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I'm having trouble understanding how to specify a model for Bayesian inference.

I have a set of measurements, each with known uncertainty, and I would like to infer the mean of the measurements with gaussian model. The mean is known to be within the interval [0,1], so I use an appropriate prior to enforce that. But I'm not sure that I'm handling the measurement uncertainty properly.

The model I have is $$ \begin{align} x_{\textrm{obs},i} &\sim \textrm{Normal}(x_{\textrm{true},i}, \sigma_{\textrm{true},i}) \\ x_{\textrm{true},i} &\sim \textrm{Normal}(\mu, \sigma) \\ \mu &\sim \textrm{Uniform}(0, 1) \\ \sigma &\sim \textrm{Exponential}(0.25) \end{align} $$ where the "obs" variables are the known values and uncertainties for my measurements.

Is this correct?

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  • $\begingroup$ Do you have repeated measurements, i.e. multiple $x_{\mathrm{obs},i}$ for each $i$? $\endgroup$
    – Durden
    Jun 17, 2023 at 22:37
  • $\begingroup$ I have known, normally distributed error for each point $\endgroup$
    – qsfzy
    Jun 19, 2023 at 2:46

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