Geographic Profile

[wesleyenglish]

What I always worry about with these models is the choice of parameters. Won't your distribution be quite different if you use different values of MeanD and Sd?

Good observation. The results can depend on these input variables. However, the default values for the input variables are typically derived from empirical observations. A regression is run on the equation using actual crime data to find the values that make the most accurate predictions. While the default patterns are based on national data, the regression can be run on a jurisdiction's local data to calibrate the model to their particular crime parts.

However, these input variables are also tools that the geographic profiler can use to adjust the profile to account for some aspect of the case. For instance, I often adjust one of the variables (of another more common distance decay function) if the distances are extreme in either direction, which scales the profile appropriately. There's other examples where a profile may interject personal judgement, but I try to limit those times and rely instead on the empirical data.

This is one of those cases where I had to scale the profile down to account for the extremely small distances involved. And, of course, I don't have empirical observations from the era to run regressions on. But I think you'll find the profile is faithful to the psychology as outlined in my case notes.

I hope that helps answer your question. Basically, we try to stick to the science but there are occasions when we have to use a little human judgement, too, if that makes sense.

tnb, I have to run now but I will be responding to your post hopefully later tonight.

[Chris]

This is one of those cases where I had to scale the profile down to account for the extremely small distances involved. And, of course, I don't have empirical observations from the era to run regressions on.

Here you put your finger on what worries me most about some of these geographical profiling models - that sometimes people have applied models which use parameters determined empirically from very different series of crimes.

Perhaps it would be useful to compare the spatial distributions obtained when the parameters are varied, to see which features are fundamental and which are sensitive to particular choices of the parameters.

[wesleyenglish]

Here you put your finger on what worries me most about some of these geographical profiling models - that sometimes people have applied models which use parameters determined empirically from very different series of crimes.

Excellent point. And the ultimate goal is to calibrate the distance decay functions based on all kinds of characteristics to reduce random factors from affecting the equation. For instance, it would be better to calibrate a function for bank robbery series involving offenders who use a gun and escape in a car. However, therein lies the biggest challenge for geographic profilers: it is extremely difficult to find good data. There is so little data that it really restricts research in this field. One of the projects I hope to begin soon is a centralized serial offender research database that I hope, through the cooperation of other researchers, to amass a huge amount of data.

Perhaps it would be useful to compare the spatial distributions obtained when the parameters are varied, to see which features are fundamental and which are sensitive to particular choices of the parameters.

This is an excellent research idea! I'm going to write it down for future work or to give to some student looking for a research topic.

I can tell you from personal experience–which means very little; empirical data is much preferred but in the absence of it and for the sake of conversation–some DDFs are more sensitive to the input variables than others. This particular one is pretty sensitive. However, the most common one I use, the negative exponential distance decay function. Is much less sensitive. The highest point of probability moves very little for most profiles when you change the input variables. What varies instead is how large the top profile region is. So basically I can throw it back to the investigators and say "how tight of a prediction do you want?" (the tighter, the more gutsy the prediction) or "how much resources do you have?" (smaller profile regions can give a good starting point for investigators) and then adjust the variable to scale the size of the top profile region. But again, the location of that top profile region stays pretty stable.

I appreciate very much your skepticism. I much rather deal with an investigator who has your attitude than one who thinks geographic profiling is a magic bullet that will solve there crime for them. Any kind of profiling deals with probabilities based on observed behavior. Not every offender follows typical behavior and that's important to note. Your kind of thinking helps us sharpen our science. So thank you!

[wesleyenglish]

Response to tnb

If it is okay with you I am going to give your work a mention and a link, with a more indepth analysis and discussion, on my website when I get a chance to update later today.

Thank you for your kind words. Feel free to include a mention, or even a screenshot modified as you see fit, on your website. Could you share the link to your site?

I would be very interested to know which other cases you plan on using for your 'infamy' series?

