30 results found
A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical limits on the accuracy of measurements, binned data is common. In order to use point processes to model such event data, tools for handling parameter estimation are essential. Here we consider parameter estimation of the Hawkes process, a type of self-exciting point process that has found application in the modeling of financial stock markets, earthquakes and social media cascades. We develop a novel optimization approach to parameter estimation of binned Hawkes processes using a modified Expectation-Maximization algorithm, referred to as Binned Hawkes Expectation Maximization (BH-EM). Through a detailed simulation study, we demonstrate that existing methods are capable of producing severely biased and highly variable parameter estimates and that our novel BH-EM method significantly outperforms them in all studied circumstances. We further illustrate the performance on network flow (NetFlow) data between devices in a real large-scale computer network, to characterize triggering behavior. These results highlight the importance of correct handling of binned data.
Cohen E, Gibberd A, 2021, Wavelet spectra for multivariate point processes, Biometrika, ISSN: 0006-3444
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams. To provide statistical tractability, a temporally smoothed wavelet periodogram is developed and shown to be equivalent to a multi-wavelet periodogram. Under a stationary assumption, the distribution of the temporally smoothed wavelet periodogram is demonstrated to be asymptotically Wishart, with the centrality matrix and degrees of freedom readily computable from the multi-wavelet formulation. Distributional results extend to wavelet coherence; a time-scale measure of inter-process correlation. This statistical framework is used to construct a test for stationarity in multivariate point-processes. The methodology is applied to neural spike train data, where it is shown to detect and characterize time-varying dependency patterns.
Patel L, David W, Owen D, et al., 2021, Blinking statistics and molecular counting in direct stochastic reconstruction microscopy (dSTORM), Bioinformatics, Vol: 37, Pages: 2730-2737, ISSN: 1367-4803
Motivation: Many recent advancements in single-molecule localization microscopy exploit the stochastic photoswitching of fluorophores to reveal complex cellular structures beyond the classical diffraction limit. However, this same stochasticity makes counting the number of molecules to high precision extremely challenging, preventing key insight into the cellular structures and processes under observation.Results: Modelling the photoswitching behaviour of a fluorophore as an unobserved continuous time Markov process transitioning between a single fluorescent and multiple dark states, and fully mitigating for missed blinks and false positives, we present a method for computing the exact probability distribution for the number of observed localizations from a single photoswitching fluorophore. This is then extended to provide the probability distribution for the number of localizations in a direct stochastic optical reconstruction microscopy experiment involving an arbitrary number of molecules. We demonstrate that when training data are available to estimate photoswitching rates, the unknown number of molecules can be accurately recovered from the posterior mode of the number of molecules given the number of localizations. Finally, we demonstrate the method on experimental data by quantifying the number of adapter protein linker for activation of T cells on the cell surface of the T-cell immunological synapse.Availability and implementation: Software and data available at https://github.com/lp1611/mol_count_dstorm.Supplementary information: Supplementary data are available at Bioinformatics online.
Boland MA, Cohen EAK, Flaxman SR, et al., 2021, Improving axial resolution in Structured Illumination Microscopy using deep learning, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 379, ISSN: 1364-503X
Boland M, Cohen E, Flaxman S, et al., 2021, Improving axial resolution in SIM using deep learning, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN: 1364-503X
Structured Illumination Microscopy is a widespreadmethodology to image live and fixed biologicalstructures smaller than the diffraction limits ofconventional optical microscopy. Using recent advancesin image up-scaling through deep learning models,we demonstrate a method to reconstruct 3D SIMimage stacks with twice the axial resolution attainablethrough conventional SIM reconstructions. We furtherdemonstrate our method is robust to noise & evaluateit against two point cases and axial gratings. Finally,we discuss potential adaptions of the method tofurther improve resolution.
