Robust Quickest Change Detection in Multi-Stream Non-Stationary Processes

Hoda Bidkhori; Taposh Banerjee; Yingze Hou

REVIEW 3 major objections 5 minor 1 cited by

Robust Quickest Change Detection in Multi-Stream Non-Stationary Processes

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read By designing a multi-stream CUSUM statistic from least favorable laws, the paper proves exact or asymptotic robust optimality for quickest change detection in non-stationary processes with unknown pre- and post-change distributions.

desk verdict A mostly sound single-stream robust QCD story wrapping a multi-stream result that, as printed, has an internal inconsistency in the key sufficient condition; likely fixable, but the theorem needs revision. read the letter →

arxiv 2412.04493 v1 pith:TB6WYIJS submitted 2024-11-27 stat.ME

Yingze Hou , Hoda Bidkhori , Taposh Banerjee This is my paper · ORCID

classification stat.ME MSC 62L1062C20

keywords quickestchangedetectionnon-stationaryprocessesmulti-streamdataleastfavorablelawsrobustoptimalityCUSUMstochasticdominanceGaussianandPoissonmodels

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper studies how to detect an abrupt change as quickly as possible when the data arrive in many independent streams whose distributions drift over time and are never exactly known. The authors propose a least-favorable-law construction: for each stream and time, pick a worst-case pre-change law and a worst-case post-change law, then run a multi-stream CUSUM statistic built from the likelihood ratios between them. They prove that if such least favorable laws exist in a stochastic-dominance sense and every likelihood ratio is continuous and monotone, this single rule is exactly or asymptotically minimax robust optimal: it meets the false-alarm constraint for every possible pre-change law and achieves the smallest worst-case detection delay uniformly over the unknown changed subset of streams. The result matters because the robust rule is a simple recursive CUSUM, unlike computationally heavy generalized-likelihood-ratio or mixture detectors, and the paper exhibits the construction for Gaussian and Poisson families and applies it to COVID-19 infection counts and aircraft approach data.

What carries the argument

The carrying mechanism is the least favorable law (LFL) pair with stochastic boundedness: a pre-change law $\bar{f}_n$ is least favorable if it stochastically dominates every member of the pre-change family, and a post-change law $\bar{g}_{n,\nu}$ is least favorable if every member of the post-change family stochastically dominates it. Because the post-change family depends on the change point $\nu$, this LFL notion is stronger than the classical one. The proof chains a stochastic-dominance comparison lemma through the CUSUM statistic's maximum-and-sum structure: the stopping-time event is a continuous, coordinatewise increasing function of the observations, so replacing true laws by the LFLs only increases the relevant tail probabilities. That yields both the false-alarm guarantee under every pre-change law and the worst-case delay identity that makes the rule minimax optimal.

What would settle it

Run the LFL-based CUSUM on a Gaussian family from Example 1 with several post-change means inside the allowed interval, compare the observed worst-case delay to the delay when the data are exactly at the LFLs; the theorem predicts no interior law is worse, so observing any law whose conditional delay exceeds the LFL delay would disprove the core identity (57) or (69).

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Extended reading notes

Core claim

The central claim is Theorem IV.2: for the robust multi-stream minimax problem (29), if each stream's uncertainty families admit a pair of least favorable laws — pre-LFL $\bar{f}_{\theta,n}$ stochastically dominating every pre-change law and every post-change law $g_{\theta,n,\nu}$ stochastically dominating the post-LFL $\bar{g}_{\theta,n,\nu}$ — and if all likelihood ratios used by the test are continuous and monotone increasing, then the LFL-based CUSUM stopping rule $\tau_{\mathrm{ms}}$ in (33) is exactly or asymptotically robust optimal. The optimality is uniform over every possible changed subset $B \in \mathcal{B}$. Equivalently, the worst-case detection delay over all unknown non-stationary laws is attained when the data actually follow the least favorable pair, and the algorithm designed for that pair cannot be beaten by any other stopping time that meets the same false-alarm constraint. The paper also gives the single-stream version (Theorem III.4) as a special case and identifies least favorable pairs for Gaussian location and Poisson rate families.

