Criminal Profiling in police practices, science and …Tommaso Fornaciari Criminal Profiling in police practices, science and fiction: from the origins to future perspectives AINL-ISMW

Tommaso Fornaciari

Criminal Profilingin police practices, science and fiction:from the origins to future perspectives

AINL-ISMW FRUCT 2015Saint Petersburg, November 12th, 2015

Outline

1 IntroductionGoalPredictions�estions

2 HistoryOriginsLiteratureThe first profilePsychoanalysis

3 The American SchoolMad BomberFBIProcessProfilesCrime scenesAssumptions

4 The European SchoolInvestigative PsychologyAuthors’ classificationComputational methods

5 Myth or reality?CriticismsFalse typologiesOutdated theoryNo compelling evidenceBiases

6 The Italian experienceUACVCriminal analysisCrime scene analysisMorellian methodThe Oxford’s sketch

7 Investigative reasoningOrientationsClinical approachStatistical approachRequirementsInferences

8 Bayesian NetworksBasic lawsBayes’ theoremMultiple variablesGraphical modelsLearning

9 ConclusionPastFuture

Outline










Goal

Criminal Profiling is the discipline aimed to support police investigationthrough the realisation of:

• Author’s profile, for supporting the identification of the unknown authorof a crime;

• Victim’s profile, which can have di�erent goals:• It can be an activity integrative of the author’s profile;• In case of suspect deaths, it can contribute to establish if the death was

caused by a homicide or a suicide. This kind of profile is also known aspsychological autopsy.

Introduction Goal 1/55

Predictions

The profiles can be focused on the prediction of:

• Psychological characteristics of the subjects, that is, typically, personalitytraits, cognitive schemes and mental illnesses;

• Socio-demographic and biographic characteristics, such as age, sex, ethnicand cultural origin, life style, technical skills and so on.

In both cases, if Criminal Profiling is a behavioral science, it is a sciencewithout subject, as the person who is investigated is absent and unknown.

The behavior cannot be observed directly, only indirect sources of informationcan be used.

Introduction Predictions 2/55

�estions

This talk will try to give answer to the following questions:

• Is it possible to carry out behavioral science without observable behaviors?

• Can such a discipline give a concrete contribution to investigation?

• Which methods and tools can be exploited?

Introduction �estions 3/55

Outline










Phrenology

The most ancient root of Criminal Profiling is the phrenology of the Germanphilosopher Franz Joseph Gall (1758-1828).

He tried to infer psychological qualities of hesubjects through the observation of thesurface of the cranium. The idea may lookingenuous nowadays, but he was the first tosense that cognitive faculties were located inbrain’s areas.

He dealt with deviant behaviors and hismodernity is shown in his statement “Thejudgment in criminal proceedings is issuedwithout taking into account the mentalorganization of the guilty party” (Selling, 1946).

He is considered as one of the fathers of the modern neurophysiology.

History Origins 4/55

Criminal anthropology and anthropometry

The second roots of Criminal Profiling are:• The criminal anthropology of Cesare Lombroso (1835-1909);• The anthropometry of Alphonse Bertillon (1853-1914).

Lombroso tried to develop the Gall’stheories in the field of criminology,looking for correlations betweenphysiognomic characteristics and criminalbehaviors.

Bertillon, in turn, realised the firstanthropometric identification systememployed in criminal investigation, whichrelied on accurate face and bodymeasurements.


The contribution

The approach of Lombroso and Bertillon was a�ected by the philosophypositivistic and deterministic of the XIX century, but while anthropometry ofBertillon developed as an independent field of research, the anthropologicalcriminology of Lombroso is abandoned.

However, their contribution spread the idea that criminals can be describedand even divided into categories.

In fact, the so-called constitutionalist schools were active until the sixties,when the discovery of the DNA moved the discussion elsewhere (De Giovanni,1891; Kretschmer, 1925; Sheldon and Stevens, 1942).But this is another story...


Literature

The possibility of classifying the criminals as belonging to di�erent categoriesis not the only assumption of Criminal Profiling.

The main assumption is that indirect behavioral evidence concerning anunknown subject can provide information reliable and useful for hisidentification.

