I have a data set that I claim is adequately modeled by a probability distribution, or more generally a family of probability distributions. How do you decide that the model is good/useful/correct under the stipulation that you can only refer to this data set? 

For concreteness, the data set could be [-3,2,1,0,10020] and the proposed model for an individual data point is a Normal(theta,1) where theta is real; additionally, the data points are independent.