# Example: The Identity Map

### Consider the following map

$$Q(\lambda_1, \lambda_2) = \{ \lambda_1, \lambda_2 \}$$

### Recall our Posterior.

$$\pi^{\dagger}_\Lambda(\lambda) := \pi_\Lambda(\lambda)\frac{\pi_{\mathcal{D}}(Q(\lambda))}{\pi^{Q}_{\mathcal{D}}(Q(\lambda))}$$

$\pi^{\dagger}_\Lambda(\lambda) := \pi_\Lambda(\lambda)\frac{\pi_{\mathcal{D}}(Q(\lambda))}{\pi^{Q}_{\mathcal{D}}(Q(\lambda))}$

We assume a Gaussian Prior in addition to the assumption of Gaussian noise.