When predictive performance testing, rather than testing model assumptions, is used for validation, the need for detailed model specification is greatly reduced. Minimum bias models trade some degree of statistical independence in data points in exchange for statistically much more tame distributions underlying individual data points. A combination of multiplicative minimum bias and credibility methods for predictively modeling losses (pure premiums, claim counts, average severity, etc.) based on explanatory risk characteristics is defined. Advantages of this model include grounding in long-standing and conceptually lucid methods with minimal assumptions. An empirical case study is presented with comparisons between multiplicative minimum bias and a typical generalized linear model (GLM). Comparison is also made with methods of incorporating credibility into a GLM.