1995, Starting as a Criminal Investigation Expert

Chapter 113 Probability Models (Seeking Initial Subscriptions)

On the system side, the authors of many domestic materials have been omitted.

Foreign theories, on the other hand, are written down without any scruples, and their names are openly displayed.

Then it introduced Kant, a figure considered the father of criminal geography.

His theory of the center of a circle is also the most frequently used theory in later generations for analyzing the activity range of criminal suspects.

In the 1970s, many criminological theories emerged.

For example, rational choice theory states that criminals will actively weigh three costs: the cost of travel distance and time, the risk cost of being witnessed and arrested, and the cost of the proceeds from the crime.

There is also the crime pattern theory, which proposes the three concepts of node, path, and edge.

In addition, there are theories such as buffer zones and psychological comfort zones.

But this is only in theory.

When a theory develops to a certain stage, practical application methods emerge.

Based on the information Li Shu saw and his own understanding, there are two main schools of thought.

One method is David Kanter's method of centering the circle.

The focus is on studying the behavioral patterns of criminal suspects, defining a specific scope before conducting the analysis.

This person is an architect and environmental designer by training; his research focuses on human living patterns.

Based on relevant theories, he devised this method.

The general process is actually quite simple: mark the crime scene on a map, then set a range to form an circumscribed circle.

All the circles joined together, searching for their geometric center point.

Therefore, the suspect most likely lives in this central area.

Another school of thought was proposed this year by a senior police officer from Canada named Kim Rosemo in his doctoral dissertation.

He also based his work on previous theories such as buffer zones and daily activities.

However, he used mathematical methods, a complex set of formulas, and various mathematical tools to perform probability calculations.

This allows us to locate the area on the map where the suspect is most likely to reside.

After that, there were many theoretical models, but they were all modifications and additions based on these two tools.

But what.

As Wang Ze'an said, neither the center-based positioning nor Rosmo's probability algorithm is applicable to cross-city crimes.

People coming from other cities don't have a so-called psychological comfort zone, so naturally, analysis is impossible.

Li Shu looked around.

In a corner of the training room, there was a small blackboard hanging, with chalk next to it.

It's for writing the duty roster.

Unfortunately, the blackboard was too small, so Li Shu simply took off his boxing gloves and beckoned Wang Ze'an to his office.

Wang Ze'an had been abroad and worked at the Second Research Institute, which gave him access to the most advanced theories both domestically and internationally.

Therefore, it knows the location of the center of the circle.

However, Rosmo's probability algorithm was only proposed this year, will be granted a US patent next year, and will only be gradually applied a few years later, so Wang Ze'an had no idea about it at all.

To be honest, even Li Shu himself couldn't explain it clearly.

Because this is an algorithm, a mathematical tool, and it contains mathematical formulas.

Li Shu really couldn't understand it.

As for math, if the formulas are written right in front of you, you might not understand them.

Li Shu could only try to understand the principles of the model and what it was trying to calculate by reading.

Then tell Wang Ze'an, ask him to understand, and ask him to help derive the specific algorithm.

Even the subsequent calculations required the help of Wang Ze'an or others.

He dragged Wang Ze'an back to his office.

His office was quite large, filled with all sorts of books, and naturally there was a large blackboard for his daily work.

Seeing Li Shu pull up the blackboard, Wang Ze'an took the initiative to find a map of Anjing City.

However, he still thought Li Shu wanted to use the center of the circle for positioning, and said, "Li Shu, as I said, this method may not be applicable to this case. Director Yang and the others have been analyzing it, and we have also analyzed it ourselves. We think that the probability of itinerant crime is higher."

The location of the center is only useful if it is said that the person is a local of Ankyo or has lived there for a long time.

Li Shu picked up the chalk and said, "It's not the center method."

The circle center method is useless, and the Rosemo model is also not applicable.

However, after reviewing a large amount of information, Li Shu also had some ideas of his own, namely, to enlarge the map.

For example, what was originally a study of one city is now encompassed by more than 20 counties and cities surrounding Anjing, treated as a whole and studied together.

"Brother Wang, do you understand what I mean?" Li Shu asked, drawing small and large circles on the blackboard.

Wang Ze'an is a top talent; his mind works incredibly fast, he understands instantly.

He immediately raised a question, saying, "Your line of thinking is certainly not wrong, but the problem is that the premise of center positioning is that the suspect is located in all crime scene areas, which is equivalent to an isolated model."

After a moment's thought, he said, "Let me give you an example."

"For example, if a crime occurs in this building, because there are guards at the entrance, outsiders cannot enter, so the crime can only be committed from inside. The center positioning is used to analyze this situation."

