Suppose we do rejection sampling. Then the universe restarts at 2000 every time a datapoint is violated. The subjective experience of entities inside such a simulation would be best described as random death with occasional survival if some arbitrary criteria are met. Writing (long-lasting) believable false reports will alter the criteria to include those reports somehow being written.
MCMC algorithm is more interesting. It introduces a strange contortion of time; we generate an initially random space-time with the known datapoints clamped, and then re-sample the unknown bits for a long time to get a good posterior distribution over the possibilities. Real time is a sometimes-nonsensical meandering through possibility-space. Time as experienced “in the simulation” is relatively normal, but it is interesting/boring to argue about whether entities living in such a simulation have experiences in a meaningful sense. Causality doesn’t work at all as it should, but it will appear to work roughly as it should most of the time. Events will conspire to bring about a random assortment of facts which are the clamped values, but the better-quality samples will make the conspiracies look like true chance.
Metropolis-hastings is an even more advanced technique, but I don’t think there is anything special about the subjective experience if the simulated entities in MH as compared to basic MCMC.
Suppose we do rejection sampling. Then the universe restarts at 2000 every time a datapoint is violated. The subjective experience of entities inside such a simulation would be best described as random death with occasional survival if some arbitrary criteria are met. Writing (long-lasting) believable false reports will alter the criteria to include those reports somehow being written.
MCMC algorithm is more interesting. It introduces a strange contortion of time; we generate an initially random space-time with the known datapoints clamped, and then re-sample the unknown bits for a long time to get a good posterior distribution over the possibilities. Real time is a sometimes-nonsensical meandering through possibility-space. Time as experienced “in the simulation” is relatively normal, but it is interesting/boring to argue about whether entities living in such a simulation have experiences in a meaningful sense. Causality doesn’t work at all as it should, but it will appear to work roughly as it should most of the time. Events will conspire to bring about a random assortment of facts which are the clamped values, but the better-quality samples will make the conspiracies look like true chance.
Metropolis-hastings is an even more advanced technique, but I don’t think there is anything special about the subjective experience if the simulated entities in MH as compared to basic MCMC.