The process has gone through a variety of evolutions to try and increase the accuracy of the profiles.
"There are two approaches to offender profiling: the top-down approach, and the bottom-up approach. The top-down approach is the approach used by the FBI, thus called the American approach. It is called the top-down approach because it tries to fit crime details into predetermined categories or typologies."
"The bottom-up is the British approach. It aims to generate an offender’s profile by looking at the evidence. There are no ‘typologies’, the profile is data-driven and emerges as more and more details of the offence are known. It makes use of ‘smallest space analysis’, a computer programme that identifies correlations across patterns of behaviour. There are two methods to the bottom-up approach, investigative psychology, and geographical profiling."
It must begin with the evidence. From that evidence attributes, characteristics will be inferred such as occupation, living arrangements etc
But the profile is in essence statistics. It's a fascinating process though.
This is a great overview:
The process has gone through a variety of evolutions to try and increase the accuracy of the profiles.