Load-bearing premise

The load-bearing premise is that for every stream and time a least-favorable pair exists — a known pre-change law stochastically larger than every pre-change law and a known post-change law stochastically smaller than every post-change law — and that all likelihood ratios in the CUSUM statistic are continuous and monotone increasing; the paper verifies these conditions only for Gaussian and Poisson families.

Editorial extensions

If this is right

Under the LFL conditions, the multi-stream stopping rule $\tau_{\mathrm{ms}}$ in (33) is exactly or asymptotically optimal for the robust minimax problem (29), uniformly over the unknown changed subset $B$.
The robust rule is a recursive CUSUM statistic, so it avoids the computational cost of generalized-likelihood-ratio or mixture detectors in non-stationary multi-stream settings.
With threshold $\log(|\mathcal{B}|/\alpha)$, the mean time to a false alarm is at least $1/\alpha$ under every pre-change law in the family, and the worst-case delay is asymptotically $|\log \alpha|/I_B$, where $I_B$ is the sum of per-stream information numbers.
The single-stream result in Theorem III.4 is the $M=1$ special case, and the case where at most one stream changes yields the simpler rule (34)-(35) that also identifies the affected stream.
The LFL construction is explicit for Gaussian location families and Poisson rate families, which covers the COVID-19 and aircraft-approach demonstrations reported in Section V.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: the same LFL construction should transfer to any exponential-family location or rate family whose likelihood ratios are monotone in the observation, so the Gaussian and Poisson examples are instances of a broader template rather than the whole scope.
Inference: the proof uses independence across streams and across time; whether robust optimality survives short-range dependence, such as Markov or autoregressive streams, remains an open question not addressed by the paper.
Inference: the worst-case-delay identity suggests a conservative design rule — choose LFL parameters at the boundary of the uncertainty class and keep the threshold $\log(|\mathcal{B}|/\alpha)$ — but a misspecified LFL would void the guarantee, which can be checked by simulation before deployment.
Inference: the change-set estimator $\hat{B}$ in (45) is a natural by-product of the stopping rule, yet the paper provides no probabilistic guarantee on correct identification; combining this detector with a misidentification-controlled diagnosis scheme would be a testable next step.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know up front. The single-stream robust QCD result is largely a restatement of the authors' own earlier paper [24], and the genuinely new contribution is the multi-stream extension with per-stream least favorable laws and a robustness reduction theorem. That reduction, Theorem IV.2, is carefully argued and the stochastic dominance proof is sound. But the multi-stream paper has a load-bearing flaw in the sufficient conditions for optimality under the LFLs: Theorem IV.3, condition (39), sums the log-likelihood over all streams while the post-change rate is only over B. Under the LFL model for true subset B, unaffected streams have negative drift, so the probability in (39) goes to 1, not 0. This is internally inconsistent with the paper's own examples (e.g., M=3 with one unaffected stream). As printed, the multi-stream asymptotic robust optimality claim is not established. It looks like a typo: the sum should be over B rather than Theta. With that fix the argument likely goes through, but the current text is wrong.

What the paper does well: the conditional robust optimality framework is clean, the LFL definition sensibly adapts the classical notion to change-point-dependent post-change models, and the Gaussian and Poisson examples verify the conditions. The single-stream proof is a nice, readable exposition of the stochastic dominance step. The real-data applications to COVID and flight data show genuine effort.

Softer spots beyond the typo: the COVID second-wave application estimates the LFL parameters from the same data being monitored, which is pragmatic but undercuts the clean robust guarantee. Exact optimality thresholds are never constructed; the paper relies on asymptotic optimality imported from [14]. The simulations show no error bars or code, so it is hard to judge variability. These are minor relative to the (39) issue.

Who gets value from this: researchers in sequential change detection, particularly those working on robust methods for non-stationary or multi-stream data. The paper deserves a serious referee: the multi-stream problem is worth solving, and the flaw is very likely fixable. I would send it out but demand a corrected condition (39), a re-check of the LFL-optimality premise, and ideally code or tighter numerical evidence before acceptance.

