Are applying Laplace's Rule of Succession to estimate a probability distribution from samples and applying Bessel's Correction (in reverse, perhaps) to estimate population statistics from sample statistics ultimately mathematically the same action?
Also, my understanding is that Laplace's Rule of Succession is based on blending sample data with the proportions of a uniform distribution. Is the idea ultimately grounded in a philosophically arbitrary application of the principle of indifference? Is there any argument for why we should assume the quantities we apply Laplace's Rule of Succession to are a priori uniform?