Bayesian hypothesis testing and experimental design for two-photon imaging data

Variability, stochastic or otherwise, is a central feature of neural activity. Yet the means by which estimates of variation and uncertainty are derived from noisy observations of neural activity is often heuristic, with more weight given to numerical convenience than statistical rigour. For two-photon imaging data, composed of fundamentally probabilistic streams of photon detections, the problem is particularly acute. Here, we present a statistical pipeline for the inference and analysis of neural activity using Gaussian Process regression, applied to two-photon recordings of light-driven activity in ex vivo mouse retina. We demonstrate the flexibility and extensibility of these models, considering cases with non-stationary statistics, driven by complex parametric stimuli, in signal discrimination, hierarchical clustering and other inference tasks. Sparse approximation methods allow these models to be fitted rapidly, permitting them to actively guide the design of light stimulation in the midst of ongoing two-photon experiments.Author summary: There are many sources of noise in recordings of neural activity, and the first challenge in neural data analysis is to separate this noise from experimentally relevant variation. This is particularly problematic for two-photon imaging data. Two-photon imaging uses fluorescent indicators to measure changes in the concentration of molecules involved in cell signalling, and adds a variety of numerical, biological and optical noise sources. We present a method for disentangling this signal and noise using Gaussian processes, a family of probabilistic models which provide a principled way of inferring mean activity and variability. In addition to signal recovery, we show that these models can test the evidence for whether and where two signals are different and that these tests can be used to look for groups in sets of signals. We explore how these models can be extended to predict how signals will change under different experimental conditions, and that these predictions can be used to select new conditions for further exploration.