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A possible solution might be to take the Fourier transform and multiply it by a dirac comb (Ш function) and take the reverse Fourier transform - or said otherwise, to take the value corresponding with ω being an integer multiple of $2 \pi$. I tried it online with the WolframAlpha website but the result are quite obfuscated : $\begin{align}ℱ_x[{x \over (x^2 ...


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I assume that the Laplace prior is on the mean of the Gaussian random variable. Sadly yes, Gaussian likelihood and Laplace prior do not yield a tractable posterior distribution. You will have to use some MCMC method such as Metropolis-Hastings or slice sampling.


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Your acceptance probability in the code does not seem consistent with what you wrote above. Also keep in mind that since the indexing is zero-based on Python, if you want to do any calculations involving the actual value of the state $\texttt{si}$, you should use $\texttt{si + 1}$.


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