I have a probability distribution function as follows:
$$ P(y|x,w, \phi) = \frac{\phi}{2\pi} \exp ^{-0.5 (y-t(x, w)'\phi (y-t(x,w)) } $$
Here $y$ and $x$ are two observed values. $\phi$ is also some given parameter and $t$ is a non-linear transformation parameterised by $w$. $w$ is a two dimensional position vector. $t$ is basically a spatial transformation of $x$. The function tells the probability of observing $y$ for a given $x$, $w$ and $phi$. So, is a normal distribution on the residual where the residual is given by $y-t(x, w)$.
Now, for my algorithm I need to express this as a function of $w$. Can someone give me a hint on how to proceed?