And this idea does not come from science... but from fiction.

History Literature 7/55

Zadig

In 1747, Voltaire published the first edition of the Zadig.

In one episode of the tale, Zadig, observingsigns on the ground, plants and rocks,carries out some brilliant inferences, whichallow him to describe precisely the dog andthe horse of the �een of Babylon, withouthaving seen them (Voltaire, 1748).

In this narrative, he showed as signsproduced by the human (or animal!)behavior can give relevant informationabout their outhor.

In fact, according to Voltaire, the nature is“the great book that God put under our eyes”(Eco and Sebeok, 2004; Bui, 2006).


Dupin

The suggestion of Voltaire was not exploited in science...

In “The murders in the Rue Morgue”, whichis considered the first crime novel inliterature, Edgar Allan Poe (1841) createsAuguste Dupin, the archetype of theinvestigator, who analyses the data startingfrom the crime scene and thorough a chainof inferences comes to identify the authorof the crime.


Sherlock Holmes

In 1887, Sir Arthur Conan Doyle, Sco�ish physician e writer, creates thecharacter of Sherlock Holmes.

Although in a fictional context, withSherlock Holmes a real investigativeepistemology is formulated, based on theobservation of facts and on the formulationof hypotheses, similarly to what happens inthe medical field.

“There’s the scarlet thread of murder runningthrough the colourless skein of life, and ourduty is to unravel it, and isolate it, and exposeevery inch of it” (Doyle, 1887).


The first profile

London, 1888. Concerning the homicides of Jack the Ripper, a physician wroteto the police (Canter, 2004)...

Dr. Thomas Bond:The murderer must have been a man of physical strength and great coolness and daring. There isno evidence he had an accomplice. He must in my opinion be a man subject to periodic a�acks ofhomicidal and erotic mania. The character of the mutilations indicate that the man may be in acondition sexually, that may be called Satyriasis. It is of course possible that the homicidal impulsemay have developed from a revengeful or brooding condition of mind, or that religious mania mayhave been the original disease but I do not think either hypothesis is likely. The murderer inexternal appearance is quite likely to be a quiet ino�ensive looking man probably middle-aged andneatly and respectably dressed. I think he might be in the habit of wearing a cloak or overcoat orhe could hardly have escaped notice in the streets if the blood on his hands or clothes were visible.Assuming the murderer be such a person as I have just described, he would be solitary andeccentric in his habits, also he is likely to be a man without regular occupation, but with somesmall income or pension. He is possibly living among respectable persons who have someknowledge of his character and habits and who may have grounds for suspicion that he is notquite right in his mind at times. Such persons would probably be unwilling to communicatesuspicions to the police for fear of trouble or notoriety, whereas if there were prospect of reward itmight overcome their scruples.

History The first profile 11/55

Psychoanalysis

In 1906, Sigmund Freud gave a seminar titled “Psychoanalysis & theEstablishment of the Facts in Legal Proceedings” (Gulo�a, 2008).

He assumed the possibility of a direct interaction with the subject, and pointedout that:

• In psychoanalysis, there is cooperation between therapist and patient, butthere may not be in police investigation between policeman and suspect;

• The culprit is aware of what he is trying to conceal, the neurotic patient isnot;

• In the unconscious dimension there is no di�erence between a fantasyand a real action: guilty feelings can be observed both in the innocent andin the culprit.

Therefore, the observation of neurotic symptoms cannot be used to decide if acertain fantasy has been acted and psychoanalysis would not be a tool forpolice investigation (Freud, 1906).

History Psychoanalysis 12/55

The case of Philippe Halsman

In 1928, the Hebrew dentist Mark Halsman died in a hiking trip in the AustrianTyrol, in unclear circumstances.

The 22 years old son, Philippe Halsman, was accused ofparricide and the case was exploited by the nazipropaganda of antisemitism. He was sentenced to tenyears in prison.

However, Freud confirmed the positions of 1906,claiming that psychic conflicts cannot be employed forthe demonstration of guilty or innocence.

