I wonder if there is any MCMC sampling method which uses the definition of the target CDF instead of the target PDF; however, I may use a proposal PDF.
I would like to use Metropolis-Hastings but it is not possible because the calculation of the acceptance ratio is defined in terms of the target PDF.
I say this because it is impossible for me to obtain the PDF associated to certain CDF without doing some kind of numerical approximation which may bias my simulation; also, my CDF might be not continuous, and therefore I cannot differenciate it to obtain the PDF
Regards!
I'm not sure, but this might help.
http://statweb.stanford.edu/~owen/students/SethTribbleThesis.pdf
Dear Diego Alvarez,
Would you please clarify your problem by describing it in some more detail?
Also: When you say "my CDF might be not continuous", do you mean that you may have a discrete distribution?
Perhaps, this paper is of help:
http://papers.nips.cc/paper/4652-continuous-relaxations-for-discrete-hamiltonian-monte-carlo.pdf
Rob
http://papers.nips.cc/paper/4652-continuous-relaxations-for-discrete-hamiltonian-monte-carlo.pdf
Hi Diego,
in case you are sampling in one dimension, inverse transform sampling might be the method of choice (instead of MCMC). You transform a uniform sampling in [0,1] to a sampling with the required distribution by choosing
x_i = F^{-1}(u_i),
u_1,...,u_n being the uniform sampling and F the CDF, see also
https://en.wikipedia.org/wiki/Inverse_transform_sampling
Best wishes,
ilja
What I mean, is that for example I would like to sample from a copula by means of MCMC. Copulas are not always differentiable.
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