Q&A Forum

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Hope everyone just finished your final week and enjoy the summer vaccation!
See you next semester and seniors on the ceremory 

Hi Cat,

I have almost missed this one as the subject is referring HW 9. 

median() provides us a sample median. We can use it to obtain an estimate; whereas,
M (Median) is a population median, that splits a population density in half in terms of the area.
So, the left hand side area is 0.5 and the right hand side area is 0.5 from the M.
(Note also that an area under a density always means probability.)

Now, the quantile function (or inverse cdf) provides us a "point" when the left-hand side probability (area) from the point is given.
When the population distribution is exponential, qexp() is the R built-in quantile function, so what would you plug in there to obtain the M?

Once you obtain the M, the notation f() is the density, given exponential we can use dexp()!

Please feel free to let me know if you have any further questions.

Sure, Kieran.

Uniform(0,0.2) is not an ideal choice, but I imposed it to create a burn-in stage in this HW.
It never generates a negative value in its initial stage,
but you could have it in its second or third stages, causing the denominator to be 0.

In general, the candidate density has a higher tendency to move to the right-hand side.
So, I would say it is quite rare to have the situation in this particular example.

Yes, Uniform(0.4,0.6) would be a better choice
since it is closer to the target density.
Then there will be essentially no burn-in stage,
so we could use the whole Markov Chain.

Hi Cat,

Please just use the sample size n=20 for your approximation, that is all.
I think that part was irrelevant, so let me erase "with degrees of freedom 20" to avoid confusion.

Hi Cat,

Sorry for this late response.
I am not sure why I didn't receive a notice for your posting.

It was just mismatching the argument and the variable in the body:
g_2 <- function(x,z){
  return(z*exp(-((z*y)^2)/2))
}
That is, we need to replace the argument x by y.

The function g_2() comes from the form of the change of variable approach on Page 30.

I will not miss new postings again!