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magfrump comments on Open Thread, November 16–30, 2012 - Less Wrong Discussion

3 Post author: VincentYu 18 November 2012 01:59PM

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Comment author: magfrump 26 November 2012 09:42:02PM 0 points [-]

I was talking with someone the other day and they suggested something that sounded to me like discrete probability theory with ordinal weights. Does anyone know either: (a) specifically what (all? Almost all? Nearly none?) parts of Bayesian probability theory work out when you have to allow ordinal numbers as weights (I can specify what I mean by this if it is necessary) or (b) just generally speaking, Bayesian probability is about distributions on real vector spaces (as I see it), to what extent has anyone investigated these problems for modules over, for example, noncommutative rings? If this is well-developed, what is a good source?

For the curious, my reason for thinking of this was comparing Optimality Theory and Harmonic Grammar when a linguist described them to me.