Approximate Inference for Constructing Astronomical Catalogs from Images

We present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a random variable with parameters that depend on the latent properties of stars and galaxies. These latent properties are themselves modeled as random. We compare two procedures for posterior inference. One procedure is based on Markov chain Monte Carlo (MCMC) while the other is based on variational inference (VI). The MCMC procedure excels at quantifying uncertainty, while the VI procedure is 1000 times faster. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50 terabytes of images in 14.6 minutes, demonstrating the scaling characteristics necessary to construct catalogs for upcoming astronomical surveys.Comment: accepted to the Annals of Applied Statistic

Reconstructing gravitational wave signals from binary black hole mergers with minimal assumptions

We present a systematic comparison of the binary black hole (BBH) signal waveform reconstructed by two independent and complementary approaches used in LIGO and Virgo source inference: a template-based analysis, and a morphology-independent analysis. We apply the two approaches to real events and to two sets of simulated observations made by adding simulated BBH signals to LIGO and Virgo detector noise. The first set is representative of the 10 BBH events in the first Gravitational Wave Transient Catalog (GWTC-1). The second set is constructed from a population of BBH systems with total mass and signal strength in the ranges that ground based detectors are typically sensitive. We find that the reconstruction quality of the GWTC-1 events is consistent with the results of both sets of simulated signals. We also demonstrate a simulated case where the presence of a mismodelled effect in the observed signal, namely higher order modes, can be identified through the morphology-independent analysis. This study is relevant for currently progressing and future observational runs by LIGO and Virgo

Determining Histories of Slip on Normal Faults With Bedrock Scarps Using Cosmogenic Nuclide Exposure Data

Cosmogenic exposure data can be used to calculate time-varying fault slip rates on normal faults with exposed bedrock scarps. The method relies on assumptions related to how the scarp is preserved, which should be consistent at multiple locations along the same fault. Previous work commonly relied on cosmogenic data from a single sample locality to determine the slip rate of a fault. Here we show that by applying strict sampling criteria and using geologically informed modeling parameters in a Bayesian-inference Markov chain Monte Carlo method, similar patterns of slip rate changes can be modeled at multiple sites on the same fault. Consequently, cosmogenic data can be used to resolve along-strike fault activity. We present cosmogenic 36Cl concentrations from seven sites on two faults in the Italian Apennines. The average slip rate varies between sites on the Campo Felice Fault (0.84 ± 0.23 to 1.61 ± 0.27 mm yr−1), and all sites experienced a period of higher than average slip rate between 0.5 and 2 ka and a period of lower than average slip rate before 3 ka. On the Roccapreturo fault, slip rate in the center of the fault is 0.55 ± 0.11 and 0.35 ± 0.05 mm yr−1 at the fault tip near a relay zone. The estimated time since the last earthquake is the same at each site along the same fault (631 ± 620 years at Campo Felice and 2,603 ± 1,355 years at Roccapreturo). These results highlight the potential for cosmogenic exposure data to reveal the detailed millennial history of earthquake slip on active normal faults

Automatic architecture selection for hierarchical mixture of experts models

Hierarchical mixture of experts (HME) is a powerful tree-structured modeling technique based on the divide and conquer principle. HME model trees consist of two types of nodes - gate nodes, which are responsible for splitting a large complex problem into several smaller subproblems, and expert nodes, which perform the corresponding subproblemsolving. Selecting the number of such nodes as well as the order in which they are arranged is, however, a non-trivial task. A commonly used approach involves fitting several architectures and using methods such as cross-validation to pick the best one. As well as being computationally intensive, this method first requires one to pick the set of architectures to consider. For complex models with a large number of architectural elements, this leads to an unmanageable number of potential options. Pre-setting model architecture also requires choosing initial parameter values, which becomes progressively more challenging as parameter dimensionality increases. The latter challenges could be addressed by growing trees during the model fitting process instead of selecting the architecture in advance. It is thus evident that HME models suffer from a lack of a flexible and adaptive way of performing automatic architecture selection. The work presented in this thesis proposes automatic architecture selection methods for HME models, which allow for adding and removing tree nodes as well as adjusting the order in which they are arranged. As part of the development, three Bayesian parameter sampling strategies are proposed and systematically evaluated resulting in a recommended strategy. An adaptation of the Reversible Jump (RJ) algorithm is then used to grow and prune HME model trees. The main downfall of the RJ, which lies in low acceptance rates, is addressed by the addition of a novel reversible jump proposal algorithm. A new Gate Swaps (GS) algorithm is then proposed to tackle the problem of changing the order in which the existing tree nodes are arranged. Both algorithms are evaluated on two real-life problems with a particular focus on the Glasgow rental property prices data. It is shown that HME models fitted using the proposed RJ GS MCMC yield accurate predictions as well as provide an exceptionally high level of model interpretability, which is unusual amongst other machine learning methods

