# Precision prior on Bayesian Linear Regression

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.

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