Bayesian inference for multidimensional NMR image reconstruction

Reconstruction of an image from a set of projections has been adapted to generate multidimensional nuclear magnetic resonance (NMR) spectra, which have discrete features that are relatively sparsely distributed in space. For this reason, a reliable reconstruction can be made from a small number of projections. This new concept is called Projection Reconstruction NMR (PR-NMR). In this paper, multidimensional NMR spectra are reconstructed by Reversible Jump Markov Chain Monte Carlo (RJMCMC). This statistical method generates samples under the assumption that each peak consists of a small number of parameters: position of peak centres, peak amplitude, and peak width. In order to find the number of peaks and shape, RJMCMC has several moves: birth, death, merge, split, and invariant updating. The reconstruction schemes are tested on a set of six projections derived from the three-dimensional 700 MHz HNCO spectrum of a protein HasA.

Information theory, inference, and learning algorithms

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

Automated 3D Structure Inference of Civil Infrastructure Using a Stereo Camera Set

The commercial far-range (>10m) infrastructure spatial data collection methods are not completely automated. They need significant amount of manual post-processing work and in some cases, the equipment costs are significant. This paper presents a method that is the first step of a stereo videogrammetric framework and holds the promise to address these issues. Under this method, video streams are initially collected from a calibrated set of two video cameras. For each pair of simultaneous video frames, visual feature points are detected and their spatial coordinates are then computed. The result, in the form of a sparse 3D point cloud, is the basis for the next steps in the framework (i.e., camera motion estimation and dense 3D reconstruction). A set of data, collected from an ongoing infrastructure project, is used to show the merits of the method. Comparison with existing tools is also shown, to indicate the performance differences of the proposed method in the level of automation and the accuracy of results.

Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

Decomposing signals into a sum of amplitude and frequency modulated sinusoids using probabilistic inference

There are many methods for decomposing signals into a sum of amplitude and frequency modulated sinusoids. In this paper we take a new estimation based approach. Identifying the problem as ill-posed, we show how to regularize the solution by imposing soft constraints on the amplitude and phase variables of the sinusoids. Estimation proceeds using a version of Kalman smoothing. We evaluate the method on synthetic and natural, clean and noisy signals, showing that it outperforms previous decompositions, but at a higher computational cost. © 2012 IEEE.

4-Channel polymeric optical bus module for board-level optical interconnections

A 4-channel polymeric optical bus module suitable for use in board-level interconnections is presented. Low-loss and low-crosstalk module performance is achieved, while -1 dB alignment tolerances better than ± 8 μm are demonstrated. © 2012 OSA.

Optimal inference of sameness.

Deciding whether a set of objects are the same or different is a cornerstone of perception and cognition. Surprisingly, no principled quantitative model of sameness judgment exists. We tested whether human sameness judgment under sensory noise can be modeled as a form of probabilistically optimal inference. An optimal observer would compare the reliability-weighted variance of the sensory measurements with a set size-dependent criterion. We conducted two experiments, in which we varied set size and individual stimulus reliabilities. We found that the optimal-observer model accurately describes human behavior, outperforms plausible alternatives in a rigorous model comparison, and accounts for three key findings in the animal cognition literature. Our results provide a normative footing for the study of sameness judgment and indicate that the notion of perception as near-optimal inference extends to abstract relations.

Statistical inference for single- and multi-band probabilistic amplitude demodulation.

Amplitude demodulation is an ill-posed problem and so it is natural to treat it from a Bayesian viewpoint, inferring the most likely carrier and envelope under probabilistic constraints. One such treatment is Probabilistic Amplitude Demodulation (PAD), which, whilst computationally more intensive than traditional approaches, offers several advantages. Here we provide methods for estimating the uncertainty in the PAD-derived envelopes and carriers, and for learning free-parameters like the time-scale of the envelope. We show how the probabilistic approach can naturally handle noisy and missing data. Finally, we indicate how to extend the model to signals which contain multiple modulators and carriers.

Model reductions for inference: generality of pairwise, binary, and planar factor graphs.

We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.

Neural mechanisms of belief inference during cooperative games.

Humans have the arguably unique ability to understand the mental representations of others. For success in both competitive and cooperative interactions, however, this ability must be extended to include representations of others' belief about our intentions, their model about our belief about their intentions, and so on. We developed a "stag hunt" game in which human subjects interacted with a computerized agent using different degrees of sophistication (recursive inferences) and applied an ecologically valid computational model of dynamic belief inference. We show that rostral medial prefrontal (paracingulate) cortex, a brain region consistently identified in psychological tasks requiring mentalizing, has a specific role in encoding the uncertainty of inference about the other's strategy. In contrast, dorsolateral prefrontal cortex encodes the depth of recursion of the strategy being used, an index of executive sophistication. These findings reveal putative computational representations within prefrontal cortex regions, supporting the maintenance of cooperation in complex social decision making.