Other intellectuals, such as Albert Einstein and ThomasMann, endorsed his innocence as well and PhilippeHalsman was released in 1930. He went to UnitedStates, where he became a famous photographer.


The contribution of Reik

Theodor Reik, disciple of Freud, carried on his ideas in the field of criminology.He claimed the psychoanalysis is not suitable for the investigation of the facts,and he warned against some possible methodological errors:

• To assume any similarity between the mental processes of investigatorsand authors of crimes, and therefore to use the firsts to interpret theseconds: they might be completely di�erent.

• To assume the crime to be motivated by a logical and conscious reasons:this might not be the case.

In spite of their prudence, Freud and Reik led the psychology into the field ofcriminal investigation. It was time for the first systematic experience ofCriminal Profiling...


Outline










Mad Bomber

The first police investigation were Criminal Profiling techniques were applied,was the American case of Mad Bomber, that is George Meteski.

In the 1940s ans 1950s carried out at least 33 bomba�acks in a number of public places, such aslibraries, o�ices, theaters, terminals. Thepsychiatrist James Brussel formulated hypothesesconcerning psychological and socio-demographiccharacteristics of the bomber and, when he wasarrested, they turned out to be correct.

A�erwards, he took part in other famous policeinvestigation, but he did not reach the samesuccess (Gulo�a, 2008; Picozzi and Zappalà, 2002).Nonetheless Criminal Profiling was born asrecognised forensic discipline.

The American School Mad Bomber 15/55

FBI

Criminal Profiling was developed as method of investigation by the FBI:

1972. Creation of the Behavioral Science Unit - BSU, at the FBI Academy of�antico.

• A program of interviews of authors of violent crimes was carriedout, with the aim of classifying those subjects. In 1983, this tookthe name of Violent Criminal Apprehension Program - VICAP.

1984. Creation of the National Center for the Analysis of Violent Crime -NCAVC.

• Realisation of the profiling process (Douglas and Burgess, 1986;Douglas et al., 1986);

• Distinction between organized e disorganized author (Ressler andBurgess, 1985).

• Publication in 1992 of the Crime Classification Manual (Douglaset al., 2013).

The American School FBI 16/55

The profiling process

The profiling process, defined by the group of John Douglas, can besummarised in the following steps.

From Douglas and Burgess (1986):1 Evaluation of the criminal act itself;

2 Comprehensive evaluation of the specifics of the crime scene(s);

3 Comprehensive analysis of the victim;

4 Evaluation of preliminary police reports;

5 Evaluation of the medical examiner’s autopsy protocol;

6 Development of profile with critical o�ender characteristics;

7 Investigative suggestions predicated on construction of the profile.

The American School Process 17/55

Authors’ profiles

From (Ressler and Burgess, 1985):

Organized Disorganized

Average to above-average intelligence Below-average intelligenceSocially competent Socially inadequateSkilled work preferred Unskilled workSexually competent Sexually incompetentHigh birth order status Low birth order statusFather’s work stable Father’s work unstableInconsistent childhood discipline Harsh discipline as childControlled mood during crime Anxious mood during crimeUse of alcohol with crime Minimal use of alcoholPrecipitating situational stress Minimal situational stressLiving with partner Living aloneMobility with car in good condition Lives/works near crime sceneFollows crime in news media Minimal interest in news mediaMay change jobs or leave town Significant behavior change

(drug/alcohol abuse, religiosity, etc.)

The American School Profiles 18/55

Authors’ crime scenes

From (Ressler and Burgess, 1985):

Organized Disorganized

Planned o�ense Spontaneous o�enseVictim a targeted stranger Victim/location knownPersonalizes victim Depersonalizes victimControlled conversation Minimal conversationCrime scene reflects overall control Crime scene random and sloppyDemands submissive victim Sudden violence to victimRestraints used Minimal use of restraintsAggressive acts prior to death Sexual acts a�er deathBody hidden Body le� in viewWeapon/evidence absent Evidence/weapon o�en presentTransports victim or body Body le� at death scene

The American School Crime scenes 19/55

Assumptions

The assumption of the American school are:

• The authors of crimes can be classified as belonging to di�erent types;• To the di�erent types correspond di�erent behaviors on the crime scene.

