Glossary page

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Point process

A point process is a series of the times or locations or both of a series of events in time or objects in space. For example:

• the times that earthquakes occur in a particular region
• the times that a neuron fires
• the locations along a highway that vehicle crashes have occurred
• the locations of trees in a forest
• the times and locations of earthquakes
• the location of stars in the galaxy.

The particular feature of a point process is that we have a series of locations in time and/or space. Each event has a single time of occurrence or a single location in space. The concept can be generalised by associating a measurement (known as a mark) with each event in the series. For example, the magnitude of an earthquake or the size of a tree or the type of a star.

Point process theory develops probability models that describe the relationship between the times and locations of the events or objects together with statistical methods for extracting this information from observed data. The aim is to get a better understanding of the physical processes that lead to the patterns, to estimate the influence that external factors have on these times and locations and perhaps to forecast the likelihood of future such events.

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Logistic & Poisson regression

Ordinary regression analysis attempts to relate an observed dependent variable to a number of predictor variables. It is usually supposed that the dependent variable is a continuous variable that is approximately normally distributed.

In a logistic regression the dependent variable can take on just two values, usually 0 or 1, and one is attempting  to relate the probability that the value is 1 to a number of predictor variables. For example:

• relate the probability that an applicant for credit will default on repayments given socio-economic and credit rating data on that applicant - use to decide whether to offer credit or set conditions;
• relate the probability that a person will suffer from a particular medical condition to medical and lifestyle information on that person - use for screening or assisting with medical advice;
• relate the probability that a motor vehicle will be involved in a particular kind of crash to information about its safety devices - use for assisting with evaluation of safety device.

In a Poisson regression the dependent variable can take on only non-negative, usually small, integer values which are assumed to have a Poisson distribution and one is attempting to relate the expected value of the Poisson distribution to a number of predictor variables. For example:

• relate the number of house fires in a district to socio-economic, population and meteorological data of the district - use to focus safety campaign;
• relate the number of vehicle crashes over a period of time at a site to the characteristics of that site such as traffic volume, skid resistance, curvature and slope - use to identify risk factors.

R statistical software

R is a statistical computing program initially developed by Robert Gentleman and Ross Ihaka at Auckland University and now being extended by statisticians and computer scientists around the world. It has syntax similar to that of the S statistical language. It provides a similar vast range of functions for carrying out statistical calculations plus the environment for allowing you to develop your own specialist analyses. See the R project web-site for more details. R is released under the Gnu license.

Statistics Research Associates can install R for you under Linux, Unix or Windows and help you get started with it.

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