Mathematical Models for Criminal Analysis

Course objectives

General Rigorous knowledge of probabilistic models from applications to relationships with other parts of mathematics, applicable to forensic contexts. Specific knowledge and understanding By the end of the course, the student will have acquired the basic concepts and results related to probability spaces, random variables, independence, laws of large numbers. characteristic functions, weak convergence, limit theorems and their application in forensic science. applying knowledge and understanding Upon completion of the course the student will be able to solve simple problems requiring the use of probabilistic techniques in both applications and pure mathematical problems. making judgements The student will have the foundation to analyze the similarities and relationships between the topics covered and topics in the Forensic Science course. communication skills Ability to expound the content in the oral part of the test and in any theoretical questions in the written test. learning skills The knowledge gained will enable a study related to more specialized aspects of the calculus of probability.

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MARCO ISOPI Lecturers' profile

Program - Frequency - Exams

Course program
Tools for reading a forensic report Basic tools of quantitative reasoning:  numbers and their representation; units of measurement. Refresh high school maths. The case of Sally Clark ·      Facts ·      Sudden Infant Death Syndrome ·      The trial ·      Munchausen Syndrome by Proxy ·      Roy Meadow as expert witness ·      Statistical errors ·      Prosecutor’s Fallacy     Basic Probability • Random Experiments • The language of Probability: Set Theory • The classical model of probability • combinatorics • counting when order matters • counting when order does not matter • Axiomatic approach to probability: the axioms of Kolmogorov • Conditional probability • Independence • Bayes’ theorem The case of Lucia De Berk ·  Investigation by the hospital ·  Unusual events ·  Multiplying p-values ·  After the trial The case of Kristen Gilbert ·  The case ·  Likelihood ·  Hidden variables alter odds Philosophy of probability ·  The Frequentistic Interpretation ·  Inadequacy in the Legal and Forensic Context ·  Epistemic Probability Assessment of evidence ·  the odds form of Bayes’ theorem ·  likelihood ratio ·  competing hypothesis and the weight of evidence ·  combination of evidence ·  updating your assessment Causality and counfounders ·  Discrimination at Berkeley ·  Simpson’s paradox Risk assessment ·  Game Theory ·  The prisoner’s dilemma ·  Risk assessment vs. terrorism ·  Airline passenger screening Networks ·  Basic Graph Theory ·  Random Networks ·  The 9-11 attack ·  Criminal networks
Prerequisites
High school mathematics.
Books
Slides for all lectures can be found on the course moodle page. Most of the material presented in class is from one of the following books: 1. Adam C., Essential mathematics and statistics for forensic science, ( Wiley-Blackwell 2010) 2. Aitken C.– Taroni F. – Bozza S., Statistics and the Evaluation of Evidence for Forensic Scientists, 3rd Ed (Wiley 2020) 3. Devlin K.– Lorden G., The Numbers Behind NUMB3RS: Solving Crime with Mathematics, (Penguin 2007) 4. Meester, R.– Slooten, K. Probability and Forensic Evidence: Theory, Philosophy, and Applications (Cambridge University Press 2021) 5. Schneps L.– Schneps C., Math on Trial, (Basic Books 2013) For basic probability any elementary textbook on the subject will contain the necessary material (and much more!). Two such books are: • Ash C. – The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everone Else!) (IEEE 1993) • Finkelstein M. Basic Concepts of Probability and Statistics in the Law, (Springer 2009)
Frequency
Attendance not mandatory, but strongly recommended.
Exam mode
In-class exam and/or presentation of a topic chosen with the instructor.
Bibliography
Papers and online resources can be found on the moodle page for the course.
Lesson mode
Mixed online and in class lectures.
  • Lesson code10603364
  • Academic year2024/2025
  • CourseCognitive Forensic Sciences
  • CurriculumSingle curriculum
  • Year1st year
  • Semester2nd semester
  • SSDMAT/05
  • CFU6
  • Subject areaDiscipline matematiche, informatiche e dell'ingegneria