These assumptions will be object of a long debate...

The American School Assumptions 20/55

Outline










Investigative PsychologyWhile in United States the FBI was developing its school of Criminal Profiling,in Europe the British psychologist David Canter, cooperating with the Londonpolice, carried out a similar experience, under the name of InvestigativePsychology.He focused on 5 factors (Turvey, 2011):Interpersonal Coherence. The assumption is that there is a relation between

psychological structures and behavior, so that the behavior withvictims and with other people should show some similarity.

Time and Place significance. Logistic and temporal constraints a�ect theauthor’s behavior and his mental maps, which need to beunderstood for their identification.

Criminal Characteristics. Canter categorises the authors’ behavior accordingto a instrumental and expressive dichotomy (Salfati and Canter,1999).

Criminal Career. The authors’ narratives, that is their autobiographicmemories are used to analyse their mental maps.

Forensic Awareness. Lastly, the behavior is evaluated on the basis of theauthors’ awareness of the technologies employed in policeinvestigation.

The European School Investigative Psychology 21/55

Authors’ classification

While the Canter’s a�empt to categorise the authors is conceptually similar tothat of FBI, he heavily criticises the outcomes of the American researchers.

In particular, he claims the distinction between organized and disorganizedbehavior is useless because on the crime scene the organized behavior ispervasive of the whole phenomenology of the homicides (Canter et al., 2004).

By contrast, he distinguishes:

Expressive aggressions. Motivated by emotional conditions of resentment andanger out of control.

Instrumental aggressions. Motivated by the pursuit of some kind of materialadvantage, which does not imply the desire of violence againstthe victim (Salfati and Canter, 1999).

The European School Authors’ classification 22/55

Computational methods

The greatest credit of Canter is to have introduced to Criminal Profiling bothcomputational methods and the idea that the boundaries between categoriesof authors can be fuzzy.

In order to evaluate the similaritybetween criminological variables(Lundrigan and Canter, 2001) and torealise the geographical profiling ofthe authors(Canter, 2000), heemployed the Multi DimensionalScaling - MDS, the well-knownmethods which allow graphicalrepresentations where the distancebetween entities symbolises thedegree of their similarity (Hastieet al., 2009).

The European School Computational methods 23/55

Outline










Criticisms

Even thanks to its relationship with the literature, Criminal Profiling gave raiseto great enthusiasm, but even to an intense debate.

From Snook et al. (2008):1 most of the typologies used to create criminal profiles are in fact false

typologies;

2 the majority of CP approaches are based on an outdated theory ofpersonality that lacks empirical support;

3 there is no compelling evidence that predictions made by professionalprofilers are significantly more accurate than those made by nonprofilers;

Myth or reality? Criticisms 24/55

False typologies

The assumptions underlying the typology of FBI are that...

From Snook et al. (2008):1 O�enses can be categorized as organized (e.g., well planned) or

disorganized (e.g., unplanned) based on the behaviors present at a crimescene;

2 O�enders can be categorized as organized (e.g., high functioning) ordisorganized (e.g., low functioning) based on the backgroundcharacteristics of the o�ender;

3 There is a correspondence between o�enses and o�enders (i.e., organizedo�enders commit organized crimes and disorganized o�enders commitdisorganized crimes).

In fact, according to the literature review of Canter et al. (2004), it turned outthat “preliminary evaluations of this typology suggest that it does not match thevariations in o�ender behavior” (Snook et al., 2008).

Myth or reality? False typologies 25/55

Outdated theory

From Snook et al. (2008):The majority of CP approaches [...] assume that criminal behavior isdetermined by underlying dispositions within o�enders that make thembehave in a particular way [...] leads to the assumption that o�enders willexhibit similar behaviors across their o�enses as traits, versus situationalfactors, are the determinants of behavior.

Criminal profilers do not seem to have recognized that a consensus began toemerge in the psychological literature some 40 years ago that to rely on traitsor personality dispositions as the primary explanation for behavior was aserious mistake. Situational factors contribute as much as personalitydispositions to the prediction of behavior.

