I'll give you a concrete instance where that was not true in a "stochastic sense". In the mid 2000s the Indian government wanted to test its water at the local

I'll give you a concrete instance where that was not true in a "stochastic sense". In the mid 2000s the Indian government wanted to test its water at the local level. A lot of time and money went into purchasing Water test kits. They set up large agencies and funded offices to be built all over the place for water points of access to be tested and the data to be written down aggregated and sent off. For quite some time the Indian government believed they had IMPECABLE water, how could that be because ... they didn't. When these offices were audited in the early 2010s it was found most of them hadn't even OPENED the test kits and were just faking the data, much like you might on your intro chem lab. Source: Me I worked on operationalizing that data collection and the engineering instrumentation of the test kits to literally track people to make sure they just did their job and what a cluster fuck that all was. What is my point though, before believe government oriented data I'd have to know something about their methodology and how it's verified. Fraud does exist whether explicitly or emergent based on some factors cultural, bad incentive structure .. ect and you can't depend on stochastic hand waving to say it's close enough. Having said that you probably COULD depend on stochastic MCMC type analysis to tell you the likelihood your measured sample data is real.