eqValBound
and withReplaceBound
find a pvalue by
changing the original constraint (that the total difference is greater than the margin),
instead placing a restriction on the
number of batches with error no larger than t
.
eqValBound
finds an exact solution with this restriction,
whereas withReplaceBound
finds a more conservative bound.
See Stark for more details about withReplaceBound
.
1 2 3 4 5 6  eqValBound(Z, t = NULL, asTaint = FALSE, asNumber = FALSE,
M = NULL, takeOutZeroMMB=TRUE, bound.col = "e.max",
calc.e_p=calc.pairwise.e_p, w_p = weight.function("no.weight"))
withReplaceBound(Z, t = NULL, asTaint = FALSE, asNumber = FALSE,
M = NULL, takeOutZeroMMB = TRUE, bound.col = "e.max",
calc.e_p=calc.pairwise.e_p, w_p = weight.function("no.weight"))

Z 
A 
t 
Value of the observed maximum, either as the MRO, as taint, or as the overstatement of the margin in votes. 
asTaint 
Set 
asNumber 
Set 
M 
A priori margin. If NULL, 
takeOutZeroMMB 
Setting 
bound.col, calc.e_p, w_p 
Arguments used to compute

Mike Higgins, Hua Yang
P.B. Stark. Conservative Statistical PostElection Audits. Annals of Applied Statistics, 2:2. 550581.
See LKPBound
for finding a pvalue through a continuous relaxation.
See BaB
for finding an exact pvalue
through solving a 01 knapsack problem.
See compute.stark.t
for computing t
through audit data.
1 2 3 4  data(MN_Senate_2006)
eqValBound(MN_Senate_2006.strat, takeOutZeroMMB = FALSE)
withReplaceBound(MN_Senate_2006.strat, t = 2, asNumber = TRUE,
takeOutZeroMMB = FALSE)

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