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Signal detection theory can be applied to modeling perception thresholds for defined stimuli, for example the detection of the presence of a specific signal. It is assumed both the stimulus intensity derived in absence and in presence of the signal are subject to random variations/noise. As I understand, gaussian noise is often assumed.

For modelling detection itself, a binary criterion can be applied by using a threshold. Wikipedia has a section on the Bayesian criterion, which enables different importances to be applied to signal detection theory problems.

I also found lecture slides that list signal detection theory in the context of Bayesian statistics, but there are no explicit mentions of whether the theory itself is a Bayesian approach.

My question is

  • Is signal detection theory a Bayesian approach? Why?
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The literature you linked to and other references employ both a Bayesian and a non-Bayesian approach to solving the problem.

In the lecture slides you can see that on slide 10 they start with a likelihood ratio test and this is not Bayesian. But on slide 25 (for example 2) they have switched to a Bayesian analysis.

So the theory itself does not specify whether it is or is not Bayesian. The kinds of analyses that are done on the data in the context of this theory do. You don't need to be a Bayesian to talk about a loss function or even a criterion for decision making these analyses can either be done using a Bayesian approach or not.

So the answer to your question is: Signal Detection Theory can be done with either a Bayesian approach or not.

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