Empirically, most uses of values of 32-bit integers (e.g. in programming in general) have magnitudes very much smaller than 2^30. A significant proportion of their empirical values are between 0 and 10. So my prior would be very much non-uniform.
I would expect something like a power law, possibly on the order of P(X >= x) ~ x^-0.2 or so except with some smaller chance of negative values as well, maybe 10-20% of that of positive ones (which the statement “nonnegative” eliminates), and a spike at zero of about 20-40% of total probability. It should also have some smaller spikes at powers of two and ten, and also one less than those.
This would still be a bad estimate for the number of children, once I found out that you were actually talking about children, but not by nearly as much.
Empirically, most uses of values of 32-bit integers (e.g. in programming in general) have magnitudes very much smaller than 2^30. A significant proportion of their empirical values are between 0 and 10. So my prior would be very much non-uniform.
I would expect something like a power law, possibly on the order of P(X >= x) ~ x^-0.2 or so except with some smaller chance of negative values as well, maybe 10-20% of that of positive ones (which the statement “nonnegative” eliminates), and a spike at zero of about 20-40% of total probability. It should also have some smaller spikes at powers of two and ten, and also one less than those.
This would still be a bad estimate for the number of children, once I found out that you were actually talking about children, but not by nearly as much.