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Built-in conditional kernels

A built-in conditional kernel represents a family of built-in kernels. In effect note that some of the built-in kernels accepts a set of parameters, for example, shape, location or scale. If we use a variable set rather than a set of scalars for these arguments then we get a family of kernels. Once the values of the variable sets are fix a kernel on the family is selected, for example by means of the method instantiate.

For example, Figure3.11 represents a conditional normal kernel with fix mean $\mu=5$ and standard deviation $\sigma \in [1,2]$. We can denote this conditional kernel as follow:

$$\varphi = P(\Omega_s \vert \Omega_k) = plCndNormal(\Omega_k,5,\Omega_k)$$

with $\Omega_s = \{[1,10]\}$ and $\Omega_k = \{[1,2]\}$.

In this section we show the functionalities of the methods instantiate and compute on built-in conditional kernels. Given a built-in conditional kernel $\varphi = P(\Omega_s\vert \Omega_s)$, $\omega_s \in \Omega_s$ and $\omega_k \in \Omega_k$ we show and comment the result of $\varphi.compute(\omega_s \cup \omega_k)$ and $\varphi.instantiate(\omega_k)$. For instance, if $\varphi = P(\Omega_s \vert \Omega_k) = plCndNormal(\Omega_k,5,\Omega_k)$ then

$$\varphi.compute(\omega_s \cup \omega_k) = \rho.compute(\omega_k)$$

and

$$\varphi.instantiate(\omega_k)=\rho$$

with $\rho = plNormal(\Omega_s,5,\omega_k)$. That is, $\rho$ is a plNormal kernel on $\Omega_k$ with mean 5 and standard deviation $\omega_k$.

Similarly to the previous section, the code and output for the first example is shown, then, for the following examples, just the output is given.

図 3.11: A family of normal distributions with fix mean and variable standard deviation