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If both the likelihood and the prior carry little information, then the posterior will be very uncertain. This is a perfect example where we can see how using a different prior, one which includes some knowledge about the problem, can help. Since nnn is an integer which is likely close to 4, I will use a geometric distribution as prior n∼3+Geom(q)n \sim 3 + \mathrm{Geom}(q)n∼3+Geom(q), with q=0.5q = 0.5q=0.5. In the piece of code below, I use pymc to do this numerically and I find nˉ=4.10\bar n = 4.10nˉ=4.10 with credible interval [4,5][4, 5][4,5]. While the interval is the same, what matters is that the distribution is edging closer to 4 (see the mean), showing our uncertainty is shrinking.
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Check a threshold and decide whether to refill input/output FIFOs, which may or may not be joined
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