Motor proteins and non-Gaussian areal data: Advances in stochastic modeling and computation

Part I: Motor Proteins.;Fluorescence microscopy is an important technique for studying processive molecular motors such as kinesins and dyneins. A typical experiment generates hundreds or thousands of images of motor assays, and each assay can contain many tens of fluorescent particles that must be localized so that individual motors can be tracked from one image to the next. Previous approaches to processing these images were more algorithmic than statistical, and those approaches typically require human intervention. We address these problems by developing science-informed stochastic models for two types of images: those that use green fluorescent proteins (GFP), and those that use quantum dots. The resulting models permit fully likelihood-based inference for particle count and location. Both procedures are computationally efficient. The procedure for GFP images is fully automatic, while the procedure for quantum dot images requires only a training run on a suitable image.;A kinesin can be furnished with extended neck linkers, i.e., longer "legs." This modification alters the behavior of the motor, most notably by permitting variable-length steps. We develop renewal-reward type models to describe the stepping of kinesins with extended neck linkers, and present corresponding matrix computational frameworks for conducting computer experiments. This matrix computational approach is much faster than previous Monte Carlo approaches and does not introduce sampling variability. We were able to use the approach to explain important experimental data and to lend support to one of several competing physical models for the neck linker.;Part II: Non-Gaussian Areal Data.;Non-Gaussian spatial data are common in many disciplines. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. Two models commonly used for spatial regression on a lattice are the Markov random field model, or automodel, and the spatial generalized linear mixed model (SGLMM), which embeds a Gaussian Markov random field within a hierarchical model. Although these models have long histories and are very widely used, they pose serious theoretical and computational difficulties: (1) for both classes of models, the regression estimates are uninterpretable due to spatial confounding; (2) for automodels, the intractable normalizing function makes maximum likelihood and Bayesian inference very challenging; and (3) for the SGLMM, the highly correlated and high-dimensional spatial random effects make computation very challenging. For a reparameterized version of the autologistic model, we develop maximum likelihood and Bayesian inferential approaches based on Monte Carlo maximum likelihood (MCML) and an auxiliary-variable MCMC algorithm, both of which employ perfect sampling. This approach addresses computational difficulties while simultaneously resolving interpretability issues. For the SGLMM, we introduce a novel reparameterization based on the underlying graph and demonstrate via extensive simulation studies that our approach alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects.