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Suppose today that I simulated a number of points $N$ from an equally weighted mixture of three normal distributions. We assume for convenience's sake that each of those three normal distributions have different means but the same variance. From this, it is trivial to fit a Bayesian model for the data using a pre-specified number of mixture components. However, I was wondering if it was possible, and how I can, fit a bayesian model to an unspecified number of mixture components. To make this problem easier, I am allowing the total number of components to range between 1 and 6. In other words, I am trying to see if I can somehow "pick-up" on how many mixture components the data came from. Does anyone know of any resources or ideas on how I can do this? thanks

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