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Bayesian De­ci­sion Theory

TagLast edit: 22 Mar 2021 19:53 UTC by someflowLT

Bayesian decision theory refers to a decision theory which is informed by Bayesian probability. It is a statistical system that tries to quantify the tradeoff between various decisions, making use of probabilities and costs. An agent operating under such a decision theory uses the concepts of Bayesian statistics to estimate the expected value of its actions, and update its expectations based on new information. These agents can and are usually referred to as estimators.

From the perspective of Bayesian decision theory, any kind of probability distribution—such as the distribution for tomorrow’s weather—represents a prior distribution. That is, it represents how we expect today the weather is going to be tomorrow. This contrasts with frequentist inference, the classical probability interpretation, where conclusions about an experiment are drawn from a set of repetitions of such experience, each producing statistically independent results. For a frequentist, a probability function would be a simple distribution function with no special meaning.

Suppose we intend to meet a friend tomorrow, and expect an 0.5 chance of raining. If we are choosing between various options for the meeting, with the pleasantness of some of the options (such as going to the park) being affected by the possibility of rain, we can assign values to the different options with or without rain. We can then pick the option whose expected value is the highest, given the probability of rain.

One definition of rationality, used both on Less Wrong and in economics and psychology, is behavior which obeys the rules of Bayesian decision theory. Due to computational constraints, this is impossible to do perfectly, but naturally evolved brains do seem to mirror these probabilistic methods when they adapt to an uncertain environment. Such models and distributions may be reconfigured according to feedback from the environment.

Further Reading & References

See also

How to Mea­sure Anything

lukeprog7 Aug 2013 4:05 UTC
92 points
52 comments22 min readLW link

Bayes’ The­o­rem Illus­trated (My Way)

komponisto3 Jun 2010 4:40 UTC
158 points
195 comments9 min readLW link

De­ci­sion The­ory FAQ

lukeprog28 Feb 2013 14:15 UTC
99 points
482 comments58 min readLW link

Bayesian Prob­a­bil­ity is for things that are Space-like Separated from You

Scott Garrabrant10 Jul 2018 23:47 UTC
74 points
22 comments2 min readLW link

Gen­er­al­iz­ing Foun­da­tions of De­ci­sion Theory

abramdemski4 Mar 2017 16:46 UTC
5 points
0 comments10 min readLW link

Beyond Bayesi­ans and Frequentists

jsteinhardt31 Oct 2012 7:03 UTC
53 points
51 comments11 min readLW link

How to come up with ver­bal probabilities

jimmy29 Apr 2009 8:35 UTC
27 points
20 comments3 min readLW link
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