Taleb Y, Cohen E, 2021, Multiresolution analysis of point processes and statistical thresholding for Haar wavelet-based intensity estimation, Annals of the Institute of Statistical Mathematics, Vol: 73, Pages: 395-423, ISSN: 0020-3157
We take a wavelet based approach to the analysis of point processes and the estimation of the first order intensity under a continuous time setting. A Haar wavelet multiresolution analysis of a point process is formulated which motivates the definition of homogeneity at different scales of resolution, termed $J$-th level homogeneity. Further to this, the activity in a point process' first order behavior at different scales of resolution is also defined and termed $L$-th level innovation. Likelihood ratio tests for both these properties are proposed with asymptotic distributions provided, even when only a single realization of the point process is observed. The test for $L$-th level innovation forms the basis for a collection of statistical strategies for thresholding coefficients in a wavelet based estimator of the intensity function. These thresholding strategies outperform the existing local hard thresholding strategy on a range of simulation scenarios. The presented methodology is applied to NetFlow data to demonstrate its effectiveness at characterizing multiscale behavior on computer networks.
Ward S, Cohen E, Adams N, 2021, Testing for complete spatial randomness on three dimensional bounded convex shapes, Spatial Statistics, Vol: 41, ISSN: 2211-6753
There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus relies on Euclidean geometry and is therefore inappropriate for analysis of point patterns observed in non-Euclidean spaces. Recently, there has been extensions to the analysis of point patterns on a sphere, however, many other shapes are left unexplored. This is in part due to the challenge of defining the notion of stationarity for a point process existing on such a space due to the lack of rotational and translational isometries. Here, we construct functional summary statistics for Poisson processes defined on convex shapes in three dimensions. Using the Mapping Theorem, a Poisson process can be transformed from any convex shape to a Poisson process on the unit sphere which has rotational symmetries that allow for functional summary statistics to be constructed. We present the first and second order properties of such summary statistics and demonstrate how they can be used to construct a test statistics to determine whether an observed pattern exhibits complete spatial randomness or spatial preference on the original convex space. We compare this test statistic with one constructed from an analogue L-function for inhomogeneous point processes on the sphere. A study of the Type I and II errors of our test statistics are explored through simulations on ellipsoids of varying dimensions.
You SY, Chao J, Cohen E, et al., 2021, A microscope calibration protocol for single-molecule microscopy, Optics Express, Vol: 29, Pages: 182-207, ISSN: 1094-4087
Single-molecule microscopy allows for the investigation of the dynamics ofindividual molecules and the visualization of subcellular structures at high spatial resolution.For single-molecule imaging experiments, and particularly those that entail the acquisition ofmulticolor data, calibration of the microscope and its optical components therefore needs tobe carried out at a high level of accuracy. We propose here a method for calibrating amicroscope at the nanometer scale, in the sense of determining optical aberrations as revealedby point source localization errors on the order of nanometers. The method is based on theimaging of a standard sample to detect and evaluate the amount of geometric aberrationintroduced in the optical light path. To provide support for multicolor imaging, it alsoincludes procedures for evaluating the geometric aberration caused by a dichroic filter and theaxial chromatic aberration introduced by an objective lens.
Patel L, Cohen E, Ober R, et al., 2019, A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores, Annals of Applied Statistics, Vol: 13, Pages: 1397-1429, ISSN: 1932-6157
Fluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.
Ward S, Cohen E, Adams N, 2019, Fusing multimodal microscopy data for improved cell boundary estimation and fluorophore localization of Pseudomonas aeruginosa, Asilomar Conference on Signals, Systems and Computers, Publisher: IEEE
With advances in experimental technologies, the use of biological imaging has grown rapidly and there is need for procedures to combine data arising from different modalities. We propose a procedure to combine yellow fluorescence protein excitation and differential interference contrast microscopy time lapse videos to better estimate the cellular boundary of Pseudomonas aeruginosa (P. aeruginosa) and localization of it's type VI secretion system (T6SS). By approximating the shape by an ellipse, we construct a penalized objective function which accounts for both sources; the minimum of which provides an elliptical approximation to their cellular boundaries. Our approach suggests improved localization of the T6SS on the estimated cell boundary of P. aeruginosa constructed using both sources of data compared to using each in isolation.
