🎰 Sequential Settings

Sequential Settings#

Decision problems where data arrive over time and choices adapt as evidence accrues.

Important

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What it is#

A sequential setting is any framework where data arrives over time and you can make decisions — stop or continue, accept or reject, reallocate traffic — as the data accumulates, rather than only at a single fixed end point. It is the opposite of a fixed-horizon design, where you pre-commit a sample size and analyse once at the end.

What makes it different#

Data comes one observation (or small batch) at a time, decisions can be adaptive, and — crucially — naive repeated testing inflates the Type I error rate: every time you “peek” at a frequentist p-value and consider stopping, you get extra chances to hit significance by chance. Sequential settings therefore demand specialised methods.

Where it shows up#

Clinical trials — interim analyses with stopping rules for efficacy, harm or futility (continuing a harmful treatment is unethical).
A/B testing — users arrive over time and teams want to peek mid-experiment; valid sequential methods let them.
Online learning / bandits — algorithms learn as data streams, shifting traffic to better variants.

The three families of methods#

Frequentist — the SPRT (sequential probability ratio test) checks a likelihood ratio continuously; group-sequential designs (O’Brien–Fleming, Pocock) analyse at pre-planned checkpoints with α-spending to keep the overall error controlled.
Bayesian — naturally sequential: the posterior updates continuously as data arrive, and you stop when a posterior probability crosses a threshold (say \(\Pr(\text{uplift} > 0) > 0.95\)), with no peeking penalty.
Adaptive / online — multi-armed bandits (\(\epsilon\)-greedy, Thompson sampling) and reinforcement learning, built for sequential decisions.

Why it matters#

Stopping early saves time and cost, avoids ethically continuing a clearly harmful trial, lets businesses adapt quickly, and matches how many ML algorithms actually receive data — provided the right method preserves statistical validity.

Theme: Sequential Methods & Bandits · All terminology

Hint

Mind map — connected ideas

Bayesian Sequential Testing · Traditional A/B Test (Fixed-Horizon A/B Test) · Thompson Sampling (TS) in Bandits (Multi-Armed Bandit Problem (MAB)) · A/B Testing · Frequentist · Bayesian Stopping Rules

Hint

More in Sequential Methods & Bandits

Bandit Algorithms · O’Brien–Fleming (OBF) Method · Pocock Method · Sequential Probability Ratio Test (SPRT) · Thompson Sampling (TS) in Bandits (Multi-Armed Bandit Problem (MAB))