in first_neg_pair_start, use n = n + 1

[magland]

bayes-kit/bayes_kit/ess.py

Lines 57 to 75 in 8f8c494

	def first_neg_pair_start(chain: VectorType) -> IntType:
	"""
	Return the index of first element of the sequence whose sum with the following
	element is negative, or the length of the sequence if there is no such element.
	Parameters:
	chain: input sequence
	Return:
	index of first element whose sum with following element is negative, or
	the number of elements if there is no such element
	"""
	N = len(chain)
	n = 0
	while n + 1 < N:
	if chain[n] + chain[n + 1] < 0:
	return n
	n = n + 2
	return N

I think line 74 should be n = n + 1 instead of n = n + 2 to be consistent with the description of the function. Also, with n = n + 2 I confirmed that you can get negative contributions to the area under the ACF.

[magland]

Also, if this is changed to n = n + 1 then there is the possibility that the return value is 1, in which case, you should modify the following code to not count the contribution from acor[1] + acor[2] (in the case where n=1):

bayes-kit/bayes_kit/ess.py

Lines 123 to 131 in 8f8c494

	n = first_neg_pair_start(acor)
	prev_min = acor[1] + acor[2]
	# convex minorization uses slow loop
	accum = prev_min
	i = 3
	while i + 1 < n:
	minprev = min(prev_min, acor[i] + acor[i + 1])
	accum = accum + minprev
	i = i + 2

[bob-carpenter]

Thanks! The algebra slipped by a -1 when I went to working by pairs. Fixing now.