"Your idea is that the suspect climbed over the wall from the Public Security University to commit the crime. So, analyzing the situation in our building alone is useless. The initial assumptions were flawed."

Li Shu nodded.

That's really smart; the thinking is clear.

"Brother Wang, don't be anxious, let me explain slowly."

Li Shu picked up the chalk and began to draw grids.

This is the core of the Rosmo algorithm.

If the entire area is divided into a grid according to a certain scale, then the crime scene becomes a coordinate.

Then, some influencing factors are added to the model calculation.

For example, distance decay.

Criminals are usually unwilling to travel too far to commit crimes; the closer they are to the crime scene, the higher the probability of success.

There is also a buffer.

Criminals will consciously avoid committing crimes near their homes, because it would be easier for acquaintances to spot them.

"For this distance, we'll use the Manhattan distance for calculations," Li said.

Wang Zening was secretly amazed.

That's impressive; you have quite a wide range of knowledge.

Li Shu immediately began writing formulas and defining arithmetic symbols.

First, determine whether it is in the buffer zone, then calculate the values ​​of the two parts, and finally calculate the probability of each cell by multiplying the contribution by the coefficient.

It's just copying what he learned; anyway, with Li Shu's math skills, he can understand the general idea.

But Wang Ze'an should be fine; I understand.

He stepped forward and carefully examined the contents of the blackboard.

After thinking for a while, he said, "Your idea is quite interesting. It's essentially a way of quantifying the circle center positioning method and using a mathematical model to calculate the probability, which is more precise."

For circular positioning, simply draw a few circles.

Li Shu's method allows for a very small scale, effectively forming a probability matrix.

"That's a very original idea."

Wang Ze'an gave his evaluation first, nodding repeatedly and saying, "Academician Shi is right. You like to use your brain and have all sorts of strange and wonderful ideas. I feel that if you went to do theoretical research, you would definitely be a master."

In research, some people are just technical workers; they do whatever they're told.

Others, however, use their brains and come up with imaginative ideas; these people are more valuable.

But then his tone suddenly changed, and he said, "However, it's still the same problem. All your ideas are based on the premise that the suspect lives in the area where the crime occurred. Once the suspect moves across cities, then all your calculations are fundamentally wrong."

After saying that, perhaps feeling that it might dampen Li Shu's enthusiasm, he quickly added, "Of course, your idea is commendable, especially this mathematical model, which I think is very comprehensive."

"It's a very good method for analyzing the scope of criminal activity. You can write a paper about it and publish it in a journal. I'll show it to my teacher too. I think it's really valuable."

In China, criminal investigations are still mainly based on experience.

Take this concept of center positioning, for example. It has been published in journals and introduced in subsequent articles, but nobody cares about it, and nobody actually uses it.

People like Li Shu, who are willing to accept, think about, and do theoretical research, are very, very rare.

Therefore, when Wang Ze'an looked at Li Shu again, his gaze changed, and he became even more appreciative.

Li Shu hurriedly said, "Brother Wang, let's not talk about the thesis for now. Do you understand what I'm saying now?"

Wang Ze'an nodded, punched Li Shu lightly, and laughed, "What, are you testing me?"

I have a bit of a low opinion of myself as a PhD.

No way.

Li Shu shook his head, then said, "Since you understand, I'll now begin to explain my true thoughts."

This is still just the prelude.

"Good heavens!"

Wang Ze'an exclaimed in surprise, "You're really going to say something shocking today!"

Based on the international mainstream theory of circle center positioning, they put forward their own ideas and even made a mature mathematical model.

This is already incredible in itself; it's a major theoretical breakthrough.

So you're telling me this was just a prelude, and you haven't even revealed your real thoughts yet?

When they first met over the phone, Wang Ze'an felt that Li Shu was a treasure trove, someone you could dig up and find amazing things.

Now it seems like a gold mine!

Li Shu smiled and quickly got to the point.

Wang Ze'an believed that centering the circle was useless, and Li Shu also noticed this point.

The reason for including all the surrounding prefectures and cities of Ankyo is to apply another theory on a larger scale.

According to the system data, around 2000, a guy named Maurice Godwin proposed a predator model.

He noticed the shortcomings of the two major schools of thought and began to study mobile crime.

He believes there are two modes of mobile crime.

One type is commuters.

He lived in City A, committed crimes in City B, and then returned to City A.

The whole process is just like commuting to work.

Another type is called a predator.

It's like a hunter searching for prey in a primeval forest, following unseen paths aimlessly.

The most crucial element of his model is the path.

That is, the road network.

