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I have the following posterior distribution for $v$ $$v\propto v^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$

Now can I say that $$v^{-1}\sim\text{Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$

I have the following posterior distribution for $v$ $$f(v)\propto v^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$

Now can I say that $$v^{-1}\sim\text{Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$

I have the following posterior distribution for $v$ $$v\propto v^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}+1,\frac{s}{2}\right)$$

Now can I say that $$v^{-1}\sim\text{Gamma}\left(\frac{p}{2}+1,\frac{s}{2}\right)$$

I have the following posterior distribution for $v$ $$v\propto v^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$

Now can I say that $$v^{-1}\sim\text{Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$

I have the following posterior distribution for $v$ $$v\propto w^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}+1,\frac{s}{2}\right)$$

Now can I say that $$v^{-1}\sim\text{Gamma}\left(\frac{p}{2}+1,\frac{s}{2}\right)$$

I have the following posterior distribution for $v$ $$v\propto v^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}+1,\frac{s}{2}\right)$$

Now can I say that $$v^{-1}\sim\text{Gamma}\left(\frac{p}{2}+1,\frac{s}{2}\right)$$