Inferring a likely full population from multinomial measurement or survey data Assume that we have one or several multinomial samples (e.g., surveys) taken from our population. While inferring characteristics (such as mean values, correlation, ...) from a multinomial sample is a common statistical task, generating a likely full population doesn't seem to be that common.
It is used in the field of transportation planning: Agent-based microsimulation models require such a full population, which the survey data usually is unable to provide. It has to be synthesized.
In which scientific fields could this (or a similar) problem be also relevant? I appreciate any hints, remarks, and literature references.
See the original question for more context. (It was probably too big, I'm splitting it into parts.)
 A: Both calibrating to the known population totals and building models for the full population are reasonably widely used ideas in survey statistics. On calibration, see Sarndal (2007) and Kott (2009). On model-based approach to inference for finite populations, see Valliant, Dorfman and Royall (2000). Microsimulations are used in economics -- I am familiar with their use in subfields of labor economics and welfare economics (taxation and distribution of income).
Version of the complete population are created while running bootstrap in small area estimation, also a subfield of survey statistics. These models are not required to be good behavioral models, they just need to have the moment structure similar to that of the population of interest.
A: I've seen microsimulation used in health, to estimate primary healthcare (GPs, pharmacists) use in the future. That has involved a complicated combination of estimates of future population (including demographic shifts, e.g. ageing population) and creating synthetic datasets of patients using data from multiple surveys. Here is an example of a microsimulation tool being used in a health-related application.
With a synthetic dataset and microsimulation, scenarios are a good approach to examine uncertainty in forecasts. At minimum, scenarios will enable you to see whether particular aspects of the simulation are affecting outcomes - so will enable sensitivity analyses to be conducted.
Obviously, there are military applications for microsimulations, here is a paper on one military scenario microsimulation tool and another paper on the same tool.
Both these tools have taken a number of people months of work to get up and running.
