Considerate Approaches to Achieving Sufficiency for ABC model selection

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared --- rather than the data directly --- information is lost, unless the summary statistics are sufficient. Here we employ an information-theoretical framework that can be used to construct (approximately) sufficient statistics by combining different statistics until the loss of information is minimized. Such sufficient sets of statistics are constructed for both parameter estimation and model selection problems. We apply our approach to a range of illustrative and real-world model selection problems

A closed-form approach to Bayesian inference in tree-structured graphical models

We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our exploration to mixtures of spanning trees. We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees. We investigate under which conditions on the priors - on both tree structures and parameters - exact Bayesian inference can be achieved. Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to {the tree model} using an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data

Statistical analysis of network data and evolution on GPUs: High-performance statistical computing

Network analysis typically involves as set of repetitive tasks that are particularly amenable to poor-man's parallelization. This is therefore an ideal application are for GPU architectures, which help to alleviate the tedium inherent to statistically sound analysis of network data. Here we will illustrate the use of GPUs in a range of applications, which include percolation processes on networks, the evolution of protein-protein interaction networks, and the fusion of different types of biomedical and disease data in the context of molecular interaction networks. We will pay particular attention to the numerical performance of different routines that are frequently invoked in network analysis problems. We conclude with a review over recent developments in the generation of random numbers that address the specific requirements posed by GPUs and high-performance computing needs

Simultaneous Representation of Proper and Unit Interval Graphs

In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where all objects share the same common structure. While the recognition problem for general simultaneous interval graphs - the simultaneous version of arguably one of the most well-studied graph classes - is NP-complete, the complexity of the sunflower case for three or more simultaneous interval graphs is currently open. In this work we settle this question for proper interval graphs. We give an algorithm to recognize simultaneous proper interval graphs in linear time in the sunflower case where we allow any number of simultaneous graphs. Simultaneous unit interval graphs are much more "rigid" and therefore have less freedom in their representation. We show they can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G=(V,E) is the union of the simultaneous graphs. We further show that both recognition problems are in general NP-complete if the number of simultaneous graphs is not fixed. The restriction to the sunflower case is in this sense necessary

Housing and Urbanization: A Socio-Spatial Analysis of Resettlement Projects in Hồ Chí Minh City

As Hồ Chí Minh City continues to undergo rapid urbanization, especially with the creation of a multitude of new urban zone developments on the periphery of the inner districts, the resettling of people has become common. Families who live within areas that are selected for urban upgrading or, as in other cases for the construction of new miniature cities, must face the realities of relocation. Many issues arise in the complicated process of resettling the displaced, due to complex land-use laws, bureaucratic dissonance, and lack of investment in actual resettlement housing. The authorities of Hồ Chí Minh City have faced palpable challenges in facilitating the many processes of resettlement, from persuading developers to invest in resettlement housing to establishing suitable compensation packages. Confusing legal labyrinths, delays in plan approval, and miscommunications between agencies, results in tangible affects on the highly vulnerable displaced families. Additionally, a serious disconnect arises between planners’ envisioned solution for resettlement housing and the real needs of the resettled, who are usually low-income workers. When the precise needs of displaced families and their prior sources of economic livelihood are disregarded, the general result is unsuitable design and the disordering of previously established socio-spatial networks. Additionally the displaced tend to be sent to occupy less advantageous space, as a result of gentrification, and are spatially repositioned in more excluded, disconnected marginal zones. Past and present resettlement procedures have faltered due especially to a lack of socio-spatial planning, which has resulted in undesirable threats to equitable metropolisation and rising potentials for urban fragmentation