The Use of Advanced Transportation Monitoring Data for Official Statistics

Traffic and transportation statistics are mainly published as aggregated information, and are traditionally based on surveys or secondary data sources, like public registers and companies’ administrations. Nowadays, advanced monitoring systems are installed in the road network, offering more abundant and detailed transport information than surv

Inference and experimental design for percolation and random graph models.

The problem of optimal arrangement of nodes of a random weighted graph is studied in this thesis. The nodes of graphs under study are fixed, but their edges are random and established according to the so called edge-probability function. This function is assumed to depend on the weights attributed to the pairs of graph nodes (or distances between them) and a statistical parameter. It is the purpose of experimentation to make inference on the statistical parameter and thus to extract as much information about it as possible. We also distinguish between two different experimentation scenarios: progressive and instructive designs. We adopt a utility-based Bayesian framework to tackle the optimal design problem for random graphs of this kind. Simulation based optimisation methods, mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain the solution. We study optimal design problem for the inference based on partial observations of random graphs by employing data augmentation technique. We prove that the infinitely growing or diminishing node configurations asymptotically represent the worst node arrangements. We also obtain the exact solution to the optimal design problem for proximity graphs (geometric graphs) and numerical solution for graphs with threshold edge-probability functions. We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice Zd and derive a range of both numerical and analytical results for these graphs. We introduce inner-outer plots by deleting some of the lattice nodes and show that the ‘mostly populated’ designs are not necessarily optimal in the case of incomplete observations under both progressive and instructive design scenarios. Finally, we formulate a problem of approximating finite point sets with lattice nodes and describe a solution to this problem

D3^3PO - Denoising, Deconvolving, and Decomposing Photon Observations

The analysis of astronomical images is a non-trivial task. The D3PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations. Its primary goal is the simultaneous but individual reconstruction of the diffuse and point-like photon flux given a single photon count image, where the fluxes are superimposed. In order to discriminate between these morphologically different signal components, a probabilistic algorithm is derived in the language of information field theory based on a hierarchical Bayesian parameter model. The signal inference exploits prior information on the spatial correlation structure of the diffuse component and the brightness distribution of the spatially uncorrelated point-like sources. A maximum a posteriori solution and a solution minimizing the Gibbs free energy of the inference problem using variational Bayesian methods are discussed. Since the derivation of the solution is not dependent on the underlying position space, the implementation of the D3PO algorithm uses the NIFTY package to ensure applicability to various spatial grids and at any resolution. The fidelity of the algorithm is validated by the analysis of simulated data, including a realistic high energy photon count image showing a 32 x 32 arcmin^2 observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO algorithm successfully denoised, deconvolved, and decomposed the data into a diffuse and a point-like signal estimate for the respective photon flux components.Comment: 22 pages, 8 figures, 2 tables, accepted by Astronomy & Astrophysics; refereed version, 1 figure added, results unchanged, software available at http://www.mpa-garching.mpg.de/ift/d3po

Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning

We seek to provide practicable approximations of the two-stage robust stochastic optimization (RSO) model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer first-stage decisions. In this paper, we propose novel divergence functions that produce practicable robust counterparts, while maintaining versatility in modeling diverse ambiguity aversions. Our functions yield robust counterparts that have comparable numerical difficulties to their nominal problems. We also propose ways to use our divergences to mimic existing f-divergences without affecting the practicability. We implement our models in a realistic location-allocation model for humanitarian operations in Brazil. Our humanitarian model optimizes an effectiveness-equity trade-off, defined with a new utility function and a Gini mean difference coefficient. With the case study, we showcase 1) the significant improvement in practicability of the RSO counterparts with our proposed divergence functions compared to existing f-divergences, 2) the greater equity of humanitarian response that our new objective function enforces and 3) the greater robustness to variations in probability estimations of the resulting plans when ambiguity is considered

Generalized Linear Models in Bayesian Phylogeography

abstract: Bayesian phylogeography is a framework that has enabled researchers to model the spatiotemporal diffusion of pathogens. In general, the framework assumes that discrete geographic sampling traits follow a continuous-time Markov chain process along the branches of an unknown phylogeny that is informed through nucleotide sequence data. Recently, this framework has been extended to model the transition rate matrix between discrete states as a generalized linear model (GLM) of predictors of interest to the pathogen. In this dissertation, I focus on these GLMs and describe their capabilities, limitations, and introduce a pipeline that may enable more researchers to utilize this framework. I first demonstrate how a GLM can be employed and how the support for the predictors can be measured using influenza A/H5N1 in Egypt as an example. Secondly, I compare the GLM framework to two alternative frameworks of Bayesian phylogeography: one that uses an advanced computational technique and one that does not. For this assessment, I model the diffusion of influenza A/H3N2 in the United States during the 2014-15 flu season with five methods encapsulated by the three frameworks. I summarize metrics of the phylogenies created by each and demonstrate their reproducibility by performing analyses on several random sequence samples under a variety of population growth scenarios. Next, I demonstrate how discretization of the location trait for a given sequence set can influence phylogenies and support for predictors. That is, I perform several GLM analyses on a set of sequences and change how the sequences are pooled, then show how aggregating predictors at four levels of spatial resolution will alter posterior support. Finally, I provide a solution for researchers that wish to use the GLM framework but may be deterred by the tedious file-manipulation requirements that must be completed to do so. My pipeline, which is publicly available, should alleviate concerns pertaining to the difficulty and time-consuming nature of creating the files necessary to perform GLM analyses. This dissertation expands the knowledge of Bayesian phylogeographic GLMs and will facilitate the use of this framework, which may ultimately reveal the variables that drive the spread of pathogens.Dissertation/ThesisDoctoral Dissertation Biomedical Informatics 201