Multiplicative Hazard Modeling for A Priori Probabilities in Criminal Cases
(2025) In Bachelor’s Theses in Mathematical Sciences MASK11 20251Mathematical Statistics
- Abstract
- The aim of this thesis is to explore how methods from survival and event history analysis, namely relative risk regression, can be used to estimate prior probabilities in criminal cases, based on the distance between the potential perpetrator’s residence and the crime scene as well as further characteristics of the potential perpetrator. The locations of potential perpetrators residences can be modeled using an isotropic spatial Poisson process that can be transformed into an inhomogeneous Poisson process on the positive real line, counting the number of potential perpetrators that live within a given distance of the crime scene. Given this model, we discuss two formulations for analyzing a dataset of real crime cases using the Cox... (More)
- The aim of this thesis is to explore how methods from survival and event history analysis, namely relative risk regression, can be used to estimate prior probabilities in criminal cases, based on the distance between the potential perpetrator’s residence and the crime scene as well as further characteristics of the potential perpetrator. The locations of potential perpetrators residences can be modeled using an isotropic spatial Poisson process that can be transformed into an inhomogeneous Poisson process on the positive real line, counting the number of potential perpetrators that live within a given distance of the crime scene. Given this model, we discuss two formulations for analyzing a dataset of real crime cases using the Cox regression model with associated maximum partial likelihood estimator and the Breslow estimator from survival analysis. The first approach, based on the single-event framework from survival analysis, treats each case as its own process and is shown to be misaligned with the aforementioned spatial model. The second approach addresses this by aggregating crime cases sharing the same covariates into one isotropic spatial Poisson process that can be transformed into a one-dimensional inhomogeneous Poisson process. The intensities of such processes can then be estimated using the relative risk regression framework from survival analysis, before mapping back to spatial intensities. (Less)
- Popular Abstract
- What is the probability that the defendant in a criminal trial is the actual perpetrator before any evidence about the identity of the perpetrator has been presented? This is the problem of the prior. In a locked-room scenario, such as a murder mystery with five potential perpetrators on a boat, this seems to be quite a simple problem. They should be equally likely and therefore all receive a one-in-five prior probability. However, in the real world, you cannot simply draw a boundary around all potential perpetrators and assign everyone inside the same prior probability. A natural idea would be to quantify the opportunity to commit a crime using the distance between the crime scene and the potential perpetrator’s residence. Can additional... (More)
- What is the probability that the defendant in a criminal trial is the actual perpetrator before any evidence about the identity of the perpetrator has been presented? This is the problem of the prior. In a locked-room scenario, such as a murder mystery with five potential perpetrators on a boat, this seems to be quite a simple problem. They should be equally likely and therefore all receive a one-in-five prior probability. However, in the real world, you cannot simply draw a boundary around all potential perpetrators and assign everyone inside the same prior probability. A natural idea would be to quantify the opportunity to commit a crime using the distance between the crime scene and the potential perpetrator’s residence. Can additional characteristics of the potential perpetrator be used? And what would be a justified way of incorporating them into the statistical estimation? To address these questions, we turn to survival and event history analysis, a branch of statistics usually used to analyze the time it takes until one or more events occur. A common application would be to analyze the time from the diagnosis of a terminal illness to the subsequent death. We repurpose these tools by treating the distance from the crime scene as time and the perpetrators’ residences as the events. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9213442
- author
- Bürger, Henri Willhelm LU
- supervisor
- organization
- course
- MASK11 20251
- year
- 2025
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor’s Theses in Mathematical Sciences
- report number
- LUNFMS-4086-2025
- ISSN
- 1654-6229
- other publication id
- 2025:K34
- language
- English
- id
- 9213442
- date added to LUP
- 2025-10-02 15:50:59
- date last changed
- 2025-10-02 15:50:59
@misc{9213442,
abstract = {{The aim of this thesis is to explore how methods from survival and event history analysis, namely relative risk regression, can be used to estimate prior probabilities in criminal cases, based on the distance between the potential perpetrator’s residence and the crime scene as well as further characteristics of the potential perpetrator. The locations of potential perpetrators residences can be modeled using an isotropic spatial Poisson process that can be transformed into an inhomogeneous Poisson process on the positive real line, counting the number of potential perpetrators that live within a given distance of the crime scene. Given this model, we discuss two formulations for analyzing a dataset of real crime cases using the Cox regression model with associated maximum partial likelihood estimator and the Breslow estimator from survival analysis. The first approach, based on the single-event framework from survival analysis, treats each case as its own process and is shown to be misaligned with the aforementioned spatial model. The second approach addresses this by aggregating crime cases sharing the same covariates into one isotropic spatial Poisson process that can be transformed into a one-dimensional inhomogeneous Poisson process. The intensities of such processes can then be estimated using the relative risk regression framework from survival analysis, before mapping back to spatial intensities.}},
author = {{Bürger, Henri Willhelm}},
issn = {{1654-6229}},
language = {{eng}},
note = {{Student Paper}},
series = {{Bachelor’s Theses in Mathematical Sciences}},
title = {{Multiplicative Hazard Modeling for A Priori Probabilities in Criminal Cases}},
year = {{2025}},
}