This might be a very strange question, but I am having a bit of trouble. Here is a posterior distribution.

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If I am reading this passage out loud, when I get near the end to π(δ1), do I read it as pi delta one? Or function of delta one? Or pi of delta one? Or something else entirely?

  • $\begingroup$ Please provide reference to the citation. $\endgroup$ – Xi'an Oct 15 at 7:26
  • $\begingroup$ I encountered these kinds of questions all the time when reading mathematical physics textbooks for blind people. The two extremes of the spectrum of strategies are (1) read the notation literally, as in "pi open parenthesis delta sub one close parenthesis" and (2) read the notation as it would be spoken in a lecture, as "pi of delta one" or "pi of delta sub one". Which is right, or even acceptable, will depend on your audience. $\endgroup$ – whuber Oct 15 at 16:25

This is a loose notation where $\pi$ means several things related to priors and posteriors:

  1. $\pi(p_1,\ldots,p_m,\delta_1|y_1,\ldots,y_m,y)$ denotes the posterior density of the entire collection of (unknown?) parameters $(p_1,\ldots,p_k,\delta_1)$ given the data $(y_1,\ldots,y_m,y)$
  2. $\pi(p_1)\cdots\pi(p_m)$ denotes the prior density of the vector $(p_1,\ldots,p_k)$ and indicates that they are a priori iid (although one cannot tell for sure about the "identically distributed" from the loose notations)
  3. $\pi(\delta_1)$ denotes the prior density on the parameter (?) $\delta_1$ and indicates that it is independent from the $p_i$'s
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  • $\begingroup$ Oh okay, so it is not read as 'pi' at all. Would I read it as simply the prior of delta 1? Or would I say the prior distribution of delta 1, or prior pdf of delta 1, or prior density of delta 1? Thanks! $\endgroup$ – Fire Oct 15 at 7:33
  • $\begingroup$ As clearly written in my answer, $\pi$ stands for density. $\endgroup$ – Xi'an Oct 15 at 8:11

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