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Methods for order restricted estimation for length biased data, with applications to crime scene prior probability estimation

Wierzchoslawska, Julia LU (2026) In Master's Theses in Mathematical Sciences MASM02 20242
Mathematical Statistics
Abstract
The objective of this thesis is to expand on previous research by implementing a new method for order-restricted estimation of length-biased data. This paper addresses the implementation and analysis of a stochastic spatial probabilistic model for characterizing the geometric relationship between perpetrator addresses and crime scene locations.
The given data are length-biased observations of a decreasing density function. The approach addresses the length-bias problem using David Cox's estimator, a known solution, while handling the order restriction through the Grenander estimator, using estimation under monotonicity.
To evaluate this new method for estimating prior probabilities from crime scenes, the following analysis was conducted.... (More)
The objective of this thesis is to expand on previous research by implementing a new method for order-restricted estimation of length-biased data. This paper addresses the implementation and analysis of a stochastic spatial probabilistic model for characterizing the geometric relationship between perpetrator addresses and crime scene locations.
The given data are length-biased observations of a decreasing density function. The approach addresses the length-bias problem using David Cox's estimator, a known solution, while handling the order restriction through the Grenander estimator, using estimation under monotonicity.
To evaluate this new method for estimating prior probabilities from crime scenes, the following analysis was conducted. Simulations were performed in which length-biased order-restricted samples were processed through the new method and then compared against both a simulated ideal estimated distribution (non-length-biased) and a theoretical ideal distribution. Following this, the new method was applied directly to the real data, where we obtained a density estimate. This density and method could be used to assign prior probabilities to suspects in real-world criminal cases. (Less)
Please use this url to cite or link to this publication:
author
Wierzchoslawska, Julia LU
supervisor
organization
course
MASM02 20242
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMS-3136-2026
ISSN
1404-6342
other publication id
2026:E15
language
English
id
9223350
date added to LUP
2026-02-27 10:54:26
date last changed
2026-02-27 10:54:26
@misc{9223350,
  abstract     = {{The objective of this thesis is to expand on previous research by implementing a new method for order-restricted estimation of length-biased data. This paper addresses the implementation and analysis of a stochastic spatial probabilistic model for characterizing the geometric relationship between perpetrator addresses and crime scene locations.
The given data are length-biased observations of a decreasing density function. The approach addresses the length-bias problem using David Cox's estimator, a known solution, while handling the order restriction through the Grenander estimator, using estimation under monotonicity.
To evaluate this new method for estimating prior probabilities from crime scenes, the following analysis was conducted. Simulations were performed in which length-biased order-restricted samples were processed through the new method and then compared against both a simulated ideal estimated distribution (non-length-biased) and a theoretical ideal distribution. Following this, the new method was applied directly to the real data, where we obtained a density estimate. This density and method could be used to assign prior probabilities to suspects in real-world criminal cases.}},
  author       = {{Wierzchoslawska, Julia}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Methods for order restricted estimation for length biased data, with applications to crime scene prior probability estimation}},
  year         = {{2026}},
}