On the application of Distributions... an example
So, recently I was both asking questions on the stan-user mailing list, and trying to be helpful with others who were asking questions too. A topic came up where no-one was answering the question, and...
View ArticleApplying Distributions to functions of data and parameters: my example
Suppose there are physics labs around the world that want to find out the length of a special unobtanium molecule. They have a variety of special laser molecular traps which can read out the length of...
View ArticleAn argument for the previous method
So, why should we believe that it works to put probability distributions on functions of both data and parameters, in a non-generative way? (see my previous example) Well, one reason is the success of...
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Generative vs Declarative models Imperative vs Declarative programs
In programming, there are a variety of "paradigms" which languages fall into. The most well known is the "imperative" style of language, typified by C/C++, Matlab, Java, Python, etc. There are also...
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Why put distributions on functions/expressions?
You might well ask, in all this declarative vs generative modeling discussion, why would you want to put distributions on expressions involving data and parameters? And the answer I'd give to that is...
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Nonlinear functions on the left hand side and all that jazz
In my posts about assigning distributions to functions of data and parameters, I mentioned the tried and true example of trying to apply a distribution to a nonlinear function of a parameter: log(foo)...
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A Generative Modeling Challenge
So, I've been discussing declarative vs generative models. Here's a case where I think the declarative model makes good sense, how would you model this? y is a vector of 1000 timeseries samples from...
View ArticleOnce more about Stan and Jacobian warnings
In Stan, if you have an expression that looks like foo ~ distrib(a,b,c); Where foo is either a function, or a transformed parameter variable, and distrib is some distribution, Stan will complain about...
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The Implicit Function Theorem and Likelihood Functions
In Bayesian statistical modeling we often use the symbol ~ which denotes a kind of "statistically equal to". Consider the following: If then this is an equation of a line, whereas if we say for example...
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