Exactly a nice blog! detail derivation, thorough discussion!

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]]>– Grateful reader

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]]>Any help on how to go about this would be highly apprecaited. I badly need to understand how to code this in R.

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]]>Thanks for the follow up and clarification.

Jim

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]]>I mean that if you have, say, X = (A,B,C) for three parameters A, B and C, then X’/X means (A’*B’*C’)/(A*B*C). This is because, the determinant of the Jacobian from a transformation from a multivariate Gaussian to a multivariate lognormal turns out to be a product. See https://stats.stackexchange.com/questions/214997/multivariate-log-normal-probabiltiy-density-function-pdf?rq=1

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]]>In my previous reply, wherever I wrote “g^-1”, I meant of course “the Jacobian of g^-1”, sorry for the confusion.

So you need the determinant of the Jacobian of g^-1.

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]]>I think you mean the determinant of X’ divided by the determinant of X if they are multidimensional, no?

And in general: the determinant of g^-1(X) divided by the determinant of g^-1(X’), if you follow your PDF sheet and Wikipedia’s notation.

In your example g^-1(X) = 1/X.

Otherwise an element-by-element division would give you a vector for the acceptance rate, what could you do with that?

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]]>Hi Jim, yes it’s element-by-element division.

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]]>Thanks for the post. Very useful.

However, there is one part of your reply to viiv of 2 October 2018 that is unclear to me.

Step 7 states “check the acceptance by looking at (pi(x1’, x2′)/pi(x1, x2)) * (pi(X’) / pi(X)) * X’/X.”

Is the last ratio, X’/X, element by element division or something else?

Best regards,

Jim

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]]>also see the reply I sent to your Github email address a few days ago

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