It’s a metaphor intended to convey the concept to people without the technical education to know or care where the diminishing returns line is going to be.
The problem is that it conveys the concept in a very misleading way.
No, it does not. In sampling-based inference, the necessary computation time grows linearly with the demanded sample size, not exponentially. There may be diminishing returns to increasingly accurate probabilities, but that’s a fact about your utility function rather than an exponential increase in necessary computational power.
This precise switch, from an exponential computational cost growth-curve to a linear one, is why sampling-based inference has given us a renaissance in Bayesian statistics.
There may be diminishing returns to increasingly accurate probabilities, but that’s a fact about your utility function
This has nothing to do with utility functions.
Sample size is a linear function of the CPU time, but the accuracy of the estimates is NOT a linear function of sample size. In fact, there are huge diminishing returns to large sample sizes.
The problem is that it conveys the concept in a very misleading way.
No, it does not. In sampling-based inference, the necessary computation time grows linearly with the demanded sample size, not exponentially. There may be diminishing returns to increasingly accurate probabilities, but that’s a fact about your utility function rather than an exponential increase in necessary computational power.
This precise switch, from an exponential computational cost growth-curve to a linear one, is why sampling-based inference has given us a renaissance in Bayesian statistics.
This has nothing to do with utility functions.
Sample size is a linear function of the CPU time, but the accuracy of the estimates is NOT a linear function of sample size. In fact, there are huge diminishing returns to large sample sizes.
Ah, ok, fair enough on that one.