Figure2. As an example, which prior is not supported by data,
imagine prior (lower) as Normal (𝛍=10, SD=2) and likelihood (upper)
Normal (0,1) is far from each other, most of the drawn samples from
prior get very small weights. The probability of sampling from\(-3\sigma\) and lower (the parts that get higher weights) is nearly
1% so out of 10000 we expected 100 non-zero weights. Posterior mean
estimated equals 1.5 while we expected 0.01 (Posterior ~
Normal (0.01, 0.01). Therefore, this approach proved inefficient in
terms of accuracy of estimate and number of sampling.