Title: Advances in Statistical Machine Learning Methods for Neural Data Science
Description: Innovations in neural data recording techniques are revolutionizing neuroscience and presenting both challenges and opportunities for statistical data analysis. This dissertation discusses several recent advances in neural data signal processing, encoding, decoding, and dimension reduction. Chapter 1 introduces challenges in neural data science and common statistical methods used to address them. Chapter 2 develops a new method to detect neurons and extract signals from noisy calcium imaging data with irregular neuron shapes. Chapter 3 introduces a novel probabilistic framework for modeling deconvolved calcium traces. Chapter 4 proposes an improved Bayesian nonparametric extension of the hidden Markov model (HMM) that separates the strength of the self-persistence prior and transition prior. Chapter 5 introduces a more identifiable and interpretable latent variable model for Poisson observations. We develop efficient algorithms to fit each of the aforementioned methods and demonstrate their effectiveness on both simulated and real data.