Direct consequence of this consideration is the idea that the criminal behaviorcan change from case to case, according to the change of the externalcondition of the crime, regardless to the author’s internal dispositions.

Myth or reality? Outdated theory 26/55

No compelling evidence

From Snook et al. (2008):Any police professional with a good knowledge of the criminological literatureshould be able to achieve this level of success simply by relying on base rateinformation. In other words, success in CP may not be based on specializedknowledge of the peculiarities and idiosyncrasies found at a given crime scene.

There are likely other o�icers who use CP but do not believe that it works. Wesuspect that some of these o�icers might use CP because they believe (or areinstructed) that it is their duty to use all available investigative techniques.Others may believe that they have nothing to lose in seeing what a profiler cano�er to an investigation. It is not known, however, whether CP is helpful orharmful to police investigation.

Myth or reality? No compelling evidence 27/55

Biases

In the opinion of Snook et al. (2008), the generalised confidence in thee�ectiveness of Criminal Profiling relies on three biases:

Self-serving bias. “Profilers might assign more personal responsibility toinvestigative success than to investigative failure.”

Overconfidence bias. They could be “more confident in their ability to makeaccurate predictions than they should be.”

Confirmation bias. That is the tendency which “involves looking for, o�enunconsciously, evidence that confirms an existing belief andignoring or filtering out evidence that disconfirms that belief.”

Hindsight bias. Which refers to the propensity to “evaluate the accuracy of aprofile a�er the apprehension of the criminal.”

Myth or reality? Biases 28/55

Outline










UACV

The Italian experience of Criminal Profiling begins in the 1990s, and this wasmaybe a fortune, as it was possible to take into account the ongoing debateconcerning the discipline and of the radical technological innovations inforensic sciences.

In 1995, within the Forensic Science Police Service, itwas constituted the Violent Crime Analysis Unit -UACV, with the aim of “supporting investigation forbloody and without apparent reason murders”(Montanaro, 1996; Fornaciari and Bui, 2005).

From the foundation until 2007, the UACV was directed by Dr. Carlo Bui.

The Italian experience UACV 29/55

Criminal analysis

The criminal analysis is aimed to:• Realise the author’s profile, in the traditional sense of Criminal Profiling;• Support the investigation on the crime scene, for finding and collecting

evidence;

The activities concern three areas:• Crime scene analysis;• Investigative information analysis;• Behavioral anaylisis.

And they are carried out through:• The Morellian method (Bui, 2006).• The logical-statistical method;

The Italian experience Criminal analysis 30/55

Crime scene analysis

The basic idea of crime scene analysis is formalised by the exchange principleof Locard (1920): every contact leaves a trace.Therefore the author will leave something of himself on the victim and on thecrime scene, and victim and crime scene will leave something of themselves onthe author.

From Kirk (1953):Wherever he steps, whatever he touches, whatever he leaves, evenunconsciously, will serve as silent evidence against him. Not only hisfingerprints or his footprints, but his hair, the fibers from his clothes, the glasshe breaks, the tool mark he leaves, the paint he scratches, the blood or semenhe deposits or collects - all these and more bear mute witness against him.This is evidence that does not forget. It is not confused by the excitement ofthe moment. It is not absent because human witnesses are. It is factualevidence. Physical evidence cannot be wrong; it cannot perjure itself; it cannotbe wholly absent. Only its interpretation can err. Only human failure to find it,study and understand it, can diminish its value.

The Italian experience Crime scene analysis 31/55

Morellian method

Introduced in criminal analysis by Bui(2006), this method was applied by thehistorian of art Giovanni Morelli in theanalysis of artworks, in particular for theauthor a�ribution of anonymous paintings.

According to Giovanni Morelli, to a�ributean anonymous work of art to its author, it isnecessary to focus on the more negligibledetails, such as ear lobes, nails, the form ofthe hands and the fingers, and not on themore striking features, that are more easilyimitated. The personality has to besearched “where the personal e�ort isweaker”, and then where the expression ismore spontaneous (Morelli, 1880).

