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Data collected as sequences of images have become increasingly popular in the sciences in order to record scientific processes in both space and time. These types of data sets often exhibit complex dependence structures, and scientific questions of interest for which the data were obtained often rely on estimating unobserved features to characterize the evolution of a scientific process. In this thesis, we develop statistical methodology to analyze and quantify uncertainty in estimates of events characterizing processes recorded through image sequences for two such applications. In Chapter 2, we present methods utilizing Bayesian reduced Fourier-form dynamic linear models to model time series of remote sensing data with the purpose of estimating with uncertainty events characterizing phenological processes. We improve model assessment and convergence properties of the MCMC samplers by introducing two new, alternative parameterizations of the dynamic linear model in Chapter 3. In Chapter 4, we introduce mixture of regression model methodology for analyzing image sequences obtained through electrochemical scanning transmission electron microscopy to quantify nanoscale processes which cause Lithium batteries to degrade and explode. Lastly, in Chapter 5 we extend upon the methods of Chapter 4 by developing a linearly constrained Bayesian form of the model for robust estimation of image background gradients, automatic selection of the number of mixture components, and uncertainty quantification in estimates of key features.

Methods for analysis and uncertainty quantification for processes recorded through sequences of images