abstracts for talks on Monday

abstracts/raphaelmorsomme.qmd

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+title: "Data-augmentation Markov chain Monte Carlo for fitting semi-Markov breast cancer models to individual screens"
+author: "Raphael Morsomme"
+date: "Oct 30, 2023"
+---
+
+
+
+
+
+## Abstract 
+
+Compartmental models offer a mechanistic representation of the evolution of breast cancer over time. These models are often assumed to possess the Markovian property for mathematical convenience. In this paper, we introduce a semi-Markov model that allows for indolent pre-clinical cancer and design a novel data-augmentation Markov chain Monte Carlo sampling algorithm for fitting this model to individual screening and diagnosis histories. Our fully Bayesian approach properly accounts for the uncertainty in the exact onset time of pre-clinical cancers by treating these as latent variables. We show that the sampling algorithm swiftly explores the joint posterior distribution of the model parameters and the latent variables and that the Markov chain underlying the algorithm is uniformly ergodic. We illustrate the usefulness of our semi-Markov model by analyzing a data set of 80,000 women from the Breast Cancer Surveillance Consortium and discuss its applicability to other processes which are partially observed such as ovarian cancer.
+
+
+
+
+### Advisor(s)
+
+Prof. Jason Xu
+

abstracts/xiaojunzheng.qmd

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+---
+title: "BLAST: Bayesian Online Structure-aware Change-point Detection"
+author: "Xiaojun Zheng"
+date: "Oct 30, 2023"
+---
+
+
+
+
+
+## Abstract 
+
+Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. Deep Gaussian Markov Random Fields (Deep GMRF) extend traditional GMRFs by integrating deep learning techniques, enabling the model to capture more complex and non-linear relationships in the data. This hybrid approach combines the interpretability and structure of GMRFs with the flexibility and representational power of deep neural networks. For image data, there are a broad array of interpretable features such as edges, blurs, and shapes, that may be useful for monitoring. We propose a new method, called Bayesian Online Structure-aware Change Detection (BLAST), which Learns important image features via offline pre-change data via the deep GMRF, and then integrates the trained model within Bayesian change-point detection for scalable monitoring. We investigate the effectiveness of BLAST in a suite of numerical experiments.
+
+
+
+
+### Advisor(s)
+
+Simon Mak