Gibberd A, Cohen E, 2019, Temporally Smoothed Wavelet Coherence for Multivariate Point-Processes and Neuron-Firing, Asilomar Conference on Signals, Systems and Computers
Patel L, Cohen E, 2019, Bayesian filtering for spatial estimation of photo-switching fluorophores imaged in Super-resolution fluorescence microscopy, Asilomar Conference on Signals, Systems and Computers
The resolution of an imaging system is a key property that, despite many advances in optical imaging methods, remains difficult to define and apply. Rayleigh’s and Abbe’s resolution criteria were developed for observations with the human eye. However, modern imaging data is typically acquired on highly sensitive cameras and often requires complex image processing algorithms to analyze. Currently, no approaches are available for evaluating the resolving capability of such image processing algorithms that are now central to the analysis of imaging data, particularly location-based imaging data. Using methods of spatial statistics, we develop a novel algorithmic resolution limit to evaluate the resolving capabilities of location-based image processing algorithms. We show how insufficient algorithmic resolution can impact the outcome of location-based image analysis and present an approach to account for algorithmic resolution in the analysis of spatial location patterns.
Gibberd A, Nobel J, Cohen E, 2018, Characterising dependency in computer networks using spectral coherence, International Conference on Time Series and Forecasting, Publisher: ITISE
The quantification of normal and anomalous traffic flowsacross computer networks is a topic of pervasive interest in network se-curity, and requires the timely application of time-series methods. Thetransmission or reception of packets passing between computers can berepresented in terms of time-stamped events and the resulting activityunderstood in terms of point-processes. Interestingly, in the disparate do-main of neuroscience, models for describing dependent point-processesare well developed. In particular, spectral methods which decomposesecond-order dependency across different frequencies allow for a richcharacterisation of point-processes. In this paper, we investigate usingthe spectral coherence statistic to characterise computer network activ-ity, and determine if, and how, device messaging may be dependent. Wedemonstrate on real data, that for many devices there appears to be verylittle dependency between device messaging channels. However, when sig-nificant coherence is detected it appears highly structured, a result whichsuggests coherence may prove useful for discriminating between types ofactivity at the network level.
Hogan J, Cohen EAK, Adams NM, 2017, Devising a fairer method for adjusting target scores in interrupted one-day international cricket, Electronic Journal of Applied Statistical Analysis, Vol: 10, Pages: 745-758, ISSN: 2070-5948
One-day international cricket matches face the problem of weather inter-ruption. In such circumstances, a so-called rain rule is used to decide theoutcome. A variety of approaches for constructing such rules has been pro-posed, with the Duckworth-Lewis method being preferred in the sport. Thereare a number of issues to consider in reasoning about the e↵ectiveness of arain rule, notably accuracy (does the rule make the right decision?) andfairness (are both teams treated equally?). We develop an approach that isa hybrid of resource-based and so-called probability-preserving approachesand provide empirical evidence that this hybrid method is superior in termsof fairness while competitive in terms of accuracy.
Griffie J, Shlomovich L, Williamson D, et al., 2017, 3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse, Scientific Reports, Vol: 7, ISSN: 2045-2322
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.Introduction.
Taleb Y, Cohen E, 2016, A wavelet based likelihood ratio test for the homogeneity of poisson processes, 2016 IEEE Statistical Signal Processing Workshop (SSP), Publisher: IEEE
Estimating the rate (first-order intensity) of a point process is a task of great interest in the understanding of its nature. In this work we first address the estimation of the rate of an orderly point process on the real line using a multiresolution wavelet expansion approach. Implementing Haar wavelets, we find that in the case of a Poisson process the piecewise constant wavelet estimator of the rate has a scaled Poisson distribution. We apply this result in the design of a likelihood ratio test for a multiresolution formulation of the homogeneity of a Poisson process. We demonstrate this method with simulations and provide Type 1 error and empirical power plots under specific models.
