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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.)

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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.

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  • $\begingroup$ Thank you. To quote from Valliant et al.: "Among the branches of statistics, survey sampling is notable for its public importance and its theoretical isolation. It ... is neglected, and when not neglected, found to be an alien subject having its own rules and orientation at odds with standard methods of statistical inference. Students of statistics catch a glimpse, shudder, and pass on." Now, given that I already have the surveyed data and perhaps a description of the sampling method, will I need to dig into survey statistics itself to understand what's going on here? Where should I start? $\endgroup$
    – krlmlr
    Commented Mar 2, 2012 at 23:14
  • $\begingroup$ Figuring out survey statistics is a long journey. It took me probably two or three years to bring myself to the concept of randomization distribution. If you want to finish your transportation project within three months or so, that's hardly an option for you. In my own microsimulations, I used the existing sample data as representative agents with sufficiently rich data to figure out their behavior, and I calibrated my weights to bring my sample up to the known population characteristics. $\endgroup$
    – StasK
    Commented Mar 3, 2012 at 0:13
  • $\begingroup$ Vaillant et al. doesn't have "randomization distribution" in its keyword index, "randomization principle" is perhaps the closest. Neither does Wikipedia. What is "randomization distribution"? Is it the same as "null distribution"? $\endgroup$
    – krlmlr
    Commented Mar 9, 2012 at 12:09
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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.

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