I'm not sure, but you suggest some excellent series. If you sned me an email, I'll keep you updated on any such posts.

in your experience is it normal for one crime to make so little difference to the whole construction?

It depends. If the distribution is fairly uniformly distributed, then removing any one crime will have little effect. This is a very good thing. We want our models to be stable, in that missing data do not dramatically affect its predictions since police are often not able to link every single crime committed by an offender to his series.

Some distance decay functions are more stable than others. In this case, I used a DDF that incorporates a buffer zone. And because we're dealing with such small distances, then the addition or deletion of a scene could that change the results noticeable. But as you saw with the removal of Stride, it's not too dramatic of a change. If I used a DDF that does not include a buffer zone, then it would be much more stable because there wouldn't be the repellant force of the buffer zone crowding this small distribution of crimes.

Again, this is such a small and uniform distribution that almost anyone can profile it if you don't include a buffer zone: just look in the middle of the crime scenes! The addition of the buffer zone, along with the inclusion or exclusion of crimes scenes, make it a bit more difficult to profile by eye.

I'm curious, do you support the inclusion of a buffer zone? Or do you think Jack would have killed in the immediate vicinity of his home?

[tnb]

Wesley,

Many thanks for your fascinating reply. Unfortunately my website is down as of last night for some 'one step back for two steps forward' maintenance - but it should be back up by tommorow afternoon, with the article on your work included. The address can be found in my signature on all my posts including this one - I look forward to your opinions on what I have to say.

I would very much appreciate updates on this interesting project - you can find my email through my profile on here.

I will answer your buffer zone question later when I have a little more time to do it justice - sorry - but I just wanted to show my appreciation for your own reply first and foremost. In (very) short, the answer is 'yes' I think one should be included, if for nothing more than the massive house-to-house enquiries that were undergone in the areas of the murders, but obviously that is a bit weak, so as I say I will flesh it out later.

'Speak' soon, Trevor.

[robhouse]

How does this geographic profile, or my comments on it, fit with your theory? Does it offer some support for your Jack (or Jill)? Or, according to your theory, is it way off?

Well, I personally believe that Aaron Kozminski is the most likely Jack the Ripper suspect, so your profile fits with that. Kozminski's exact address during 1888 is not known, but it is likely that he lived either on Greenfield Street, or on a street very nearby... Yalford Street for example. This falls basically within your red zone.

In my opinion, the epicenter of the crimes was St Mary Matfelon, which is the very center of your red zone. I think the Ripper may have hung around this area, and possibly considered it his jumping off point.

Rob H

[Ben]

Welcome to the boards, Wesley.

I'd be interested to see how the inclusion of Tabram and McKenzie and the exclusion of Stride would alter the results.

Best regards,
Ben

[curious]

St. Mary Matfelon

In my opinion, the epicenter of the crimes was St Mary Matfelon, which is the very center of your red zone. I think the Ripper may have hung around this area, and possibly considered it his jumping off point.

Rob H

What was in that area? Is it known?

Curious

[robhouse]

Well, the church was there obviously. It was on Whitechapel Road.

Admittedly, this is just a feeling I have, but several of the early events seem to have occurred around that area. Polly Nichols was last seen across from St. Mary's, and Emma Smith was accosted by a gang of youths hanging around the church. Tabram was murdered just a few hundred feet from here. And after the Stride murder, it was next to the church where a man was seen sitting on a door stoop wiping his hands.

Not an exact science by any means.

Rob H

[Garry Wroe]

Please excuse my ignorance, Wesley, but would it be inappropriate if the apron disposal site (Goulston Street) was to be included in your analysis?

Best wishes.

Garry Wroe.

[wesleyenglish]

Please excuse my ignorance, Wesley, but would it be inappropriate if the apron disposal site (Goulston Street) was to be included in your analysis?

The inclusion of various locations in a geographic profiling is left up to human judgement to an extent, but there are a couple rules of thumb.

