Please consider the following Bayes Network:

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We can express density $p(\mathbf{x}_1 | \mathbf{x}_0, \mathbf{y}_1)$ in terms of measurement and motion models by ignoring normalization constants as:

$$\begin{align}p(\mathbf{x}_1 | \mathbf{x}_0, \mathbf{y}_1) \propto &\ p(\mathbf{x}_1, \mathbf{x}_0, \mathbf{y}_1) \\ =&\ p(\mathbf{x}_1 | \mathbf{x}_0) p(\mathbf{y}_1 | \mathbf{x}_1) \end{align}$$

Since $x_0$ is assumed to be known, thus the prior, $p(x_0)$, would evaluate to a constant and we ignored it in factorised density.

My question is how we can find the $p(x_0)$ from the expression above?


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