Fast spatial inference in the homogeneous Ising model

The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction are intractable. We provide accurate approximations that make it possible to calculate these quantities numerically. Simulation studies indicate good performance when compared to Markov Chain Monte Carlo methods and at a tiny fraction of the time. The methodology is also used to perform Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment.Comment: 18 pages, 1 figure, 3 table

Spatial inference of traffic transition using micro-macro traffic variables

This paper proposes an online traffic inference algorithm for road segments in which local traffic information cannot be directly observed. Using macro-micro traffic variables as inputs, the algorithm consists of three main operations. First, it uses interarrival time (time headway) statistics from upstream and downstream locations to spatially infer traffic transitions at an unsupervised piece of segment. Second, it estimates lane-level flow and occupancy at the same unsupervised target site. Third, it estimates individual lane-level shockwave propagation times on the segment. Using real-world closed-circuit television data, it is shown that the proposed algorithm outperforms previously proposed methods in the literature

Developing Stochastic Models for Spatial Inference: Bacterial Chemotaxis

Background: Biological systems are inherently inhomogeneous and spatial effects play a significant role in processes such as pattern formation. At the cellular level proteins are often localised either through static attachment or via a dynamic equilibrium. As well as spatial heterogeneity many cellular processes exhibit stochastic fluctuations and so to make inferences about the location of molecules there is a need for spatial stochastic models. A test case for spatial models has been bacterial chemotaxis which has been studied extensively as a model of signal transduction. Results: By creating specific models of a cellular system that incorporate the spatial distributions of molecules we have shown how the fit between simulated and experimental data can be used to make inferences about localisation, in the case of bacterial chemotaxis. This method allows the robust comparison of different spatial models through alternative model parameterisations. Conclusions: By using detailed statistical analysis we can reliably infer the parameters for the spatial models, and also to evaluate alternative models. The statistical methods employed in this case are particularly powerful as they reduce the need for a large number of simulation replicates. The technique is also particularly useful when only limited molecular level data is available or where molecular data is not quantitative