Mechanistic Statistical Models of the Environment

Abstract

Statistical models are often abstract in nature. However, in environmental contexts, data are often limited and important insight can be gained by applying knowledge of real-world mechanisms. In this dissertation, I present three mechanistic statistical models, applied to the environment. In my second chapter, I model the effect of sociality on the migration of adult Pacific salmon past large-scale dams in the Columbia River Basin, USA. I explicitly break down and model the process by which a salmon passes a dam. In all three steps of this process, I evaluate the effect of the density of conspecifics, to determine whether sociality plays a role in dam passage. In my third chapter, I present a method for inferring the source of a signal which has been deformed by well-understood linear dynamics. I use as an example the case of a pollutant which, upon entering the environment, is subject to advective-diffusive transport. I show how to incorporate a mechanistic linear partial differential equation (PDE) model into the classic stochastic PDE (SPDE) method from spatial statistics, and how to invert the transport dynamics within a statistical model. In my fourth chapter, I present a mixed integer linear program (MILP) model for constructing optimal sampling design under complex logistical or budgetary constraints. I use as an example the case of the US Forest Service (USFS) Forest Inventory and Analysis (FIA) program in Tanana, Alaska. I compare solutions of this model with three randomized, design-based benchmarks based on MSE and feasibility.