The Italian experience Morellian method 32/55

The Oxford’s sketch

This sketch of the Oxford’scollection is supposed to be made byRa�aello Sanzio...

The Fornarina is a famous paintingof Ra�aello...

The Italian experience The Oxford’s sketch 33/55


Freud agreed with Morelli, saying that the Morellian method is “strictly relatedto the approach of medical psychoanalysis. Also the psychoanalytical method isused to penetrate secret and hidden things on the basis of unappreciated orunperceived elements, debris or ‘rubbish’ of our observation” (Freud, 1913).



However, in the perspective of Morelli, not the deep and hidden meaning ofthe behavior is investigated, but its spontaneous and overlooked expression.

This idea, with the exchange principle of Locard, is the basis for crime sceneinvestigation.


Outline










Clinical vs. statistical approach

The task of Criminal Profiling is to formulate inferences having the highestprobability of being correct or, in Popperian terms, of resisting falsification.

From Snook et al. (2008):Although there are no standardized techniques for making these predictions,the di�erent approaches to CP can be broadly classified as having a clinical orstatistical orientation.

Clinically oriented profilers draw on their training, knowledge, experience,and/or intuition to predict o�ender characteristics.

By contrast, statistically oriented predictions are derived from an analysis ofo�enders who have previously commi�ed crimes that are judged as similar tothose being investigated.

Investigative reasoning Orientations 36/55

Clinical approach

The clinical approach is essentially deductive: it produces predictions relyingon theories about criminal behavior, and it applies general principles toparticular cases.

It has noble origins:

From Douglas and Burgess (1986):The process used by the person preparing a criminal personality profile is quitesimilar to that used by clinicians to make a diagnosis and treatment plan: datais collected and assessed, the situation reconstructed, hypotheses areformulated, a profile developed and tested, and the results reported back.

Investigative reasoning Clinical approach 37/55

Clinical approach

The persuasive and well wri�en statement of Douglas and Burgess (1986)made generations of aspirant profilers (especially psychologists ) to dream.Unfortunately...

1 No clinical method exists without direct interaction with the subject;

2 Clinical method are aimed to the healing of a known subject, CriminalProfiling is aimed to the identification of an unknown subject;

From Snook et al. (2008):Empirical research has shown that clinical experience has a limited e�ect onthe accuracy of psychologists’ and psychiatrists’ judgments across a range oftasks.

In addition, Faust and Ziskin (1988) found low intra- and interclinicianconsistency in judgments of mental health status and argued that whenclinicians’ predictions are compared against objectively determinable harddata their error rate o�en exceeds their accuracy rate.


Clinical approach







Clinical approach







Clinical approach







Statistical approach

The statistical approach is essentially inductive: it produces predictions relyingon data about criminal behavior, and it generalises to new cases theobservations carried out in previous cases.

The accent is not on the personal characteristics of the subjects, but on thesituational factors which can a�ect the behavior.

Investigative reasoning Statistical approach 39/55

Practical cases

Case A Case B

Age 20 33Sex Female FemaleLifestyle Prostitution Prostitution

DrugsPlace of discovery Countryside CountrysidePosition of the body Prone ProneNaked Yes YesOther conditions Sexual areas shown Sexual areas shownWeapon Blunt object KnifePosition of the wounds Head, temporal area Breasts

Head, frontal area Right armRight gluteus

Writings on the scene Yes No


Practical cases

Case C Case D

Age 36 16Sex Female FemaleLifestyle Normal NormalPlace of discovery Indoor IndoorPosition of the body Supine SupineNaked Yes NoOther conditions Sexual areas shown Sexual areas shownWeapon Knife KnifePosition of the wounds Throat ThroatWritings on the scene No No


Requirements

As the previous slides should have suggested, an e�ective Criminal Profilingneeds:

• A systematic data collection, aimed to build a reliable basis of knowledgeof the phenomenons;

• The ability to carry out good inferences.