Extraction of Unfoliaged Trees from Terrestrial Image Sequences

This thesis presents a generative statistical approach for the fully automatic three-dimensional (3D) extraction and reconstruction of unfoliaged deciduous trees from wide-baseline image sequences. Tree models improve the realism of 3D Geoinformation systems (GIS) by adding a natural touch. Unfoliaged trees are, however, difficult to reconstruct from images due to partially weak contrast, background clutter, occlusions, and particularly the possibly varying order of branches in images from different viewpoints. The proposed approach combines generative modeling by L-systems and statistical maximum a posteriori (MAP) estimation for the extraction of the 3D branching structure of trees. Background estimation is conducted by means of mathematical (gray scale) morphology as basis for generative modeling. A Gaussian likelihood function based on intensity differences is employed to evaluate the hypotheses. A mechanism has been devised to control the sampling sequence of multiple parameters in the Markov Chain considering their characteristics and the performance in the previous step. A tree is classified into three typical branching types after the extraction of the first level of branches and more specific Production Rules of L-systems are used accordingly. Generic prior distributions for parameters are refined based on already extracted branches in a Bayesian framework and integrated into the MAP estimation. By these means most of the branching structure besides tiny twigs can be reconstructed. Results are presented in the form of VRML (Virtual Reality Modeling Language) models demonstrating the potential of the approach as well as its current shortcomings.Diese Dissertationsschrift stellt einen generativen statistischen Ansatz für die vollautomatische drei-dimensionale (3D) Extraktion und Rekonstruktion unbelaubter Laubbäume aus Bildsequenzen mit großer Basis vor. Modelle für Bäume verbessern den Realismus von 3D Geoinformationssystemen (GIS), indem sie Letzteren eine natürliche Note geben. Wegen z.T. schwachem Kontrast, Störobjekten im Hintergrund, Verdeckungen und insbesondere der möglicherweise unterschiedlichen Ordnung der Äste in Bildern von verschiedenen Blickpunkten sind unbelaubte Bäume aber schwierig zu rekonstruieren. Der vorliegende Ansatz kombiniert generative Modellierung mittels L-Systemen und statistische Maximum A Posteriori (MAP) Schätzung für die Extraktion der 3D Verzweigungsstruktur von Bäumen. Hintergrund-Schätzung wird auf Grundlage von mathematischer (Grauwert) Morphologie als Basis für die generative Modellierung durchgeführt. Für die Bewertung der Hypothesen wird eine Gaußsche Likelihood-Funktion basierend auf Intensitätsunterschieden benutzt. Es wurde ein Mechanismus entworfen, der die Reihenfolge der Verwendung mehrerer Parameter für die Markoff-Kette basierend auf deren Charakteristik und Performance im letzten Schritt kontrolliert. Ein Baum wird nach der Extraktion der ersten Stufe von Ästen in drei typische Verzweigungstypen klassifiziert und es werden entsprechend Produktionsregeln von spezifischen L-Systemen verwendet. Basierend auf bereits extrahierten Ästen werden generische Prior-Verteilungen für die Parameter in einem Bayes’schen Rahmen verfeinert und in die MAP Schätzung integriert. Damit kann ein großer Teil der Verzweigungsstruktur außer kleinen Ästen extrahiert werden. Die Ergebnisse werden als VRML (Virtual Reality Modeling Language) Modelle dargestellt. Sie zeigen das Potenzial aber auch die noch vorhandenen Defizite des Ansatzes

Dependent mixtures and random partitions

This work develops new methodology for Bayesian dependent mixture models and dependent random partitions with applications to biomedical data. A mixture model implies a random distribution over partitions by randomly assigning individual observations to latent subpopulations that correspond to the distinct components of the mixture. Subpopulations are typically homogeneous, but heterogeneous accross groups. In the biomedical applications studied here, the mixture components capture different levels of gene/protein expression, distinct stages of cellular development or the response to exposition to distinct drugs. Multiple forms of dependence are considered in order to more accurately model biological features of the studied applications, including dependence over time, dependence by arrangement on a tree and by shared match with paired cell lines.Statistic