| suplist {hyper2} | R Documentation |
Basic functionality for lists of hyper2 objects, allowing the
user to concatenate independent observations which are themselves
composite objects such as returned by ggrl().
## S3 method for class 'suplist' Ops(e1, e2) ## S3 method for class 'suplist' sum(x,...,na.rm=FALSE) suplist_add(e1,e2) as.suplist(L)
e1,e2 |
Objects of class |
x,...,na.rm |
In the |
L |
A list of |
A suplist object is a list of hyper2 objects. Each
element is a hyper2 object that is consistent with an
incomplete rank observation R; the list elements are exclusive
and exhaustive for R. If S is a suplist object,
and S=list(H1,H2,...,Hn) where the Hi are hyper2
objects, then
\(\mbox{Prob}(p|H_1)+\cdots+\mbox{Prob}(p|H_n)\).
This is because the elements of a suplist object are disjoint
alternatives.
It is incorrect to say that a likelihood function \(\mathcal{L}_S(p)\) for p is the sum of separate likelihood functions. This is incorrect because the arbitrary multiplicative constant messes up the math, for example we might have \(\mathcal{L}_{H_1}(p)=C_1\mathrm{Prob}(p|H_1)\) and \(\mathcal{L}_{H_2}(p)=C_2\mathrm{Prob}(p|H_2)\) and indeed \(\mathcal{L}_{{H_1}\cup H_2}(p)=C_{12}\left(\mathrm{Prob}(p|H_1)+\mathrm{Prob}(p|H_2)\right)\) but
\[\mathcal{L}_{H_1}(p)+\mathcal{L}_{H_2}(p) \neq C_1\mathrm{Prob}(p|H_1)+C_2\mathrm{Prob}(p|H_2)\](the right hand side is meaningless).
Functions suplist_add() and sum.suplist() implement
“S1+S2” as the support function for independent
observations S1 and S2. The idea is that the support
functions “add” in the following sense. If
S1=list(H1,...,Hr) and S2=list(I1,...,Is) where
Hx,Ix are hyper2 objects, then the likelihood function
for “S1+S2” is the likelihood function for S1
followed by (independent) S2. Formally
However, S1+S2 is typically a large and unwieldy object, and
can be very slow to evaluate. These functions are here because they
provide slick R idiom.
Returns a suplist object.
Robin K. S. Hankin
W <- hyper2(pnames=letters[1:5]) W1 <- ggrl(W, 'a', letters[2:3],'d') # 2-element list W2 <- ggrl(W, 'e', letters[1:3],'d') # 6-element list W3 <- ggrl(W, 'c', letters[4:5],'a') # 2-element list # likelihood function for independent observations W1,W2,W3: W1+W2+W3 # A 2*6*2=24-element list like_single_list(indep(equalp(W)),W1+W2+W3) ## Not run: dotchart(maxplist(W1+W1+W3),pch=16) # takes a long time