Investigative reasoning Requirements 42/55

Inferences

Taroni et al. (2010) summarised the requirements the inferences should meet:

Balance. The inferences should be impartial: “an interpretation is withoutmeaning unless the scientist clearly states the alternatives he hasconsidered” (Eve�, 1996);

Transparency. That is the possibility of “explaining in a clear and explicit waywhat we have done, why we have done it and how we have arrivedat our conclusions” (Jackson, 2000);

Robustness. The “ability to explain the grounds for his opinion together withhis degree of understanding of the particular evidence type”(Taroni et al., 2010);

Added value. The ability of giving a substantial contribution to the case;

Flexibility. That is “a form of reasoning [...] generally applicable, [...] notlimited to particular subject ma�er” (Taroni et al., 2010);

Logic. This requirement concern the principles that qualify aninference as ‘rational’, especially in conditions of uncertainty.

Investigative reasoning Inferences 43/55

Outline










Logic

The basic idea is that the degree of reliability of a prediction should beexpressed in terms of probabilities:

From Taroni et al. (2010):The mathematical theory of probability can be interpreted as a logical calculusfor fi�ing together judgments of uncertainty: as the laws of deductive logiccan be used to define formal notions of coherence for beliefs entertained withcertainty, and provide constraints to deductive reasoning by means of rules ofinference, so the laws of probability can be used as a standard of coherence forbeliefs you entertain to a certain degree only, and can be used as rules ofinference for reasoning under uncertainty.

Bayesian Networks 44/55

Basic laws of probability

Statistical independence. Variables X and Y are statistical independent if:

P(x, y) = P(x) P(y)

implying: P(x | y) = P(x) P(y | x) = P(y)

Conditional probability. Probability of x once y is observed:

P(x | y) = P(x, y)P(y)

Sum rule. The marginal distribution of a variable is obtained from a jointdistribution summing over all possible values of the othervariable:

P(x) =∑y∈Y

P(x, y) P(y) =∑x∈X

P(y, x)

Product rule. Conditional probability definition implies:

P(x, y) = P(x | y) P(y) = P(y | x) P(x)

Bayesian Networks Basic laws 45/55

Bayes’ theorem

The Bayes’ theorem is a straightforward consequence of the product rule:

P(y | x) = P(x | y) P(y)P(x)

It allows the ‘inversion’ of the statistical connections between variables. Inother words, the relationship between observation x and its ‘cause’ y can berepresented as

posterior =likelihood × prior

evidence

Bayesian Networks Bayes’ theorem 46/55

Multiple variables

The basic rules can be applied to any number of exclusive and exhaustiveuncertain propositions.

Their manipulations allow to model a certain probability given knowledge ofsome related ones.

They can be applied to multiple variables:

P(y) =∑

x

∑z

P(x, y, z) Sum rule

=∑

x

∑z

P(y | x, z) P(x, z) Product rule

=∑

x

∑z

P(x | y, z) P(y | z) P(x, z)P(x | z)

Bayes rule

Bayesian Networks Multiple variables 47/55

Graphical models

All probabilistic inference and learning come from repeated applications of thesum and product rules.

From Taroni et al. (2010):A Bayesian network is an acyclic directed graph where:

• Nodes are variables with a finite set of mutually exclusive states;• Arrows represent direct probabilistic relevance relationships among

nodes.;• To each node X with parents Y1, . . . ,Yn, is associated a probability table

containing all the conditional probabilities P(X | Y1, . . . ,Yn). If X has noparents, then its probability table reduces to probabilities P(X),unconditional on other nodes in the graph.

Judgments of dependence, and conditional independence, among variablesreflect your structural analysis of the problem.

Bayesian Networks Graphical models 48/55

Joint probability

The joint probability of a Bayesian network with K nodes is computed as theproduct of the probabilities of the nodes given their parents:

p(x) =K∏

i=1

p(xi | pai)

Variables:x1 The author is a man;

x2 A blunt object was used;

x3 The body was hidden;

x4 The victim was naked;

x5 The victim knew the author.

x1 x2

x3 x4

x5

The joint probability for the Bayesian Network above can be wri�en as follows:

p(x1)p(x2)p(x3 | x1, x4)p(x4 | x1, x2)p(x5 | x1, x3, x4)


Conditional independence

Conditional independence assumptions can be tested through the repeatedapplication of the sum and product rules.