Li Shu pointed to a spot on the outskirts of Anjing on the map and then said, "Assuming the suspect lives here, if he wants to commit a crime in Anjing, whether he takes a car, drives himself, or even walks, he relies on the transportation network."

Li Shu swished and drew random lines towards the center of the circle, using this point as the center.

"My idea is that every county and city surrounding Anjing is a starting point."

"So, starting from each point, there are different paths to reach the crime scene."

"We assign different weights to different paths, put them into my previous model for calculation, and then consider the time."

The suspect committed 43 crimes over a period of more than two years, averaging one crime every two weeks.

Some intervals were less than half a month.

During this timeframe, the suspect would travel from another location to Anjing, search for the target, track the target, commit the crime, escape, and then return home.

These are all variables that can be considered.

"We have a total of 43 cases as a sample, which allows us to analyze a large number of variables from these cases, and then create a mathematical model to analyze all the surrounding counties and cities to see which county or city has the highest probability and prioritize its investigation."

"Brother Wang, did you understand?"

Li Shu countered with a question.

This idea was inspired by the Rossmore model and predator theory.

But Li Shu didn't understand how to calculate it or how to create such a mathematical model.

He could only explain it to Wang Ze'an, guiding him to understand and asking this highly educated PhD to help him with the calculations.

"you----"

Wang Ze'an was about to speak subconsciously, but he only managed to utter one word before stopping.

He crossed his arms, his eyebrows furrowed, and stared intently at the blackboard.

After thinking for a while, he said, "I think—"

He only managed to say two words before getting stuck again.

He still hugged his arms tightly, deep in thought.

Li Shu didn't dare to interrupt his train of thought and watched him nervously.

At first, Wang Ze'an only thought about it.

A few minutes later, he picked up the chalk and started writing and drawing on the blackboard.

Li Shu felt dizzy after just one glance.

I knew he was writing mathematical formulas, but when I looked at it, it was all English letters.

This is why Li Shu doesn't like math; it's too difficult.

And we agreed to only study numbers.

He wrote and erased, wrote and erased, pondered for a long time, but still had no idea.

Finally, he simply threw down the chalk and said, "Well, I'm not very good at math. Here, you go ahead and do your thing. I need to ask someone about this."

After saying that, he turned and ran out the door.

He ran a few steps, then quickly ran back, poking his head out and saying, "Don't erase the blackboard, I'll take another look later."

He turned back, but after taking only two steps, he turned around again, leaned forward, and gave Li Shu a thumbs up.

Impressed!

Without saying a word, he turned and left, hurriedly went downstairs, got in his car, and headed straight for Peking University.

Li Shu knew that he had gone to call for reinforcements.

There are plenty of talented people in Ankyoreh now, so they should be able to solve this problem.

However, this analytical model is a safety net.

If, as Wang Ze'an said, we can be more optimistic and positive, and if the fingerprints match directly, then we won't have to go through all this trouble.

So everyone went about their own business. Li Shu returned to his room and continued analyzing fingerprints.

As soon as you sit down, you automatically get into the zone.

The system is constantly gaining experience, and it's doing complex fingerprint guessing and puzzle-solving quite quickly.

Li Shu didn't care and devoted himself wholeheartedly to his work.

Before you know it, several hours have passed, and Tan Ligang comes over to tell Li Shu to get off work.

"I'll watch for a while longer."

Anyway, there's nothing to do back at the guesthouse.

Tan Ligang nodded, turned around to get his lunchbox, went to the cafeteria to get his food, brought it back, and asked Li Shu how things were going.

"It's alright. I estimate it should be ready in another two or three days."

As I've said before, the progress here is so obvious that the results are clear at a glance.

"Then we have to wait for Academician Shi to do the fingerprint comparison. The main problem is that the conditions are too poor. I don't think we can extract a single fingerprint that is good enough for comparison."

Tan Ligang nodded slightly, patted Li Shu on the shoulder appreciatively, said "thank you for your hard work," and told Li Shu to eat first and then continue cooking.

Li Shu also felt dizzy and lightheaded, seeing stars before his eyes. He stretched, got up and moved around for a while, then ate his meal.

While they were eating, Wang Ze'an rushed in with one other person.

It was a man of similar age to him, with a thin face and a scholarly air. He looked at Li Shu curiously after entering the room.

Let me introduce myself.

Wang Ze'an pointed at the man and said, "Geng Zheng, you're from the same hometown as me, from Peng'an, Ningjiang. You're now in the Department of Probability and Statistics at Peking University, oh no, it should be called the School of Mathematical Sciences now, since you merged with the Department of Mathematics this year."

"Professor, specializing in probability and statistics, causal inference, this is your level in the country."

He proudly gave a thumbs up.