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I'm currently using Jags to fit a Bayesian linear regression to the Swiss dataset in R.

The model is that $\text{Fertility}_i \sim \text{N}(\mu_i,\tau)$ with precision $\tau$ and mean: $$\mu_i = \beta_1+\beta_2\text{Argiculture}_i+\beta_3\text{Examination}_i+\beta_4\text{Education}_i+\beta_5\text{Catholic}_i+\beta_6\text{Infant.Mortality}_i$$

We use a uniform(-100,100) prior on all the $\beta$ coefficients. $\tau$ is unknown and we have to use a reference prior: $p(\tau)\propto \frac{1}{\tau}$.

I'm not sure how to implement $\tau$ in this model?

model{ 
    for (i in 1:N){
            Y[i] ~ dnorm(mu[i], tau)
            mu[i] <- beta1 + beta2*X[i,1] + beta3*X[i,2] + beta4*X[i,3] + beta5*X[i,4] + beta6*X[i,5]
    }
    beta1 ~ dunif(-100,100)
    beta2 ~ dunif(-100,100)
    beta3 ~ dunif(-100,100)
    beta4 ~ dunif(-100,100)
    beta5 ~ dunif(-100,100)
    beta6 ~ dunif(-100,100)
    tau ~ 
}

Y corresponds to Fertility and $\text{X}_i$ represent the respective explanatory variables as defined above.

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  • $\begingroup$ My guess is to use $\tau \sim \Gamma(\epsilon,\epsilon)$? with some $\epsilon > 0$ $\endgroup$ Apr 4, 2020 at 12:19

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