For an individual to successfully complete the task of decision-making, a set of temporally-organized events must occur: stimuli must be detected,

potential outcomes must be evaluated, behaviors must be executed or inhibited, and outcomes

(such as reward or punishment) must be experienced. Due to the complexity of this process,

it is very likely the case that decision-making is encoded by the temporally-precise interactions

among a population of neurons. Most existing statistical models, however, are inadequate for analyzing such sophisticated phenomenon as they either analyze a small number of neurons (e.g., pairwise analysis) or only provide an aggregated measure of interactions by assuming a constant dependence structure among neurons over time.

We start by proposing a scalable hierarchical semi-parametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time). To this end, we model the spike train ( sequence of 1's (spike) and 0's (silence) ) for each neuron using the logistic function of a continuous latent variable with a Gaussian Process prior. Then we model the joint probability distribution of multiple neurons as a function of their corresponding marginal distribution using a parametric copula model. Our approach provides a flexible framework for modeling the underlying firing rates of each neuron. It also also allows us to make inference regarding both contemporaneous and lagged synchrony. We evaluate our approach using several simulation studies and apply it to analyze real data collected from an experiment designed for investigating the role of the prefrontal cortex of rats in reward-seeking behaviors.

Next, we propose a non-stationary Bayesian model to capture the dynamic nature of neuronal activity (such as the time-varying strength

of the interactions among neurons). Our proposed method yields results that provide new insights into the dynamic nature of population coding in the prefrontal cortex during decision making. In our analysis, we note that while some neurons in the prefrontal cortex do not synchronize their firing activity until the presence of a reward, a different set of neurons synchronize their

activity shortly after the onset of stimulus. These differentially synchronizing sub-populations of

neurons suggests a continuum of population representation of the reward-seeking task. Our analyses also suggest that the degree of synchronization differs between the

rewarded and non-rewarded conditions.

Finally we propose a novel statistical model for detecting neuronal communities involved in decision-making process. Our method characterizes the non-stationary activity of multiple neurons during a basic cognitive task by modeling their joint probability distribution dynamically. Our proposed model can capture the time-varying dependence structure among neurons while allowing the neuronal activity to change over time. This way, we are able to identify time-varying neuronal communities. By identifying communities of neurons that vary under different decisions, we expect our method to provide insights into the decision-making process in particular as well as into a broad range of cognitive functions.