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I have been trying to implement a Bayesian inference procedure from scratch for a specific problem, but I have implemented the procedure, and it doesn't seem to work.

Since, I can't just post the code online and ask community to debug my code, I was wondering if someone could provide with a broader checklist when going about coding up a Bayesian inference procedure. (regardless of language)

EDIT: Specifics of the problem

I am trying to implement the procedure described in Section 5 of this paper on MATLAB . Briefly put, the procedure I've implemented is -

  1. I have 3 zero mean variables (i.e., $D = 3$ time series) for $500$ timepoints. I'm using initial $N = 350$ data points as training sample.
  2. The covariance function I'm using is a squared exponential kernel with 1 hyperparameter - characteristic length scale $l$. I'm assuming it to be the same for all 3 timeseries.
  3. I'm keeping degrees of freedom constant, $\nu = D + 1$.
  4. $L$, the lower Cholesky decomposition of the scale matrix $V$ is computed as the $D \times D$ covariance matrix of the $N \times D$ training dataset.
  5. The sampling procedure essentially involves 2 steps (using Gibbs sampling)

    5.1 Sample $u$ ($N \times D \times \nu$) dimensional vector, assuming Gaussian process prior (as defined in equation 19 of the paper). I've assumed a Gaussian likelihood function (as defined in equation 24). For this I'm using Elliptical Slice Sampling

    5.2 Sample GP hyperparameter $l$, using a lognormal prior (assumption, $mean=1.5$, $var = 1$). I've used slice sampling for this with posterior as product of GP prior(eq. 19) and lognormal density.

I let this Gibbs sampler run for $10000$ iterations ($5000$ burn-in). But convergence plot of $u$ doesn't seem to converge.

I also tried this with smaller $N$ (~ $50$) and increased no. of iterations but didn't work.

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    $\begingroup$ Can you at least say something about what kind of statistical problem you are dealing with, which kind of model you are using and which numerical method you are planning to use? Bayesian inference is a very broad topic - at the moment you are basically asking for a checklist for all statistical problems that we can think of! $\endgroup$ – MånsT Jun 12 '13 at 18:50
  • $\begingroup$ Agreed with the above comment. You can state most, if not all, of the probabilistic assumptions without deidentifying data. Knowing which software you're using is helpful too, i.e. winbugs or R's mcmc package. $\endgroup$ – AdamO Jun 12 '13 at 18:53
  • $\begingroup$ I have added details about the problem, Let me know if I should provide any other details. $\endgroup$ – steadyfish Jun 12 '13 at 19:06

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