Statistics and epochs

Statistics come in two flavours. The formal variety are based on samples with a known distribution. The empirical variety are drawn using a real-world process. If there is a known distribution then we know the ‘rules of the situation’ and hence are in a single epoch, albeit one that may have sub-epochs. In Cybernetic terms there is usually an implicit assumption that the situation is stable or in one of the equilibria of a polystable system. Hence, that the data was drawn from a single epoch. Otherwise the statistics are difficult to interpret.

Statistics are often intended to be predictive, by extrapolation. But this depends on the epoch enduring. Hence the validity of a statistic is dependent on it being taken from a single epoch, and the application of the statistic is dependent on the epoch continuing.

For example, suppose that we have found that all swans are white. We cannot conclude that we will never see black swans, only that if:

  • we stick to the geographic area from which we drew our conclusion
  • our sample of swans was large enough and representative enough to be significant
  • we are extrapolating over a time-period that is short compared with any evolutionary or other selective processes
  • there is no other agency that has an interest in falsifying our predictions.

then we are unlikely to see swans that are not white.

In particular the ‘law of large numbers’ should have appropriate caveats.

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

4 Responses to Statistics and epochs

  1. Pingback: Mathematics and real systems | djmarsay

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