Patrick Rubin-Delanchy

On Testing for Impropriety of Complex-Valued Gaussian Vectors

We consider the problem of testing whether a complex-valued random vector is proper, i.e., is uncorrelated with its complex conjugate. We formulate the testing problem in terms of real-valued Gaussian random vectors, so we can make use of some useful existing results which enable us to study the null distributions of two test statistics. The tests depend only on the sample-size n and the dimensionality of the vector p . The basic behaviors of the distributions of the test statistics are derived and critical values (thresholds) are calculated and presented for certain (n,p) values. For one of these tests we derive a distributional approximation for a transform of the statistic, potentially very useful in practice for rapid and simple testing. We also study the power (detection probability) of the tests. Our results mean that testing for propriety can be a practical and undaunting procedure.

Bayesian cluster identification in single-molecule localization microscopy data.

Single-molecule localization-based super-resolution microscopy techniques such as photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) produce pointillist data sets of molecular coordinates. Although many algorithms exist for the identification and localization of molecules from raw image data, methods for analyzing the resulting point patterns for properties such as clustering have remained relatively under-studied. Here we present a model-based Bayesian approach to evaluate molecular cluster assignment proposals, generated in this study by analysis based on Ripleys K function. The method takes full account of the individual localization precisions calculated for each emitter. We validate the approach using simulated data, as well as experimental data on the clustering behavior of CD3ζ, a subunit of the CD3 T cell receptor complex, in resting and activated primary human T cells.

Kinematics of Complex-Valued Time Series

The contribution to a stationary complex-valued time series at a single frequency magnitude takes the form of a random ellipse, and its properties such as aspect ratio (which includes rotational direction) and orientation are of great interest in science. A case when both the aspect ratio and orientation are fixed is found, and their variability, in general, results from the additional influence of an orthogonal ellipse. It is shown how a magnitude squared coherence coefficient controls both the relative influences of these components and the variation of both the orientation and aspect ratio of the resultant ellipse. Realizations of random ellipses are recovered very accurately from simulated time series. The mean orientation of the random ellipse is formally derived.

Simulation of Improper Complex-Valued Sequences

An algorithm is proposed for the simulation of improper (noncircular) complex-valued second-order stationary stochastic processes having specified second-order properties. Three examples are given. Generated processes are shown to obey necessary distributional properties.

An algorithm to compute the power of Monte Carlo tests with guaranteed precision

This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that achieves this aim for almost any Monte Carlo test. Previous research has focused on obtaining as accurate a result as possible for a fixed computational effort, without providing a guaranteed precision in the above sense. The algorithm we propose does not have a fixed effort and runs until a confidence interval with a user-specified length and coverage probability can be constructed. We show that the expected effort required by the algorithm is finite in most cases of practical interest, including situations where the distribution of the p-value is absolutely continuous or discrete with finite support. The algorithm is implemented in the R-package simctest, available on CRAN.

A Bayesian cluster analysis method for single-molecule localization microscopy data

Cell function is regulated by the spatiotemporal organization of the signaling machinery, and a key facet of this is molecular clustering. Here, we present a protocol for the analysis of clustering in data generated by 2D single-molecule localization microscopy (SMLM)—for example, photoactivated localization microscopy (PALM) or stochastic optical reconstruction microscopy (STORM). Three features of such data can cause standard cluster analysis approaches to be ineffective: (i) the data take the form of a list of points rather than a pixel array; (ii) there is a non-negligible unclustered background density of points that must be accounted for; and (iii) each localization has an associated uncertainty in regard to its position. These issues are overcome using a Bayesian, model-based approach. Many possible cluster configurations are proposed and scored against a generative model, which assumes Gaussian clusters overlaid on a completely spatially random (CSR) background, before every point is scrambled by its localization precision. We present the process of generating simulated and experimental data that are suitable to our algorithm, the analysis itself, and the extraction and interpretation of key cluster descriptors such as the number of clusters, cluster radii and the number of localizations per cluster. Variations in these descriptors can be interpreted as arising from changes in the organization of the cellular nanoarchitecture. The protocol requires no specific programming ability, and the processing time for one data set, typically containing 30 regions of interest, is ∼18 h; user input takes ∼1 h.

3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse

Single-molecule localisation microscopy (SMLM) allows the localisation of fluorophores with a precision of 10–30 nm, revealing the cell’s nanoscale architecture at the molecular level. Recently, SMLM has been extended to 3D, providing a unique insight into cellular machinery. Although cluster analysis techniques have been developed for 2D SMLM data sets, few have been applied to 3D. This lack of quantification tools can be explained by the relative novelty of imaging techniques such as interferometric photo-activated localisation microscopy (iPALM). Also, existing methods that could be extended to 3D SMLM are usually subject to user defined analysis parameters, which remains a major drawback. Here, we present a new open source cluster analysis method for 3D SMLM data, free of user definable parameters, relying on a model-based Bayesian approach which takes full account of the individual localisation precisions in all three dimensions. The accuracy and reliability of the method is validated using simulated data sets. This tool is then deployed on novel experimental data as a proof of concept, illustrating the recruitment of LAT to the T-cell immunological synapse in data acquired by iPALM providing ~10 nm isotropic resolution.

Network-wide anomaly detection via the Dirichlet process

Statistical anomaly detection techniques provide the next layer of cyber-security defences below traditional signature-based approaches. This article presents a scalable, principled, probability-based technique for detecting outlying connectivity behaviour within a directed interaction network such as a computer network. Independent Bayesian statistical models are fit to each message recipient in the network using the Dirichlet process, which provides a tractable, conjugate prior distribution for an unknown discrete probability distribution. The method is shown to successfully detect a red team attack in authentication data obtained from the enterprise network of Los Alamos National Laboratory.

Choosing between methods of combining

Summary Combining

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