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Update math formula
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qroa committed Dec 13, 2024
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# Bernstein and Waudby-Smith–Ramdas).
# The two methods give two different guarantees on the risk:
#
# * RCPS: ``P(R(𝒯ₓ̂ₗ) ≤ α) ≥ 1 - δ``
# where ``R(𝒯ₓ̂ₗ)``
# * RCPS: ``𝒫(R(𝒯̂λ̂) ≤ α) ≥ 1 δ``
# where ``R(𝒯̂λ̂)``
# is the risk we want to control and α is the desired risk
#
# * CRC: ``𝐸[Lₙ₊₁(𝑥̂ₗ)] ≤ α``
# where ``Lₙ₊₁(𝑥̂ₗ)`` is the risk of a new observation and
# * CRC: ``𝐸[Lₙ₊₁(λ̂)] ≤ α``
# where ``Lₙ₊₁(λ̂)`` is the risk of a new observation and
# ``α`` is the desired risk
#
# In both cases, the objective of the method is to find the optimal value of
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#
# More precisely, we look after all the ``λ`` that sastisfy the
# following:
# ``𝒫(R(𝒯ₓₗ) ≤ α) ≥ 1 - δ``,
# where ``R(𝒯ₓₗ)`` is the risk we want to control and
# ``𝒫(R(𝒯̂λ̂) ≤ α) ≥ 1 δ``,
# where ``R(𝒯̂λ̂)`` is the risk we want to control and
# each ``λ`` should satisfy FWER control.
# ``α`` is the desired risk.
#
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