Only one location per "crime" is included in the profile. This prevents any one incident from weighting the profile too heavily. I put crime in quotes because its definition is a little nebulous in this context. For instance, on this case "crime" is usually defined as an offenses committed with a cooling off period before then next offense. So if a criminal goes on a killing spree, then it is generally a good idea to only include one of the locations in the spree in the profile.

Which brings up an interesting point. If Jack was interrupted just after Stride's murder and went on to kill Eddowes so he could fullfil the act of mutilation, then it might actually be a good idea to include only one of those scenes. But since that point remains a little fuzzy, I included both scenes and I can turn one of them off if needed.

Other crimes might have multiple locations such as an abduction site, the murder site, and the site of the body dump. Only one of those locations should be included.

So how do you know which location to include? The rule of thumb is to include the location that reveals the most about the shape of the offender's cognitive map "activity space," which put simply, is the areas he frequents throughout the normal routines of his life.

Consequently, I generally recommend including the abduction site in the profile because it tends to reveal more about the offender's routine activity space than the body dump site which he may had to have searched for and rarely, if ever, have visited in the past.

I apply the same logic for a crime spree. So if we were to include only one of Jack's murders the night of September 30, 1888, then I would include Stride who is believed to have been killed first if I am not mistaken.

With those notes in mind, I leave you to make your own judgement about whether to include the apron site or not.

[Clueless]

Question

Hello, everyone. I've been reading this thread with interest, though I can't say I understand all the complex mathematics involved. This is only my second post, but I wonder if I might ask Wesley a question?

My question is whether this geographic model assumes that the killer had only one "home" location for all of these crimes?

I ask because I've heard the theory that the killer knew the area very well and may have had multiple "bolt-holes". That idea makes pretty good sense sense to me in light of his ability to make his escape and sort of disappear into the surrounding neighborhoods.

Does your geophysical model take this possibility into account or allow for it? Is it possible that the killer had 2 "safe-houses" within the highlighted area? Or even more?

I realize I may be misunderstanding how this all works, but I couldn't help wondering if it would help to make multiple models, each with a slightly different choice of variables, and then compare them and see if one area stays "hot", or is this impractical for some reason? (I mean besides someone having to do all that math.)

By the way Wesley, your work is impressive.

Thank you very much,
Clueless

[JRJ]

Wesley, even if it is inappropriate and just to satisfy those who would like to see it, could you include the apron disposal site; even if you have to add a disclaimer?

If it is not too much trouble I'm sure many would like to see the following scenarios:
Apron + C5
Apron + C5 + Martha Tabrum
Apron + C5 Minus Not universally accepted victim Liz Stride
Apron + C5 Minus Not universally accepted victim MJK
Apron + C5 Minus Not universally accepted victims Liz Stride & MJK

Thanks,

JRJ

[Garry Wroe]

Many thanks, Wesley. Like you, I believe that, in general terms, the place of initial contact reveals more about the offender's cognitive anchors than do the body disposal sites. If I understand you correctly, however, one of the limitations of geoprofiling relates to its inbuilt tendency to predict a marauding rather than a commuting model - a factor which, as I'm sure you will appreciate, assumes special significance with respect to the Whitechapel Murders. Were one applying the traditional, non-mathematical approach, this difficulty might to a certain extent be overcome by the consideration of ancillary factors such as the apron disposal site, which appears to provided a relatively unambiguous indication of an offender retreating back towards his trawling grounds rather than away from them as would be the case had he been a 'commuter.' So whilst the Goulston Street venue may not have been a crime scene, I feel that it is crucial in any attempt to determine the offender's residential orbit.

And, for what it's worth, I regard the Stride killing as a 'Type 2 Error.'

Many thanks again for sharing and explaining your work.

Regards.

Garry Wroe.

[Septic Blue]

Wesley, even if it is inappropriate and just to satisfy those who would like to see it, could you include the apron disposal site; even if you have to add a disclaimer?

