Log likelihood functions

Returns a log-likelihood for a given hyper2 or hyper3 object at a specific point in probability space

loglik(p, H, log = TRUE)
loglik_single(p,H,log=TRUE)
like_single_list(p,Lsub)
like_series(p,L,log=TRUE)

Arguments

H

An object of class hyper2 or hyper3

p

A probability point. See details

log

Boolean with default TRUE meaning to return the log-likelihood and FALSE meaning to return the likelihood

L,Lsub

A list of hyper2 objects, or a list of list of loglik objects

Details

Function loglik() is a straightforward likelihood function. It can take a vector of length n=size(H) or size(H)-1. If given the vector \(p=\left(p_1,\ldots,p_{n-1}\right)\) it appends the fillup value, and then returns returns the (log) likelihood (names are discarded in this case). If given a vector \(p=\left(p_1,\ldots,p_{n}\right)\) [notionally summing to 1] it requires a named vector, and names must match those of H. The vector is reordered if necessary.

If p is a matrix, the rows are interpreted as probability points.

Function loglik_single() is a helper function that takes a single point in probability space. Functions like_single_list() and like_series() are intended for use with ggrl().

Note

Likelihood is defined up to an arbitrary multiplicative constant. Log-likelihood (also known as support) is defined up to an arbitrary additive constant.

If function loglik() is given a probability vector of length n, the vector must satisfy the unit sum constraint (up to a small tolerance). Also, it must be a named vector with names (collectively) equal to the pnames of argument H.

  > pnames(chess)
  [1] "Topalov" "Anand"   "Karpov"
  > loglik(c(Topalov=0.7,Anand=0.2,Karpov=0.1),chess)
  [1] -69.45364
  > loglik(c(Karpov=0.1,Topalov=0.7,Anand=0.2),chess)  # identical, just a different order
  [1] -69.45364
  

But if given a vector of length n-1 [e.g. the value of indep()], then the names are ignored and the entries are interpreted as the BT strengths of pnames(H)[seq_len(n-1)]:

  > loglik(c(0.7,0.2),chess)
  [1] -69.45364
  > loglik(c(foo=0.7,bar=0.2),chess)  # names are ignored
  [1] -69.45364
  

(the above applies for H a hyper2 or hyper3 object).

Empty brackets are interpreted consistently: that is, zero whatever the probability vector (although the print method is not perfect).

Author

Robin K. S. Hankin

See also

maxp

Examples

data(chess)
loglik(c(1/3,1/3),chess)
#> [1] -60.99695

loglik(rp(14,icons),icons)
#>  [1] -184.3772 -184.3772 -184.3772 -184.3772 -184.3772 -184.3772 -184.3772
#>  [8] -184.3772 -184.3772 -184.3772 -184.3772 -184.3772 -184.3772 -184.3772

if (FALSE)  # takes too long
like_series(masterchef_maxp,masterchef)
like_series(indep(equalp(masterchef)),masterchef)
#> Error in UseMethod("pnames"): no applicable method for 'pnames' applied to an object of class "list"
 # \dontrun{}

W <- hyper2(pnames=letters[1:6])
W1 <- ggrl(W, 'a', letters[2:5],'f')              # 24-element list
W2 <- ggrl(W, c('a','b'), c('c','d'),c('e','f'))  # 2^3=8 element list

like_single_list(rep(1/6,5),W1)      # information from first observation
#> [1] 0.03333333
like_series(rep(1/6,5),list(W1,W2))  # information from both observations
#> [1] -7.901007

# hyper3 objects:
H3 <- ordervec2supp3(letters[c(1,2,3,3,2,1,2)])
loglik(c(a=1,b=2,c=3)/6,H3)
#> [1] -8.805875
loglik(c(a=1,c=3,b=2)/6,H3) # identical
#> [1] -8.805875