Occam's Razor

For the number guessing problem, suppose we say that the numbers being given to us are uniformly sampled from the set.

Now if there are two candidate sets, then the probability that the numbers have been sampled from the larger set if much lower in comparison to the smaller set

where $n$ is the size of the set and $k$ is the number of numbers we've received.

This means that if we have two competing sets, the smaller one is more likely.

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Backlinks

• Posterior Predictive Distribution