Referee Report

3 major / 5 minor

Summary. The paper studies robust quickest change detection (QCD) for multi-stream non-stationary processes in which both pre-change and post-change distributions are unknown and time-varying. It defines least favorable laws (LFLs) through stochastic boundedness conditions adapted to change-point-dependent post-change models, proposes CUSUM-type statistics based on these LFLs, and proves (in Theorems III.4 and IV.2) that if the proposed rule is optimal or asymptotically optimal under the LFLs, then it is robustly optimal for the original minimax problem. The paper gives Gaussian and Poisson examples where LFLs can be identified and illustrates the tests on simulated data, COVID-19 case counts, and airport flight data. The single-stream treatment is carefully argued, and the stochastic dominance arguments are the right tool for the false-alarm and delay comparisons. However, the multi-stream optimality theorem relies on a sufficient condition in Theorem IV.3 whose printed form is internally inconsistent: Eq. (39) averages log-likelihood ratios over all streams, while the post-change drift is confined to the true subset B. This invalidates the stated verification of the LFL-optimality premise for the multi-stream algorithm.

Significance. If the multi-stream robust optimality claim were established, the paper would be a useful contribution to robust QCD in a practically relevant non-stationary multi-stream setting. The single-stream result and the LFL identification for Gaussian and Poisson families are plausible and potentially transferable. The paper also provides real-data demonstrations, which are valuable for conveying the intended application. That said, the advertised multi-stream contribution is currently not supported because the main sufficient condition (Theorem IV.3, Eq. (39)) fails under the paper's own model, and the exact-optimality branch of Theorem IV.2 requires a threshold construction that is never provided. The strengths of the paper are the clear stochastic-dominance proof technique for the single-stream case and the concrete LFL examples; the weakness is the load-bearing error in the multi-stream asymptotic optimality condition.

major comments (3)

[Theorem IV.3, Eq. (39)] Condition (39) is internally inconsistent with the stated LFL model. Under the LFL post-change law for the true subset B, streams in B have per-unit-time drift I_theta, while streams outside B remain at bar f_theta and contribute negative drift -D(bar f_theta || bar g_theta) (where D(p||q) >= 0 denotes KL divergence). The average in (39) therefore converges almost surely to I_B - sum_{theta notin B} D(bar f_theta || bar g_theta), which is strictly less than I_B whenever M > |B|. For any delta smaller than that gap, the event in (39) has probability tending to 1, not 0, contradicting the required limit. This is not a minor wording issue: it removes the only general sufficient condition that Theorem IV.2 uses to establish the LFL-optimality premise, so the multi-stream asymptotic robust optimality claim is left without a verified instance. The condition should be corrected, presumably by averaging only over theta in B (or by requiring the condition uniformly over B in B), and the Gaussian and Poisson examples in Section V-B should then be checked against the corrected condition.
[Theorem IV.2(b) and Theorem IV.3(2)] Theorem IV.2 part 1 requires thresholds {A_{n,alpha}} with E^{bar F}_infty[tau_ms] = 1/alpha, but Theorem IV.3(2) proposes the threshold log(|B|/alpha) and proves only E^{bar F}_infty[tau_ms] >= 1/alpha. No construction of thresholds attaining equality is given, so the exact-optimality branch of Theorem IV.2 is not realized by the paper's algorithm. The asymptotic branch may not require equality, but the text should separate these two cases explicitly and state which threshold choice supports which claim.
[Section IV-E after Theorem IV.3] The sentence 'All the examples given in Section III-E will work for the multi-stream case as well' is asserted without proof. In particular, the paper does not verify condition (39) (or any corrected version) for the Gaussian and Poisson multi-stream examples used in Section V-B. Since condition (39) is false as printed, the current text does not connect the LFL examples to the multi-stream optimality theorem, and the numerical simulations in Section V-B cannot substitute for that verification.

minor comments (5)

