The evaluation of petrophysical logs in terms of rock and fluid compositions can be ambiguous in the presence of possible complex lithology types, deep invasion effects, etc. In such circumstances the evaluation results tend to be strongly influenced by the choice of petrophysical evaluation parameters such as rock and fluid density, acoustic and electrical properties. In addition, different lithology types may require the use of different interpretation models or equations. Given these total or partial unknowns a rigorous log evaluation needs to scan through all possible combinations of evaluation parameters and models to determine which combinations of rock and fluid component abundances explain the measurements. It may be obvious that such an exercise can result in multiple solutions and that some type of Monte Carlo analysis is an appropriate mechanism to sample through all the combinations. The amount of calculations required to do this using a regular Monte Carlo analysis scheme is prohibitive large: in the order of 10^20. An implementation of a Bayesian inference method based on a Markov Chain Monte Carlo algorithm dramatically reduces the amount of evaluations required to some 1000 to 10000 per log increment. Any available geological, geophysical or production derived knowledge can be incorporated in the MCMC evaluation as a modification of the prior probability distributions for the evaluation parameters and models. The resulting properly correlated rock and fluid component abundances also enables the calculation of tool response probability distributions for (not yet) acquired logging tools and enables a quick analysis of the potential evaluation uncertainty reduction by those tools. A few carbonate and sandstone application examples illustrate log evaluation uncertainty with respect to rock mineral composition and oil/gas saturations and how the ability to predict the range of possible measurement results for possible additional logging tools can help optimize data acquisition programs.