-art software engineering and computer hardware to implement these financial models, often in real-time.

Whether one is interested in technology or not, there is a kernel of core financial ideas at the heart of the global free market capitalist system that every literate citizen should understand. Whether we agree with their principles or with the inequities that are, arguably, the result, these ideas are in place across most of the world today. A closer look at mathematical finance will offer a better understanding of the mechanics of the modern financial world.

In this article, I’ll motivate the need for financial mathematics through a simplified account of the rise of the modern financial marketplace.

Continue reading this article…

Note to Readers!

Our Google+ (Buzz) page is where we publish more regular, shorter content that isn't quite full article length. Feel free to check it out & join in! This is still the location for full length articles.