[Definition IV.1] The word 'Defintion' in Definition IV.1 should be 'Definition'.
[Figure 2 caption] The caption contains the typo 'Pittsburgh-Butler Reginal Airport'; it should be 'Regional'.
[Section V-B, Eq. (50)] In the Gaussian multi-stream model of Eq. (50), the parameter condition is written as 'lambda_{theta,n,nu} >= 1.5'; this should be mu_{theta,n,nu} >= 1.5, since lambda is used elsewhere for Poisson rates.
[Section V-A-1 and V-B-2] There are several malformed expressions such as 'Pois(lambda_{1,n}, 1)' and 'g_{theta,n,nu} = Pois(lambda_{theta,n,nu})' in the Poisson multi-stream experiments; the extra '1' and the use of N(.,.) notation for Poisson distributions should be cleaned up.
[Section V-B-3] The threshold is written as log(|B|/alpha) = log(7175 x 10); the notation for alpha in the simulations is not defined consistently with the theoretical alpha in Section IV, and a brief explanation of how alpha=0.1 is chosen would improve reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the robust optimality proof reduces to optimality under externally defined least favorable laws; self-citations are present but not load-bearing. A separate internal inconsistency in Theorem IV.3 condition (39) is flagged as a correctness gap, not circularity.

full rationale

The derivation chain is not circular. The central theorem (Theorem IV.2) takes as its premise that the multi-stream CUSUM rule tau_ms is optimal under the least favorable laws (bar-F, bar-G), and proves via stochastic dominance (Lemma III.3, from Unnikrishnan et al. [26]) and monotone continuous likelihood ratios that the LFL pair is the worst-case law: WADD^{bar-F,bar-G,B}(tau_ms) >= sup_{F in F, G in G} WADD^{F,G,B}(tau_ms). The LFLs are defined externally by stochastic boundedness (Definition IV.1, Eqs. (30)-(31)), not in terms of tau_ms, and their existence is verified independently for Gaussian and Poisson families by monotone likelihood ratio calculations. No fitted parameter is renamed as a prediction; numerical LFL choices in Section V (e.g., Pois(mu+2sigma) for the COVID second-wave analysis) calibrate thresholds from pre-change baseline data rather than predicting the quantity being detected. Self-citations ([16], [24]) appear in the literature review and as citations for sufficient conditions for LFL-optimality, but the robust-optimality proof itself is self-contained and cites external works (Lai [14]; Unnikrishnan et al. [26]); the self-citations are therefore not load-bearing. I separately flag an internal correctness gap, not a circularity: Theorem IV.3(3), condition (39), requires P((1/n) sum_{i=k}^{k+n} sum_{theta in Theta} Zbar_{theta,i,k} <= I_B - delta) -> 0, but under the LFL post-change law only streams in B have positive drift I_theta; streams outside B remain at fbar and contribute negative mean -D(fbar || gbar). Hence the average over all Theta converges almost surely to I_B - sum_{theta not in B} D(fbar_{theta} || gbar_{theta}) < I_B for M > |B|, so the probability in (39) tends to 1, not 0. This makes the printed sufficient condition fail in the paper's own multi-stream examples (Section V-B, M=3 with unaffected streams), so Theorem IV.3 does not establish the LFL-optimality premise of Theorem IV.2 as stated. That is missing support for the theorem, but it is not a self-referential reduction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The theoretical claim rests on least favorable law existence, monotonicity, and imported optimality theorems. No new particles or mediators are introduced. Application demonstrations introduce data-fitted least favorable law parameters, which are listed as free parameters.

free parameters (4)

COVID second-wave pre-LFL parameters Pois(70) and Pois(138) = 70, 138
Estimated from the monitored COVID data as sample mean plus 2 standard deviations over days 56 to 99 in Section V-A2.
COVID second-wave post-LFL parameters Pois(93) and Pois(171) = 93, 171
Chosen as sample mean plus 3 standard deviations from the same data in Section V-A2.
Flight-data LFL means = 0 and 0.5 for N(0,1) and N(0.5,1)
Chosen by hand for the airport demonstration without a specified uncertainty class in Section V-B3.
Simulation thresholds = log(150), log(1000), log(10|Theta|), log(10|B|), log(7175 times 10)
Set to satisfy false alarm constraints in examples; they are not part of the theoretical proof but affect numerical results.

