How do you incorporate uncertainty and variability in your statistical simulation?

When defining the problem, it can be very useful to write out a structural equation for a model of what you think is going on. Even a cartoon model can be useful - it will make it very clear what sources of variability need to be simulated independently vs what will be conditionally dependent.

A general principle to keep in mind when developing models is that less can actually be more. That means, a complex model doesn't necessarily mean that is better. It is important to find the right balance between complexity and practicality. A good model that is interpretable and actionable will always beat a mathematically superior model that is more abstract. Include elements of responsible and ethical modeling (such as responsible AI or unbiased data sets for training) when choosing a model.

The picked overall structural model along with its fully specified statistical variation models determines the answer(s) from such simulation exercises. It is highly recommended that simulation be an iterated process where one actively tests the sensitivity of the system with respect to one's modeling assumptions. Modeling assumptions can also be checked by the analysis of existing subsets of data that shed specific light on which variability and distributional models which may be considered most applicable to ones specific modeling situation. High complexity models, while intellectually entertaining, often will fail to represent real world processes well enough. Unexpected results require questioning of the modeling systems structure.

Prior data bias: It's important to consider sources of estimates, particularly in social science or clinical trial simulations. Often, groups (such as minority women) were left out of prior studies or parameters vary across prior studies, potentially skewing distributions obtained in those prior studies. In epidemic simulations, it's often hard to know exact parameters for spreading processes, so it is advantageous to run many scenarios considered realistic in the current scenario. For instance, infectiousness and death rates vary in Ebola outbreaks; an upper and lower bound for simulation parameters can give a wide range of potential epidemic behaviors that might happen in the wild.

Simulation based on biased data will to generate more biased data. Additionally, some models and some simulation processes are inherently biased. Running the simulation for a long enough period of time; running the simulation multiple times; running the simulation on variety of data sources; and using sensitivity analysis are some techniques that can minimize bias in simulated data.