The general Bayes' theorem is well known as:
$$P(X|Y) = \frac{P(Y|X) \cdot P(X)}{P(Y)} $$
where $P(X)$ a prior probability distribution (belief), and $P(Y)$ a data probability distribution (observation). Let all distributions discrete over a state space for vectors $X$ and $Y$, with $x_k=1...K$ and $y_m=1...M$.
Regard a chain of Bayesian update steps of the same, such that:
$$ P(X|Y)_n = \frac{P(Y|X)_n \cdot P(X)_n}{P(Y)_n} $$
as a process with $n=1...N$ iterations:
$$P(X)_{n+1}=P(X|Y)_n$$
A transition rate (a probability distribution per unit step $\tau$) of $w(n \rightarrow n+1)$ be assigned for the iteration from $n$ to $n+1$. Furthermore, we assume Markov property.
What is the Master Equation for
$$\frac{P(X|Y)_{n+1}-P(X|Y)_n}{\tau}$$
that describes this process?