assumptions (6)

domain assumption Observations are independent across time and streams, conditioned on the change point (Eqs. (9) and (24)).
The model excludes autocorrelation and cross-stream dependence beyond the change point.
domain assumption The uncertainty classes {P^{F,theta}_n} and {P^{G,theta}_{n,nu}} are known to the decision maker.
Least favorable laws are defined relative to these classes; Sections III-A and IV-A.
domain assumption All densities in the uncertainty classes are mutually absolutely continuous.
Stated in Section III-C to ensure likelihood ratios are well defined.
ad hoc to paper A least favorable pair exists with stochastic boundedness and monotone increasing continuous likelihood ratios.
This is the main sufficient condition; without it Theorems III.4 and IV.2 do not apply.
standard math Stochastic dominance lemma (Lemma III.3) from [26] holds.
Central tool used in both false alarm and delay parts of the proofs.
standard math The asymptotic optimality conditions in Theorems III.5 and IV.3, imported from [14], [16], and [2], hold for the least favorable laws.
The paper does not prove these; it cites them and uses them to establish optimality under the least favorable laws, which is the premise for robust optimality.

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Cite this review

Pith. "Pith review of Robust Quickest Change Detection in Multi-Stream Non-Stationary Processes." pith.science (2026). https://pith.science/paper/TB6WYIJS

@misc{pith2026241204493,
  author       = {Pith},
  title        = {Pith review of: Robust Quickest Change Detection in Multi-Stream Non-Stationary Processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TB6WYIJS}},
  note         = {Machine review of arXiv:2412.04493}
}

read the original abstract

The problem of robust quickest change detection (QCD) in non-stationary processes under a multi-stream setting is studied. In classical QCD theory, optimal solutions are developed to detect a sudden change in the distribution of stationary data. Most studies have focused on single-stream data. In non-stationary processes, the data distribution both before and after change varies with time and is not precisely known. The multi-dimension data even complicates such issues. It is shown that if the non-stationary family for each dimension or stream has a least favorable law (LFL) or distribution in a well-defined sense, then the algorithm designed using the LFLs is robust optimal. The notion of LFL defined in this work differs from the classical definitions due to the dependence of the post-change model on the change point. Examples of multi-stream non-stationary processes encountered in public health monitoring and aviation applications are provided. Our robust algorithm is applied to simulated and real data to show its effectiveness.

Figures

Figures reproduced from arXiv: 2412.04493 by the authors.

**Figure 2.** Distance measurements and corresponding signals extracted from a database on aircraft trajectories collected from [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Evaluating effectiveness of τss with Gaussian data following (46). [Left] τss with ¯fn = N (1, 1) and g¯n,ν = N (2, 1) tested on three scenarios of {Xn}. [Middle] τss tested on 10 random observations {Xn}. [Right] Non-robust CUSUM test with f = N (0, 1) and g = N (3, 1), tested on 10 LFL observation {Xn} [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: Evaluating effectiveness of τss with Poisson data following (47). [Left] τss with ¯fn = Pois(0.5) and g¯n,ν = Pois(1) tested on three scenarios of {Xn}. [Middle] τss tested on 10 random observations {Xn}. [Right] Non-robust CUSUM test with f = Pois(0.4) and g = Pois(1.…

**Figure 5.** Figure 5: Robust test τss for detecting COVID-19 outbreak in Allegheny County. [Left] Daily increase of confirmed infection cases with Pois(1) noise added. [Middle] For the first-wave detection, τss is designed with pre-LFL being Pois(1) and post-LFL being Pois(2). [Right] For t…

**Figure 6.** Figure 6: Robust test τss for detecting COVID-19 outbreak in St. Louis County. [Left] Daily increase of confirmed infection cases with Pois(1) noise added. [Middle] For the first-wave detection, τss is designed with pre-LFL being Pois(1) and post-LFL being Pois(2). [Right] For t…

