Sampling from an unknown distribution I am using the principle of maximum entropy to fit a density to a given set of samples. I want to generate new set of samples from the approximated density. Is there any way to draw samples from a density obtained by maximum entropy approach?
 A: Construct a piecewise probability distribution curve to fit the data and then use rejection sampling (e.g. see Ziggurat Algorithm to see how to implement rejection sampling).
A: As Iocster said, you can use rejection sampling if you have an appropriate proposal density. Here is another approach that is a rather computationally intensive answer to the question that you can use for any density estimate, regardless of whether it was fit by maximum entropy:
If you have an estimated density, $\hat{f}$, you can get an estimated cumulative distribution function
$$ \hat{F}(y) = \int_{-\infty}^{y} \hat{f}(x) dx $$ 
this integral can be estimated numerically using, for example, the integrate() function in R. Next, you can numerically estimate the inverse cumulative distribution function (i.e. the quantile function) 
$$ \hat{Q}(x) = \hat{F}^{-1}(x) = \inf \{ y : \hat{F}(y) = x \} $$ 
Assuming $\hat{F}$ is monotonically increasing, the intermediate value theorem applies, and $Q(x)$ can be calculate using any standard root finding algorithm. Once you have $\hat{Q}$, you can apply Inverse Transform Sampling, which says $\hat{Q}(U)$, where $U \sim {\rm Uniform}(0,1)$, is a draw from a distribution with CDF $\hat{F}$ (and therefore density $\hat{f}$). 
