New answers tagged monte-carlo
1
The previous answer pretty sums up my understanding on this problem. I just want to add 2 solid references on this regard (Both are from an astrophysics context).
The paper by Hogg et al provides a pretty hands-on approach while the the survey of Sharma is more of a survey of MCMC analysis usage in astrophysics.
I am not from the astrophysics community, but ...
4
As I understand, your ultimate goal is to solve an inverse problem (i.e., infer some parameters from given data / observations). To this end, you want to apply Bayesian Inference, which relates the posterior (i.e., the probability distribution of the unknown parameters) to the likelihood (i.e., the probability model of observing some values given the ...
3
The algorithm for perfoming a single HMC step is as follows:
Input: Some initial configuration $\vec{y}_i$ and momentum $\vec{p}_i$.
Output: Next configuration $\vec{y}_{i+1}$ and momentum $\vec{p}_{i+1}$
Draw a random momentum $\vec{p}_*$ from a Gaussian distribution.
Numerically solve Hamilton's equations of motion for some time (i.e., perform some ...
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