# Bounds on Ratio of Likelihood to Marginal?

Bayesian inference tells us that the posterior over parameters $$\theta$$ given data $$X$$ is given by:

$$p(\theta|X) = \frac{p(X|\theta)}{p(X)} p(\theta)$$

Are there any known bounds on the ratio of the likelihood divided by marginal $$\frac{p(X|\theta)}{p(X)}$$?