 Solution

ID: past-exam-of-the-simulation-and-statistical-programming-course-of-the-university-of-oxford/2023/3/c/iii/solution

Σ = L L^{T}

. If

B = L^{- 1}

, reversal of factors in a matrix inverse gives

Σ^{- 1} = (L^{T})^{- 1} L^{- 1} = B^{T} B .

Hence the required R implementation is

invsigma <- function(sigma) {
  L <- mychol(sigma)
  B <- ltinv(L)
  crossprod(B)
}

Here crossprod(B) computes

B^{T} B

. Using tcrossprod(B) would compute

B B^{T}

, which generally differs from

Σ^{- 1}

. Both helper functions preserve the one-by-one matrix case.

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