**Figure 7.** Figure 7: [Left] Detecting the change in the three experiments using robust algorithm designed using [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

**Figure 8.** Figure 8: [Left] Detecting the change in three experiments using the robust algorithm designed using [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

**Figure 9.** Figure 9: [Left] Detecting change with multi-stream robust statistic [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 10.** Figure 10: [Left] Detecting change time with multi-stream robust statistic [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

**Figure 11.** Figure 11: [Left] Flight signals for the last 100 seconds of 35 randomly chosen aircraft arriving at the Pittsburgh-Bulter [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

**Figure 12.** Figure 12: [Left] Detecting change via multi-stream robust statistic [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]

**Figure 13.** Figure 13: [Upper left] Noisy COVID-19 daily infection of 67 counties in AL. [Upper right] Detecting the earliest onset [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]

**Figure 14.** Figure 14: [Top left] Noisy COVID-19 daily infection of 67 counties in PA. [Top right] Detecting the earliest onset time via [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]

Discussion (0). Continue with ORCID to comment.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Robust Quickest Change Detection with Sampling Control
stat.ME 2024-12 conditional novelty 5.0 of 10

RDE-CUSUM combines robust CUSUM with on-off sampling control to detect distribution changes with unknown post-change laws while skipping a controlled fraction of observations, and is claimed asymptotically robust optimal.

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · cited by 1 Pith paper

[24]

Robust quickest change detection in nonstationary processes,

Y . Hou, Y . Oleyaeimotlagh, R. Mishra, H. Bidkhori, and T. Banerjee, “Robust quickest change detection in nonstationary processes,” Sequential Analysis, vol. 43, no. 3, pp. 275–300, 2024

work page 2024
[14]

Information bounds and quick detection of parameter changes in stochastic systems,

T. L. Lai, “Information bounds and quick detection of parameter changes in stochastic systems,” IEEE Transactions on Information Theory, vol. 44, no. 7, pp. 2917 –2929, Nov. 1998

work page 1998
[1]

V . V . Veeravalli and T. Banerjee, Quickest Change Detection . Academic Press Library in Signal Processing: V olume 3 – Array and Statistical Signal Processing, 2014

work page 2014
[2]

A. G. Tartakovsky, I. V . Nikiforov, and M. Basseville, Sequential Analysis: Hypothesis Testing and Change-Point Detection , ser. Statistics. CRC Press, 2014

work page 2014
[3]

H. V . Poor and O. Hadjiliadis, Quickest detection. Cambridge University Press, 2009

work page 2009
[4]

On optimum methods in quickest detection problems,

A. N. Shiryaev, “On optimum methods in quickest detection problems,” Theory of Probability and Its Applications , vol. 8, pp. 22–46, 1963

work page 1963
[5]

General asymptotic Bayesian theory of quickest change detection,

A. G. Tartakovsky and V . V . Veeravalli, “General asymptotic Bayesian theory of quickest change detection,” Theory of Probability and its Applications, vol. 49, no. 3, pp. 458–497, Sep. 2005

work page 2005
[6]

Tartakovsky, Sequential change detection and hypothesis testing: general non-iid stochastic models and asymptotically optimal rules

A. Tartakovsky, Sequential change detection and hypothesis testing: general non-iid stochastic models and asymptotically optimal rules . CRC Press, 2019

work page 2019

Show all 33 references

[7]

A Bayesian theory of change detection in statistically periodic random processes,

T. Banerjee, P. Gurram, and G. T. Whipps, “A Bayesian theory of change detection in statistically periodic random processes,” IEEE Transactions on Information Theory , vol. 67, no. 4, pp. 2562–2580, 2021

2021
[8]

A bayesian partially observable online change detection approach with thompson sampling,

J. Guo, H. Yan, and C. Zhang, “A bayesian partially observable online change detection approach with thompson sampling,” Technometrics, vol. 65, no. 2, pp. 179–191, 2023

2023
[9]

Bayesian quickest change-point detection with an energy harvesting sensor and asymptotic analysis,

