# Priors

TagLast edit: 27 Oct 2012 6:54 UTC by

In the context of Bayes’s Theorem, Priors refer generically to the beliefs an agent holds regarding a fact, hypothesis or consequence, before being presented with evidence. Upon being presented with new evidence, the agent can multiply their prior with a likelihood distribution to calculate a new (posterior) probability for their belief.

## Examples

Suppose you had a barrel containing some number of red and white balls. You start with the belief that each ball was independently assigned red color (vs. white color) at some fixed probability. Furthermore, you start out ignorant of this fixed probability (the parameter could be anywhere between 0 and 1). Each red ball you see then makes it more likely that the next ball will be red, following a Laplacian Rule of Succession. For example, seeing 6 red balls out of 10 suggests that the initial probability used for assigning the balls a red color was .6, and that there’s also a probability of .6 for the next ball being red.

On the other hand, if you start out with the prior belief that the barrel contains exactly 10 red balls and 10 white balls, then each red ball you see makes it less likely that the next ball will be red (because there are fewer red balls remaining).

Thus our prior affects how we interpret the evidence. The first prior is an inductive prior—things that happened before are predicted to happen again with greater probability. The second prior is anti-inductive—the more red balls we see, the fewer we expect to see in the future.

As a real life example, consider two leaders from different political parties. Each one has his own beliefs—priors—about social organization and the roles of people and government in society. These differences in priors can be attributed to a wide range of factors, ranging from their educational backgrounds to hereditary differences in personality. However, neither can show that his beliefs are better than those of the other, unless he can show that his priors were generated by sources which track reality better1.

Because carrying out any reasoning at all seems to require a prior of some kind, ideal Bayesians would need some sort of priors from the moment that they were born. The question of where an ideal Bayesian would get this prior from has occasionally been a matter of considerable controversy in the philosophy of probability.

## Updating prior probabilities

In informal discussion, people often talk about “updating” their priors. This is technically incorrect, as one does not change their prior probability, but rather uses it to calculate a posterior probability. However, as this posterior probability then becomes the prior probability for the next inference, talking about “updating one’s priors” is often a convenient shorthand.

## Blog posts

1. Robin Hanson (2006). “Uncommon Priors Require Origin Disputes”. Theory and Decision 61 (4) 319–328. http://​​hanson.gmu.edu/​​prior.pdf

# Pri­ors as Math­e­mat­i­cal Objects

12 Apr 2007 3:24 UTC
51 points

# Against im­proper priors

26 Jul 2011 23:50 UTC
6 points

# A Priori

8 Oct 2007 21:02 UTC
80 points

# Learn­ing the prior

5 Jul 2020 21:00 UTC
92 points
(ai-alignment.com)

# Learn­ing the prior and generalization

29 Jul 2020 22:49 UTC
34 points

# Separat­ing the roles of the­ory and di­rect em­piri­cal ev­i­dence in be­lief for­ma­tion: the ex­am­ples of min­i­mum wage and an­thro­pogenic global warming

25 Jun 2014 21:47 UTC
38 points

# The Solomonoff Prior is Malign

14 Oct 2020 1:33 UTC
168 points

# The prior of a hy­poth­e­sis does not de­pend on its complexity

26 Aug 2010 13:20 UTC
34 points

# Re­vis­ing pri­ors and an­thropic reasoning

6 Feb 2011 5:42 UTC
3 points

# Against im­proper priors

26 Jul 2011 23:50 UTC
6 points

# Cry­on­ics priors

20 Jan 2013 22:08 UTC
9 points

# Sim­plic­ity pri­ors with re­flec­tive oracles

15 Nov 2014 6:39 UTC
1 point

# Trapped Pri­ors As A Ba­sic Prob­lem Of Rationality

12 Mar 2021 20:02 UTC
141 points

# The uni­ver­sal prior is malign

30 Nov 2016 22:31 UTC
16 points
(ordinaryideas.wordpress.com)

# Chap­ter 49: Prior Information

14 Mar 2015 19:00 UTC
19 points

# Believ­ing oth­ers’ priors

22 Nov 2018 20:44 UTC
8 points

# Pri­ors and Surprise

3 Mar 2010 8:27 UTC
23 points

# Pri­ors Are Useless

21 Jun 2017 11:42 UTC
2 points

# [Question] What are some low-in­for­ma­tion pri­ors that you find prac­ti­cally use­ful for think­ing about the world?

7 Aug 2020 4:37 UTC
27 points

# Fre­quen­tist prac­tice in­cor­po­rates prior in­for­ma­tion all the time

7 Nov 2020 20:43 UTC
18 points