Are there any advantages to using a Bayesian approach for the analysis of zero inflated count data, specifically dental caries data? Any references that would support that analysis?
Not enough information in the question but following may be helpful to you:
Count data with excess zeroes are widely encountered in the fields of biomedical, medical and public health survey. Here, Zero-inflated Poisson (ZIP) regression model is an useful tool to analyze such data.
It really depends where the zeros are coming from. Bayesian models have the principled advantage that one can integrate prior knowledge into the data in a natural way.
For example, assume that a rare event (e.g. a rare disease) did not occur in your study. With frequentist statistics, your estimate for the probability of this event would be zero. However, if you have prior information from previous studies telling you that the probability of this event is, say 0.01, then you could use a prior distribution peaked around 0.01 and combine this with your data. Then, after combining your data (Likelihood) with the prior, the posteriors probability distribution of this rare disease probability would have a peak somewhere below 0.01 (because it did not happen in your data). However, the event would still not be considered impossible, just rare.
As Kerav said, it depends what the situation is. But if this is your problem, you could go for a Bayesian model. Otherwise, ZIP models are also a way of dealing with it.
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