A. Naha and S. Dey, “Bayesian quickest change-point detection with an energy harvesting sensor and asymptotic analysis,” IEEE Transactions on Signal Processing, 2024

2024
[10]

Optimal detection of a change in distribution,

M. Pollak, “Optimal detection of a change in distribution,” Annals of Statistics , vol. 13, no. 1, pp. 206–227, Mar. 1985

1985
[11]

Procedures for reacting to a change in distribution,

G. Lorden, “Procedures for reacting to a change in distribution,” Annals of Mathematical Statistics , vol. 42, no. 6, pp. 1897–1908, Dec. 1971

1908
[12]

Continuous inspection schemes,

E. S. Page, “Continuous inspection schemes,” Biometrika, vol. 41, no. 1/2, pp. 100–115, Jun. 1954

1954
[13]

Optimal stopping times for detecting changes in distributions,

G. V . Moustakides, “Optimal stopping times for detecting changes in distributions,” Annals of Statistics, vol. 14, no. 4, pp. 1379–1387, Dec. 1986

1986
[15]

Quickest change detection with non-stationary post-change observations,

Y . Liang, A. G. Tartakovsky, and V . V . Veeravalli, “Quickest change detection with non-stationary post-change observations,” IEEE Transactions on Information Theory , vol. 69, no. 5, pp. 3400–3414, 2022

2022
[16]

Modeling and quickest detection of a rapidly approaching object,

T. Brucks, T. Banerjee, and R. Mishra, “Modeling and quickest detection of a rapidly approaching object,” Sequential Analysis, vol. 42, no. 4, pp. 387–403, 2023

2023
[17]

Sequential multi-sensor change-point detection,

Y . Xie and D. Siegmund, “Sequential multi-sensor change-point detection,” THE ANNALS of STATISTICS , pp. 670–692, 2013

2013
[18]

Large-scale multi-stream quickest change detection via shrinkage post-change estimation,

Y . Wang and Y . Mei, “Large-scale multi-stream quickest change detection via shrinkage post-change estimation,”IEEE Transactions on Information Theory, vol. 61, no. 12, pp. 6926–6938, 2015. 25

2015
[19]

Multistream quickest change detection: Asymptotic optimality under a sparse signal,

G. Fellouris, G. V . Moustakides, and V . V . Veeravalli, “Multistream quickest change detection: Asymptotic optimality under a sparse signal,” in 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) . IEEE, 2017, pp. 6444–6447

2017
[20]

Optimum multi-stream sequential change-point detection with sampling control,

Q. Xu, Y . Mei, and G. V . Moustakides, “Optimum multi-stream sequential change-point detection with sampling control,” IEEE Transactions on Information Theory, vol. 67, no. 11, pp. 7627–7636, 2021

2021
[21]

Multi-stream quickest detection with unknown post-change parameters under sampling control,

Q. Xu and Y . Mei, “Multi-stream quickest detection with unknown post-change parameters under sampling control,” in 2021 IEEE International Symposium on Information Theory (ISIT) . IEEE, 2021, pp. 112–117

2021
[22]

Active quickest detection when monitoring multi-streams with two affected streams,

——, “Active quickest detection when monitoring multi-streams with two affected streams,” in 2022 IEEE International Symposium on Information Theory (ISIT). IEEE, 2022, pp. 1915–1920

2022
[23]

Quickest change detection in statistically periodic processes with unknown post-change distribution,

Y . Oleyaeimotlagh, T. Banerjee, A. Taha, and E. John, “Quickest change detection in statistically periodic processes with unknown post-change distribution,” Sequential Analysis, vol. 42, no. 4, p. 404–437, 2023

2023
[25]

TrajAir: A General Aviation Trajectory Dataset,

J. Patrikar, B. Moon, S. Ghosh, J. Oh, and S. Scherer, “TrajAir: A General Aviation Trajectory Dataset,” 6 2021. [Online]. Available: https://kilthub.cmu.edu/articles/dataset/TrajAir A General Aviation Trajectory Dataset/14866251

2021
[26]

