Modeling of Locally Scaled Spatial Point Processes, and Applications in Image Analysis

Spatial point processes provide a statistical framework for modeling random arrangements of objects, which is of relevance in a variety of scientific disciplines, including ecology, spatial epidemiology and material science. Describing systematic spatial variations within this framework and developing methods for estimating parameters from empirical data constitute an active area of research. Image analysis, in particular, provides a range of scenarios to which point process models are applicable. Typical examples are images of trees in remote sensing, cells in biology, or composite structures in material science. Due to its real-world orientation and versatility, the class of the recently developed locally scaled point processes appears particularly suitable for the modeling of spatial object patterns. An unknown normalizing constant in the likelihood, however, makes inference complicated and requires elaborate techniques. This work presents an efficient Bayesian inference concept for locally scaled point processes. The suggested optimization procedure is applied to images of cross-sections through the stems of maize plants, where the goal is to accurately describe and classify different genotypes based on the spatial arrangement of their vascular bundles. A further spatial point process framework is specifically provided for the estimation of shape from texture. Texture learning and the estimation of surface orientation are two important tasks in pattern analysis and computer vision. Given the image of a scene in three-dimensional space, a frequent goal is to derive global geometrical knowledge, e.g. information on camera positioning and angle, from the local textural characteristics in the image. The statistical framework proposed comprises locally scaled point process strategies as well as the draft of a Bayesian marked point process model for inferring shape from texture

Bayesian causal inference of cell signal transduction from proteomics experiments

Cell signal transduction describes how a cell senses and processes signals from the environment using networks of interacting proteins. In computational systems biology, investigators apply machine learning methods for causal inference to develop causal Bayesian network models of signal transduction from experimental data. Directed edges in the network represent causal regulatory relationships, and the model can be used to predict the effects of interventions to signal transduction. Causal inference approaches applied to proteomics experiments use statistical associations between observed signaling protein concentrations to infer a causal Bayesian network model, but there is no experimental and analysis framework for applying these methods to this experimental context. The goal of this dissertation is to provide a Bayesian experimental design and modeling framework for causal inference of signal transduction. We evaluate how different high-throughput experimental settings affect the performance of algorithms that detect conditional dependence relationships between proteins. We present a Bayesian active learning approach for designing intervention experiments that reveal the direction of causal influence between proteins. Finally, we present a Bayesian model for inferring the parameters of the conditional probability density functions in a causal Bayesian network. The parameters are directly interpretable as a function of the rate constants in the biochemical reactions between interacting proteins. The work pays special attention to analysis of single-cell snapshot data such as mass cytometry, where each cell is a multivariate cell-level replicate of signal transduction at a single time point. We also address the role of large-scale bulk experiments such as mass-spectrometry-based proteomics, and small-scale time-course experiments in causal inference

A Tutorial on Bayesian Nonparametric Models

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.Comment: 28 pages, 8 figure