Sequential Bayesian Detection of Spike Activities from Fluorescence Observations

Extracting and detecting spike activities from the fluorescence observations is an important step in understanding how neuron systems work. The main challenge lies in that the combination of the ambient noise with dynamic baseline fluctuation, often contaminates the observations, thereby deteriorating the reliability of spike detection. This may be even worse in the face of the nonlinear biological process, the coupling interactions between spikes and baseline, and the unknown critical parameters of an underlying physiological model, in which erroneous estimations of parameters will affect the detection of spikes causing further error propagation. In this paper, we propose a random finite set (RFS) based Bayesian approach. The dynamic behaviors of spike sequence, fluctuated baseline and unknown parameters are formulated as one RFS. This RFS state is capable of distinguishing the hidden active/silent states induced by spike and non-spike activities respectively, thereby \emph{negating the interaction role} played by spikes and other factors. Then, premised on the RFS states, a Bayesian inference scheme is designed to simultaneously estimate the model parameters, baseline, and crucial spike activities. Our results demonstrate that the proposed scheme can gain an extra $12\%$ detection accuracy in comparison with the state-of-the-art MLSpike method

Bayesian Spike Train Inference via Non-Local Priors

Advances in neuroscience have enabled researchers to measure the activities of large numbers of neurons simultaneously in behaving animals. We have access to the fluorescence of each of the neurons which provides a first-order approximation of the neural activity over time. Determining the exact spike of a neuron from this fluorescence trace constitutes an active area of research within the field of computational neuroscience. We propose a novel Bayesian approach based on a mixture of half-non-local prior densities and point masses for this task. Instead of a computationally expensive MCMC algorithm, we adopt a stochastic search-based approach that is capable of taking advantage of modern computing environments often equipped with multiple processors, to explore all possible arrangements of spikes and lack thereof in an observed spike train. It then reports the highest posterior probability arrangement of spikes and posterior probability for a spike at each location of the spike train. Our proposals lead to substantial improvements over existing proposals based on L1 regularization, and enjoy comparable estimation accuracy to the state-of-the-art L0 proposal, in simulations, and on recent calcium imaging data sets. Notably, contrary to optimization-based frequentist approaches, our methodology yields automatic uncertainty quantification associated with the spike-train inference

Modern Statistical/Machine Learning Techniques for Bio/Neuro-imaging Applications

Developments in modern bio-imaging techniques have allowed the routine collection of a vast amount of data from various techniques. The challenges lie in how to build accurate and efficient models to draw conclusions from the data and facilitate scientific discoveries. Fortunately, recent advances in statistics, machine learning, and deep learning provide valuable tools. This thesis describes some of our efforts to build scalable Bayesian models for four bio-imaging applications: (1) Stochastic Optical Reconstruction Microscopy (STORM) Imaging, (2) particle tracking, (3) voltage smoothing, (4) detect color-labeled neurons in c elegans and assign identity to the detections

Empirical Bayesian significance measure of neuronal spike response

Background: Functional connectivity analyses of multiple neurons provide a powerful bottom-up approach to reveal functions of local neuronal circuits by using simultaneous recording of neuronal activity. A statistical methodology, generalized linear modeling (GLM) of the spike response function, is one of the most promising methodologies to reduce false link discoveries arising from pseudo-correlation based on common inputs. Although recent advancement of fluorescent imaging techniques has increased the number of simultaneously recoded neurons up to the hundreds or thousands, the amount of information per pair of neurons has not correspondingly increased, partly because of the instruments' limitations, and partly because the number of neuron pairs increase in a quadratic manner. Consequently, the estimation of GLM suffers from large statistical uncertainty caused by the shortage in effective information. Results: In this study, we propose a new combination of GLM and empirical Bayesian testing for the estimation of spike response functions that enables both conservative false discovery control and powerful functional connectivity detection. We compared our proposed method's performance with those of sparse estimation of GLM and classical Granger causality testing. Our method achieved high detection performance of functional connectivity with conservative estimation of false discovery rate and q values in case of information shortage due to short observation time. We also showed that empirical Bayesian testing on arbitrary statistics in place of likelihood-ratio statistics reduce the computational cost without decreasing the detection performance. When our proposed method was applied to a functional multi-neuron calcium imaging dataset from the rat hippocampal region, we found significant functional connections that are possibly mediated by AMPA and NMDA receptors. Conclusions: The proposed empirical Bayesian testing framework with GLM is promising especially when the amount of information per a neuron pair is small because of growing size of observed network

Modeling and Analysis of Neural Spike Trains

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