Upper probabilities based only on the likelihood function

In the problem of parametric statistical inference with a finite parameter space, we propose some simple rules far defining posterior upper and lower probabilities directly from the observed likelihood function, without using any prior information. The rules satisfy the likelihood principle and a ba sic consistency principle ('avoiding sure loss'), they produce vacuous infe rences when the likelihood function is constant, and they have other symmet ry, monotonicity and continuity properties. One of the rules also satisfies fundamental frequentist principles. The rules can be used to eliminate nui sance parameters, and to interpret the likelihood function and to use it in making decisions. To compare the rules, they are applied to the problem of sampling from a finite population. Our results indicate that there are obj ective statistical methods which can reconcile three general approaches to statistical inference: likelihood inference, coherent inference and frequen tist inference.