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Correlations between the spiking of pairs of neurons are often used to study the brain’s representation of sensory or motor variables and neural circuit function and dysfunction. Previous statistical techniques have shown how time-averaged spike-spike correlations can be predicted by the time-averaged relationships between the individual neurons and the local field potential (LFP). However, spiking and LFP are both nonstationary, and spike-spike correlations have nonstationary structure that cannot be accounted for by time-averaged approaches. Here we develop parametric models that predict spike-spike correlations using a small number of LFP-based predictors, and we then apply these models to the problem of tracking changes in spike-spike correlations over time. Parametric models allow for flexibility in the choice of which LFP recording channels and frequency bands to use for prediction, and coefficients directly indicate which LFP features drive correlated spiking. Here we demonstrate our methods in simulation and test the models on experimental data from large-scale multi-electrode recordings in the mouse hippocampus and visual cortex. In single time windows, we find that our parametric models can be as accurate as previous nonparametric approaches, while also being flexible and interpretable. We then demonstrate how parametric models can be applied to describe nonstationary spike-spike correlations measured in sequential time windows. We find that although the patterns of both cortical and hippocampal spike-spike correlations vary over time, these changes are, at least partially, predicted by models that assume a fixed spike-field relationship. This approach may thus help to better understand how the dynamics of spike-spike correlations are related to functional brain states. Since spike-spike correlations are increasingly used as features for decoding external variables from neural activity, these models may also have the potential to improve the accuracy of adaptive decoders and brain machine interfaces. 

Accurately decoding external variables from observations of neural activity is a major challenge in systems neuroscience. Bayesian decoders, that provide probabilistic estimates, are some of the most widely used. Here we show how, in many common settings, the probabilistic predictions made by traditional Bayesian decoders are overconfident. That is, the estimates for the decoded stimulus or movement variables are more certain than they should be. We then show how Bayesian decoding with latent variables, taking account of low-dimensional shared variability in the observations, can improve calibration, although additional correction for overconfidence is still needed. Using data from males, we examine: 1) decoding the direction of grating stimuli from spike recordings in primary visual cortex in monkeys, 2) decoding movement direction from recordings in primary motor cortex in monkeys, 3) decoding natural images from multi-region recordings in mice, and 4) decoding position from hippocampal recordings in rats. For each setting we characterize the overconfidence, and we describe a possible method to correct miscalibration post-hoc. Properly calibrated Bayesian decoders may alter theoretical results on probabilistic population coding and lead to brain machine interfaces that more accurately reflect confidence levels when identifying external variables. Significance Statement Bayesian decoding is a statistical technique for making probabilistic predictions about external stimuli or movements based on recordings of neural activity. These predictions may be useful for robust brain machine interfaces or for understanding perceptual or behavioral confidence. However, the probabilities produced by these models do not always match the observed outcomes. Just as a weather forecast predicting a 50% chance of rain may not accurately correspond to an outcome of rain 50% of the time, Bayesian decoders of neural activity can be miscalibrated as well. Here we identify and measure miscalibration of Bayesian decoders for neural spiking activity in a range of experimental settings. We compare multiple statistical models and demonstrate how overconfidence can be corrected. 

Abstract In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and may provide information about the external world beyond the information provided by the average neural activity. To flexibly track time-varying neural response properties, we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and overdispersed relative to the Poisson distribution. Here we track parameters of the CMP distribution as they vary over time. Using simulations, we show that a normal approximation can accurately track dynamics in state vectors for both the centering and shape parameters (λ and ν). We then fit our model to neural data from neurons in primary visual cortex, “place cells” in the hippocampus, and a speed-tuned neuron in the anterior pretectal nucleus. We find that this method outperforms previous dynamic models based on the Poisson distribution. The dynamic CMP model provides a flexible framework for tracking time-varying non-Poisson count data and may also have applications beyond neuroscience. 

Modern neural recording techniques allow neuroscientists to observe the spiking activity of many neurons simultaneously. Although previous work has illustrated how activity within and between known populations of neurons can be summarized by low-dimensional latent vectors, in many cases what determines a unique population may be unclear. Neurons differ in their anatomical location, but also, in their cell types and response properties. Moreover, multiple distinct populations may not be well described by a single low-dimensional, linear representation.To tackle these challenges, we develop a clustering method based on a mixture of dynamic Poisson factor analyzers (DPFA) model, with the number of clusters treated as an unknown parameter. To do the analysis of DPFA model, we propose a novel Markov chain Monte Carlo (MCMC) algorithm to efficiently sample its posterior distribution. Validating our proposed MCMC algorithm with simulations, we find that it can accurately recover the true clustering and latent states and is insensitive to the initial cluster assignments. We then apply the proposed mixture of DPFA model to multi-region experimental recordings, where we find that the proposed method can identify novel, reliable clusters of neurons based on their activity, and may, thus, be a useful tool for neural data analysis.