# Marginal posterior distribution, likelihood mean sum of two standardnormal priors

How would I compute the marginal posterior distribution of $$\mu_1$$ and $$\mu_2$$ if the likelihood $$(y | \mu_1,\mu_2) \sim N(\mu_1+\mu_2,1)$$ and $$\mu_i \sim N(0,1)$$

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## 1 Answer

Your model is not identifaible. since

$$f(y|\mu_1=1,\mu_2=2)=f(y|\mu_1=2,\mu_2=1)$$ but $$(1,2)\neq (2,1)$$

For resolving identifaibility problem, you should work with $$\mu=\mu_1+\mu_2$$ like $$y|\mu \sim N(\mu,\sigma^2)$$ or make a condition that guarantee identifaibility.