Graphical models allow to verify them through the d-separation criterion(where d stands for directional), in three cases:

Tail-to-tail. x1 and x3 are not conditionallyindependent but they areconditionally independent given x2; x1

x2

x3

Head-to-tail. x1 and x3 are not conditionallyindependent but they areconditionally independent given x2;

x1 x2 x3

Head-to-head. x1 and x3 are conditionallyindependent but they are notconditionally independent given x2;

x1

x2

x3


Learning Bayesian Networks

From Taroni et al. (2010):A probabilistic model is basically a hypothesis about the mathematical form ofthe [conditional] probability distribution that provides the likelihoods of theobserved results; this form contains one or more characteristics of thepopulation, called parameters, which are not known.

For the estimation of the parameters, it is assumed as given:

• The structure of the model;• A dataset of examples D = x(1), . . . , x(N);• Each example x(i) is a configuration for:

• All variables in the model: the parameters are estimated simply by thenormalization of the frequencies in the Conditional Probability Tables - CPT;

• Some variables in the model. This is the frequent case of incomplete data,where:

• Imaginary prior probabilities can be provided through the experts’ experience;• Approximation methods can be employed, such as Expectation-Maximization -

EM (Dempster et al., 1977).

Bayesian Networks Learning 51/55

Summary

Bayesian Networks are graphical representations of the qualitative aspects ofprobability distributions allowing to:

• Visualize the structure of a probabilistic model in a simple and intuitiveway;

• Discover properties of the model, such as conditional independencies, byinspecting the graph;

• Express complex computations for inference and learning in terms ofgraphical manipulations;

• Represent multiple probability distributions with the same graph,abstracting from their quantitative aspects (e.g. discrete vs continuousdistributions).

• Propagate the evidence with the coherent updating of the probabilities ofnodes according to the receipt of new inputs;

• Carry out some countermeasures in case of lack of data;• Assign clear degrees of probability to the inferences.

Bayesian Networks Learning 52/55

Outline










Past

Assumptions, methodological approaches and usefulness of Criminal Profilingas it was known until 20/25 years ago, were questioned. But at that time thestate of the art of forensic sciences was pre�y primitive:

• There was no Forensic Biology;• There were no modern computers;• There was no connectivity for the transmission of information and images.

The evaluation of the history of the discipline must consider the historical andtechnological context where it developed.

Conclusion Past 53/55

Future

In spite of some interesting outcomes, such as those of Baumgartner et al.(2008), where the use of Bayesian Networks allowed to make predictions muchmore accurate than those of a team of forensic psychiatry experts, in literaturethe use of computational methods in the field of Criminal Profiling is stillrarely documented.

There are probably two main reasons for this situation:• Practitioners and researchers in the field of Criminal Profiling, who are

mostly experts in behavioral sciences (e.g. psychologist, psychiatrists orpolice o�icers) usually do not have a strong background in machinelearning.By contrast, statisticians and computer scientists rarely deal withCriminal Profiling.

• The collection of complete and reliable datasets is usually very di�icult, ifnot impossible.

Conclusion Future 54/55

Future

Nonetheless, while in the past the Criminal Profiling was mainly oriented tothe interpretation of the data, the future of the discipline depends on thesuccess (or the failure) of a three steps process, which involves the collection,the analysis and the interpretation of investigative data.

This leads to a multidisciplinary approach, as the comprehension of complexcriminal phenomena requires a set of skills in a wide range of disciplines,including at least forensic and behavioral sciences, police investigation anddata analysis.

Conclusion Future 55/55

Thanks!

Michelangelo Buonarroti, The Moses, 1513-1515San Pietro in Vincoli, Rome

“What if we were a�ributing weightand meaning to singularities thatwere indi�erent to the author... Todetails that he would haverepresented to his liking or for anyformal reasons, without anything ofsecret?

And if we were fallen victims to thesame destiny of many interpreters,who are convinced to see clearlythings that the author did not meanto create, consciously orunconsciously?

These are questions I am not able torespond.”

Sigmund FreudDer Moses des Michelangelo, 1913

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