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.

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* 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.

Statistics Research Associates
Limited, PO Box 12-649, Thorndon, Wellington 6144, New Zealand

**phone:** +64 4
972 6531; **www:**
http://www.statsresearch.co.nz