# #StackBounty: #bayesian-optimization #map-estimation Bayesian parameter estimation with unit observations

### Bounty: 50

I am trying to do a MAP estimation of the model below, which comes from the literature in non-Bayesian form ($$y = normalcdf(frac{1}{alpha} * log(A/beta)$$). Because the model function has a normalcdf, the outcome of the model is in the range $$0-1$$. My observations are bound to the same range. However, using a Gaussian distribution for the likelihood means that the uncertainty bounds are sometimes outside the $$0-1$$ range (see Figure below). Statistically speaking, is this a problem, and if so, what would be a better solution?

$$R_i sim mathcal{N}(mu,sigma)$$

$$mu_i = normalcdf(frac{1}{alpha} * log(A/beta) )$$

$$alpha sim mathcal{N}(0.35, 0.1)$$

$$betasim mathcal{N}(70, 10)$$

$$sigma sim mathcal{U}(0, 0.3)$$

Get this bounty!!!

This site uses Akismet to reduce spam. Learn how your comment data is processed.