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Suppose that I have prior belief B. Then I get an information D from the source S. I update B with D. However, my update magnitude depends on my trust T(S) in S. Also, the marginal update diminishes with difference D-B, as does my trust in T(S).

Can this be expressed in Bayesian terms, or is this Bayesian at all?

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    $\begingroup$ Can you provide quantitative definitions or descriptions of "belief," "information," "source," "update", and--especially--"trust"? If so, we might be able to answer; if not, then this isn't a statistical question. $\endgroup$
    – whuber
    May 1, 2019 at 20:59
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    $\begingroup$ If the "belief updating" step is a likelihood, can "trust" not be thought of as a weight? Essentially, this would rigorous establish the idea that a lack of trust is the same as having a stronger prior. $\endgroup$
    – AdamO
    Jan 15, 2020 at 22:04

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You should update your confidence in B by comparing the probability of seeing D given that B is true versus the probability given that it is false. This is Bayesian updating. It's unclear what your discussion of "trust" means. Presumably, you mean something along the lines of "S said that X was true, but I don't have complete confidence in S's accuracy, so I'm not certain that X is true". But Bayesian updates are on what you see. If you see S claiming that X is true, then the Bayesian update is done based on the probability of seeing S claim that X is true. Whether X is in fact true is not important, because that's not what the update is based on.

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