Cohen E, Kim D, Ober RJ, 2015, The Cramer Rao lower bound for point based image registration with heteroscedastic error model for application in single molecule microscopy, IEEE Transactions on Medical Imaging, Vol: 34, Pages: 2632-2644, ISSN: 1558-254X
Cohen EAK, 2014, Multi-wavelet coherence for point processes on the real-line, IEEE International Conference on Acoustics, Speech and Signal Processing, Pages: 2649-2653
Rossy J, Cohen EAK, Gaus K, et al., 2014, Method for Co-Cluster Analysis in Multichannel Single Molecule Localization Data., Histochemisty and Cell Biology, Vol: In Press, ISSN: 0948-6143
Cohen EAK, Ober RJ, 2013, Analysis of point based image registration errors with applications in single molecule microscopy, IEEE Transactions on Signal Processing, Vol: 61, Pages: 6291-6306, ISSN: 1053-587X
We present an asymptotic treatment of errors involvedin point-based image registration where control point (CP)localization is subject to heteroscedastic noise; a suitable modelfor image registration in fluorescence microscopy. Assuming anaffine transform, CPs are used to solve a multivariate regressionproblem. With measurement errors existing for both sets of CPsthis is an errors-in-variable problem and linear least squaresis inappropriate; the correct method being generalized leastsquares. To allow for point dependent errors the equivalence of ageneralized maximum likelihood and heteroscedastic generalizedleast squares model is achieved allowing previously publishedasymptotic results to be extended to image registration. For aparticularly useful model of heteroscedastic noise where covariancematrices are scalar multiples of a known matrix (includingthe case where covariance matrices are multiples of the identity)we provide closed form solutions to estimators and derive theirdistribution. We consider the target registration error (TRE) anddefine a new measure called the localization registration error(LRE) believed to be useful, especially in microscopy registrationexperiments. Assuming Gaussianity of the CP localization errors,it is shown that the asymptotic distribution for the TRE and LREare themselves Gaussian and the parameterized distributions arederived. Results are successfully applied to registration in singlemolecule microscopy to derive the key dependence of the TRE andLRE variance on the number of CPs and their associated photoncounts. Simulations show asymptotic results are robust for lowCP numbers and non-Gaussianity. The method presented here isshown to outperform GLS on real imaging data.
Cohen EAK, Ober RJ, 2013, Measurement errors in fluorescence microscopy image registration., Asilomar Conference on Signals, Systems and Computers, Pages: 1602-1606, ISSN: 1058-6393
Walden AT, Cohen EAK, 2012, Statistical Properties for Coherence Estimators From Evolutionary Spectra, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 60, Pages: 4586-4597, ISSN: 1053-587X
Cohen EAK, Ober RJ, 2012, Image Registration Error Analysis with applications in single molecule microscopy., IEEE Biomedical Imaging Symposium - From Nano to Macro, Pages: 996-999, ISSN: 1945-7928
Cohen EAK, Ober RJ, 2012, IMAGE REGISTRATION ERROR ANALYSIS WITH APPLICATIONS IN SINGLE MOLECULE MICROSCOPY, Proc I S Biomed Imaging, Pages: 996 --- 999-996 --- 999
Cohen EAK, Ober RJ, 2012, Measurement Errors in Fluorescence Microscopy Experiments, Conf Rec Asilomar C, Pages: 1602 --- 1606-1602 --- 1606
Cohen E, 2011, A statistical study of wavelet coherence for stationary and non-stationary processes
Cohen EAK, Walden AT, 2011, Wavelet Coherence for Certain Nonstationary Bivariate Processes, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 59, Pages: 2522-2531, ISSN: 1053-587X
Cohen EAK, Walden AT, 2010, A Statistical Study of Temporally Smoothed Wavelet Coherence, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 58, Pages: 2964-2973, ISSN: 1053-587X
Cohen EAK, Walden AT, 2010, A Statistical Analysis of Morse Wavelet Coherence, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 58, Pages: 980-989, ISSN: 1053-587X
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