Minimax robust quickest change detection,

J. Unnikrishnan, V . V . Veeravalli, and S. P. Meyn, “Minimax robust quickest change detection,” IEEE Transactions on Information Theory , vol. 57, no. 3, pp. 1604 –1614, Mar. 2011

2011
[27]

A binning approach to quickest change detection with unknown post-change distribution,

T. S. Lau, W. P. Tay, and V . V . Veeravalli, “A binning approach to quickest change detection with unknown post-change distribution,” IEEE Transactions on Signal Processing , vol. 67, no. 3, pp. 609–621, 2018

2018
[28]

Average run lengths of an optimal method of detecting a change in distribution,

M. Pollak, “Average run lengths of an optimal method of detecting a change in distribution,” Annals of Statistics , vol. 15, no. 2, pp. 749–779, Jun. 1987

1987
[29]

Algorithms for change detection with sparse signals,

A. Jain, P. Sarvepalli, S. Bhashyam, and A. P. Kannu, “Algorithms for change detection with sparse signals,” IEEE Transactions on Signal Processing, vol. 68, pp. 1331–1345, 2020

2020
[30]

Minimax robust quickest change detection in systems and signals with unknown transients,

T. L. Molloy and J. J. Ford, “Minimax robust quickest change detection in systems and signals with unknown transients,” IEEE Transactions on Automatic Control, vol. 64, no. 7, pp. 2976–2982, 2018

2018
[31]

Minimax asymptotically optimal quickest change detection for statistically periodic data,

T. Banerjee, P. Gurram, and G. Whipps, “Minimax asymptotically optimal quickest change detection for statistically periodic data,” Signal Processing, vol. 215, p. 109290, 2024

2024
[32]

Krishnamurthy, Partially Observed Markov Decision Processes

V . Krishnamurthy, Partially Observed Markov Decision Processes . Cambridge University Press, 2016

2016
[33]

Worst-case misidentification control in sequential change diagnosis using the min-cusum,

A. Warner and G. Fellouris, “Worst-case misidentification control in sequential change diagnosis using the min-cusum,” IEEE Transactions on Information Theory, 2024

2024

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [24]

Robust quickest change detection in nonstationary processes,

Y . Hou, Y . Oleyaeimotlagh, R. Mishra, H. Bidkhori, and T. Banerjee, “Robust quickest change detection in nonstationary processes,” Sequential Analysis, vol. 43, no. 3, pp. 275–300, 2024

work page 2024

[2] [14]

Information bounds and quick detection of parameter changes in stochastic systems,

T. L. Lai, “Information bounds and quick detection of parameter changes in stochastic systems,” IEEE Transactions on Information Theory, vol. 44, no. 7, pp. 2917 –2929, Nov. 1998

work page 1998

[3] [1]

V . V . Veeravalli and T. Banerjee, Quickest Change Detection . Academic Press Library in Signal Processing: V olume 3 – Array and Statistical Signal Processing, 2014

work page 2014

[4] [2]

A. G. Tartakovsky, I. V . Nikiforov, and M. Basseville, Sequential Analysis: Hypothesis Testing and Change-Point Detection , ser. Statistics. CRC Press, 2014

work page 2014

[5] [3]

H. V . Poor and O. Hadjiliadis, Quickest detection. Cambridge University Press, 2009

work page 2009

[6] [4]

On optimum methods in quickest detection problems,

A. N. Shiryaev, “On optimum methods in quickest detection problems,” Theory of Probability and Its Applications , vol. 8, pp. 22–46, 1963

work page 1963

[7] [5]

General asymptotic Bayesian theory of quickest change detection,

A. G. Tartakovsky and V . V . Veeravalli, “General asymptotic Bayesian theory of quickest change detection,” Theory of Probability and its Applications, vol. 49, no. 3, pp. 458–497, Sep. 2005

work page 2005

[8] [6]

Tartakovsky, Sequential change detection and hypothesis testing: general non-iid stochastic models and asymptotically optimal rules

A. Tartakovsky, Sequential change detection and hypothesis testing: general non-iid stochastic models and asymptotically optimal rules . CRC Press, 2019

work page 2019