# Can inferencing come from incomplete rule sets?

I have some data for medical diagnosis, consisting of some rules about relationship of diseases and their symptoms, for example disease D1 frequently has symptom S1 or disease D2 rarely has symptom S1. Given some symptoms, I want to somehow calculate most probable diseases based on this data.

I thought about using a naive bayes model, but using that needs some assumptions about disease prevalence or probability of some symptoms given a disease that are not present in my rules set. Is there an standard way of doing this kind of analysis? For example are fuzzy systems used in this situation?

NOTE: I think that in the cases where relation between a disease and a symptom is not explicitly stated as a rule it is an indication of either independence or a very low probability of the symptom given that disease.

• Bayesian methods do not require that you know the exact incidence, do you know a range in which the incidence of a disease sits, such as between .01% and .125%? You could be uniform over that region or the region (0,.125) and half normal beyond. You could then integrate over the region (0,1) although this does imply an expectation if you do that without any actual data. The problem, if you do not assign numbers, is that you cannot show that "rarely has symptoms" is the same, in meaning, for disease 1 and disease 2. – Dave Harris Mar 11 '17 at 17:34
• Thank you @DaveHarris, your comment is helpful. I don't know a range for probability of incidence of a disease unfortunately, but do you think it is a good idea to make a choice for that range by testing results for different ranges? – Dandelion Mar 11 '17 at 18:06
• both fuzzy systems and Bayesian systems are going to require some incidence or prevalence measures, depending on what you are using it for. If you are constructing an expert system and can't find public data on either levels or percentages, your best bet would be to kidnap some physicians and ask them "if you saw this symptom what would be your first bet, second bet...etc." From that, you could back into probabilities from their relative levels. – Dave Harris Mar 11 '17 at 18:21