Approach summary:For streaming daily p-values we should use an online FDR procedure (BH is batch) — practical choices are alpha-investing / LORD / SAFFRON which control FDR sequentially without storing all past p-values. I'll sketch a simple LORD-style algorithm (allocates significance levels over time based on past rejections) plus notes on data structures, cost, and practical integration.Pseudocode (python-like):python
# LORD-lite: allocate alpha_t each test based on initial wealth w0 and rejections
def init(alpha=0.05, w0=0.05, gamma_seq=None):
# gamma_seq: precomputed non-increasing sequence summing to 1, e.g., gamma_t ~ C / t^1.6
return {"alpha": alpha, "w": w0, "gamma": gamma_seq, "t": 0, "R": 0}
def next_threshold(state):
state["t"] += 1
t = state["t"]
# base allocation scaled by remaining wealth
alloc = state["alpha"] * state["gamma"][t-1]
# use min(alloc, current wealth)
thresh = min(alloc, state["w"])
return thresh
def process_pvalue(state, p):
thresh = next_threshold(state)
reject = p <= thresh
if reject:
# reward: increase wealth by fixed amount (here thresh)
state["w"] += state["alpha"] * state["gamma"][state["t"]-1]
state["R"] += 1
else:
# spend the threshold
state["w"] -= thresh
# prevent negative wealth
state["w"] = max(state["w"], 0.0)
return reject, thresh