If it is not too much trouble I'm sure many would like to see the following scenarios:
Apron + …
Apron + …
Apron + …
Apron + …
Apron + …

"even if it is inappropriate and just to satisfy those who would like to see it, ..."

It would not only be "inappropriate": It would be very misleading!

Do you wish to see the product of meaningful analysis; or do you simply wish to be entertained?

I would suggest the following:
1) That you include the location of Eddowes Apron on Goulston Street as a data point, …

I first considered doing so when I began work on this endeavor (over a year ago). I have pondered the idea again, since reading your suggestion, but I must stand by my initial conclusion: That the apron 'deposit' in Goulston Street was not an observed 'event' in itself; rather it was a component of the Eddowes 'event'. Therefore, any factorization of this 'sub-event' into the overall 'equation' would have to be 'weighted' (e.g. 25% of a data point); thereby reducing the weight of the Eddowes murder-site accordingly (i.e. to 75% of a data point).

The concept of 'weighted' data points can be easily put to the test, and in certain instances, shown to be very useful, in the type of analysis that I am conducting:

- Pinpointing the murder-site 'Mean-Center'

- Determining the 'Standard Deviation' from the murder-site 'Mean-Center'

- Utilizing the 'Standard Deviation' for the establishment of a 'Probability Distribution' that relates to an assumed perception of late November 1888 that this series of murders would continue ad infinitum; and the accordant expectations that should have prevailed, regarding the distribution of subsequent murder-sites

- Utilizing the 'Standard Deviation' for the establishment of a Geographic Profile 'Probability Distribution' that is based on the very simple premise that the probability of a serial murderer operating from within his 'killing field' is generally 50%; but that the probability decreases in cases of smaller 'killing fields' / increases in cases of larger 'killing fields'.

I could, for example, determine a 'Mean-Center' and generate its accordant 'Probability Distribution', on the basis of the following 'weightings':

- Tabram: 62.50% (i.e. 5/8)
- Nichols: 100.00%
- Chapman: 100.00%
- Stride: 75.00% (i.e. 6/8 or '3/4')
- Eddowes: 100.00%
--- {Murder-Site: 90.00%}
--- {Apron Deposit-Site: 10.00%}
- Kelly: 87.50% (i.e. 7/8)

- Total: 525.00% (i.e. 5 1/4 Data Points; Providing 4 1/4 'Degrees of Freedom')

Or ...

- Tabram: 50.00% (i.e. 3/6 or '1/2')
- Nichols: 100.00%
- Chapman: 100.00%
- Stride: 66.67% (i.e. 4/6 or '2/3')
- Eddowes: 100.00%
--- {Murder-Site: 75.00%}
--- {Apron Deposit-Site: 25.00%}
- Kelly: 83.33% (i.e. 5/6)

- Total: 500.00% (i.e. 5 Data Points; Providing 4 'Degrees of Freedom')

Or any other weightings that I deemed appropriate; depending of course, upon how strongly I felt about the inclusions of Tabram, Stride and Kelly in the overall 'Ripper' tally.

***But, either way; if I wished to afford the Eddowes murder the same level of significance as that of the Nichols and Chapman murders; then the Apron deposit would have to be considered a 'subset' of the Eddowes murder. And, unless the site of that 'subset' were afforded a 'weighting' of 0.00%, the Eddowes murder-site would invariably be granted a lesser level of significance than that of the Nichols and Chapman murder-sites.***

I know literally nothing about the complexities of applying Distance Decay Functions, to individual 'cells', in a determined 'Search Area'. So, whether 'weighted' data points (i.e. 'observations') would be even remotely practical is Wesley's call.

But, either way; the Apron deposit-site should not be included, unless as a 'subset' of the Eddowes murder-site.

Imagine the look of horror on Ben's face, if he were to see one of Wesley's 'Buffer Zones', extending from the doorway of 108-119 Wentworth Model Dwellings, to the main entrance to the Victoria Home for Working Men!