  Conventional analysis of neuroscience data involves computing average neural
activity over a group of trials and/or a period of time. This approach may be
particularly problematic when assessing the response patterns of neurons to
more than one simultaneously presented stimulus. In such cases, the brain must
represent each individual component of the stimuli bundle, but
trial-and-time-pooled averaging methods are fundamentally unequipped to address
the means by which multi-item representation occurs. We introduce and
investigate a novel statistical analysis framework that relates the firing
pattern of a single cell, exposed to a stimuli bundle, to the ensemble of its
firing patterns under each constituent stimulus. Existing statistical tools
focus on what may be called "first order stochasticity" in trial-to-trial
variation in the form of unstructured noise around a fixed firing rate curve
associated with a given stimulus. Our analysis is based upon the theoretical
premise that exposure to a stimuli bundle induces additional stochasticity in
the cell's response pattern, in the form of a stochastically varying
recombination of its single stimulus firing rate curves. We discuss challenges
to statistical estimation of such "second order stochasticity" and address them
with a novel dynamic admixture Poisson process (DAPP) model. DAPP is a
hierarchical point process model that decomposes second order stochasticity
into a Gaussian stochastic process and a random vector of interpretable
features, and, facilitates borrowing of information on the latter across
repeated trials through latent clustering. We present empirical evidence of the
utility of the DAPP analysis with synthetic and real neural recordings.
