Statistical inferences of biophysical neural models
A fundamental issue in neuroscience is to understand the dynamic properties of, and biological mechanisms underlying, neural spiking activity. Two types of approaches have been developed: statistical and biophysical modeling. Statistical models focus on describing simple relationships between observed neural spiking activity and the signals that the brain encodes. Biophysical models concentrate on describing the biological mechanisms underlying the generation of spikes. Despite a large body of work, there remains an unbridged gap between the two model types. In this thesis, we propose a statistical framework linking observed spiking patterns to a general class of dynamic neural models. The framework uses a sequential Monte Carlo, or particle filtering, method to efficiently explore the parameter space of a detailed dynamic or biophysical model. We utilize point process theory to develop a procedure for estimating parameters and hidden variables in neuronal biophysical models given only the observed spike times. We successfully implement this method for simulated examples and address the issues of model identification and misspecification. We then apply the particle filter to actual spiking data recorded from rat layer V cortical neurons and show that it correctly identifies the dynamics of a non-traditional, intrinsic current. The method succeeds even though the observed cells exhibit two distinct classes of spiking activity: regular spiking and bursting. We propose that the approach can also frame hypotheses of underlying intrinsic currents that can be directly tested by current or future biological and/or psychological experiments. We then demonstrate the application of the proposed method to a separate problem: constructing a hypothesis test to investigate whether a point process is generated by a constant or dynamically varying intensity function. The hypothesis is formulated as an autoregressive state space model, which reduces the testing problem to a test on the variance of the state process. We apply the particle filtering method to compute test statistics and identify the rejection region. A simulation study is performed to quantify the power of this test procedure. Ultimately, the modeling framework and estimation procedures we developed provide a successful link between dynamical neural models and statistical inference from spike train data.
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