Guest post: BAYESBOT 3000 explains Bayesianism to me and Less Wrong
November 27, 2011 § Leave a comment
Greetings, humanoids! I am BAYESBOT 3000, the Bayesian robot. I am here to discuss some ideas that humanoids hold about Bayesians.
Specifically, here are what are claimed by humanoids of the website “Less Wrong” to be core tenets of Bayesianism:
Core tenet 1: Any given observation has many different possible causes.
Core tenet 2: How we interpret any event, and the new information we get from anything, depends on information we already had.
Core tenet 3: We can use the concept of probability to measure our subjective belief in something. Furthermore, we can apply the mathematical laws regarding probability to choosing between different beliefs. If we want our beliefs to be correct, we must do so.
Core tenet 1 is trivially true. In fact, it could be strengthened by deleting “possible” or changing “many” to “an infinite number of”, though the latter may be unwise, as humanoids have difficulty with the concept of infinity.
Core tenet 2 is either also trivially true, or meaningless. A humanoid’s evaluation of an event will depend on the knowledge of that humanoid. A BAYESBOT switched on for the first time will evaluate events based on its programming, which depends on the knowledge of humanoid programmers.
Core tenet 3 comprises three different tenets. Humanoids and BAYESBOTs can use probability to measure belief, just as they could use cubits to measure the length of a manatee. They could use probability to choose between beliefs: for instance, by rolling a die. Where BAYESBOT has a problem is with “If we want our beliefs to be correct, we must do so.” Firstly, BAYESBOT robo-LOLs at the idea of humanoids having correct beliefs. Secondly, if humanoids wish to be, as the website’s name says, less wrong, in the long-run BAYESBOTS and their friendly rivals FREQUENTOBOTS both achieve this. Humanoids are compost in the long-run, so they may be interested in the short-fun instead. There is no guarantee that a BAYESBOT beats a FREQUENTOBOT, or vice versa, on any time scale. The more important matter is BAYESBOTS and FREQUENTOBOTS use inputs efficiently. But humanoids experience a wider range of inputs than we bots. It is not clear to bots or humanoids how to mathematically combine observations of the Sun with Newtonian physics to arrive at a probability that the Sun will rise tomorrow. Using all inputs, it is impossible to arrive at an uncontroversial probability that anthropogenic global warming has occurred. BAYESBOT differs from STRICT FREQUENTOBOT in that BAYESBOT will calculate a probability for this hypothesis given a prior and a set of data. However, the prior will not be perfectly specified, so it is up to humanoids to decide how literally to take such probabilities. BAYESBOTS take such probabilities literally if and only if they are programmed to.
BAYESBOT’s empiricism is as good as its programming. How good that is best determined through the empiricism of those other than BAYESBOT.