PACE is a form of Directed Evolution: which use a bacteriophage with a bit of its gene removed; then, engineer a virus to infect the bacteria, which will only successfully complete infection if the missing area is provided.

The mutation of this virus, then, essentially RNG-s mutations of new functions and will only produce successful new generations of bacteriologist when it works.

PACE is hard

The only way to check that PACE worked in the direction you want is by sampling the bacteria and hope that they are evolving in the correct direction

a parameter of probability distribution govern the probabilities associated with different conditions in that distribution. It is usually a vector:

For instance, for uniform \(Uni(\alpha, \beta)\), parameter \(\theta = [\alpha, \beta]\).

importantly, for a discrete distribution system with 6 parameters, we only need 5 independent parameters to be able to satisfy the entire system. This is because a probability distribution must sum to 1.

however, for a conditional probability:

\begin{equation} p(x|a) \end{equation}

we need to specificity \((n-1)m\) parameters, whereby \(m\) is the number of states \(a\) can take, and \(n\) the number of states \(n\) can take. Each group of \(m\) has to add up to \(1\).