ABSTRACT
Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 9.4 Bibliography Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 9.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
This chapter introduces the use of simulation for model checking and inference. Simulation, often known as the Monte Carlo simulation, is a technique widely used in statistics and in environmental modeling. In environmental and ecological modeling, Monte Carlo simulation is primarily used for assessing model uncertainty in response to uncertain model parameters and other inputs. In statistics, simulation represents a class of computational algorithms that rely on repeated random sampling to compute results. We use these methods when computing an exact result with a deterministic algorithm that is infeasible or impossible. In this chapter, I emphasize the concept of using simulation for model checking. The chapter starts with an introduction of the basic concepts of simulation, followed by introductions on model-based simulation for estimation problems and for regression model checking. The use of simulation generated predictive distributions and their tail-areas as a tool for model checking is largely borrowed from the Bayesian p-value concept. The chapter concludes with a resampling method-based simulation method.
