Interpretation of log data density in DYNARE

Dynare help (legacy posts)
1

Dear colleagues,

I have a question regarding the number reported as log data density
in DYNARE’s Bayesian estimation. Can we interpret this number as
marginal likelihood?

If so, shouldn’t the number of log data density be negative, rather
than positive? DYNARE always reports the positive number of
log data density and I was not sure how to interpret this number.

I very much appreciate your guidance in this regard. Thank you.

sincerely,
Nishi

2

There is no reason why the marginal likelihood should be less than one.

Best

Michel

3

How can this be explaind if Adolfson et al. 2005 report negative marginal likelihood at page 60, 61, 62 of the pdf or Table 2-3…

4

If you are replicating the study of Adolfson and your getting positive values, you are still doing something wrong. However, if you are estimating a different model or you are using a different data set or sample, the marginal likelihood will be different and may even be positive. The reason is that the marginal likelihood may be larger than 1 so that its log is positive (Think of a normal distribution with infinitesimally small variance. In this case the density around the mean will go to infinity. Only for discrete distributions is the marginal density always negative.)

5

Thank you for your answer. I am using their model but I am using a different data set.

6

Would it be too much to ask if you could please post the mod file?

Thank you, if possible.