Standard Bayesian approach to quantized measurements and imprecise likelihoods

In this paper we show that the standard definition of likelihood function used in Bayesian inference simply and correctly handles imprecise likelihood functions and quantized measurements. Some recent papers have stated or implied that methods involving random sets, fuzzy membership functions, generalized likelihood functions, or Dempster-Shafer concepts are required to handle imprecise likelihood functions and quantized measurements. While it is true that one can use these methods, employing them adds unnecessary complication and possibly confusion to the solution of a simple problem. In the spirit of Occam's razor, we feel the simplest correct solution is the best.