{"id":"eac64840-0693-4e56-bf84-88bf97dfabec","arxiv_id":"2607.15157","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A Bayesian spike-and-slab frequency-selection method with a refined grid and hierarchical multivariate extension recovers oscillatory components from wearable time series.","lead":"This paper builds a Bayesian spike-and-slab method that automatically picks which frequencies in a time series matter, using a dense frequency grid to estimate rhythms precisely. It applies the method to wearable actigraphy and skin-temperature signals, finding circadian and ultradian rhythms that are shared or distinct across signals.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (5) appears to omit the proposal density and move-probability ratio, so the sampler's invariance is unproven and all posterior summaries rest on an incomplete MCMC specification.","rationale":"The paper is a serious attempt at a useful methodology: the spike-and-slab spectral model, the minimum-separation constraint, and the conjugate updates are standard, the simulation studies are extensive, and the supplementary material includes misspecification checks, sensitivity analyses, and a link to Julia code. My concern is not with the model or the applications but with the written sampler. Eq. (5) is the only acceptance probability supplied for the joint add/delete update, and it is written as a ratio of target terms with no proposal density for beta_prop and no move-selection probabilities. The text attempts to justify validity by claiming irreducibility and then 'Hence, the sampler is valid and converges,' but irreducibility alone is insufficient; detailed balance is required. If the implemented code contains the omitted terms, this is a presentation error that a corrected Eq. (5) would fix, and the conditional verdict stands. If the code matches Eq. (5), every posterior summary in Sections 4 and 5 is not a posterior summary, and the central claim collapses. This is the single most load-bearing assumption, and I agree with the reader's identification of sampler validity as the weakest point. The reader's other concerns, such as the comparison grid and clinical language, are real but secondary; the sampler issue is the one that must be settled first.","tokens_in":28159,"tokens_out":13207,"duration_ms":125647,"concrete_test":"Download the released Julia code (github.com/Beniamino92/BayesFreqSelect). Construct a small enumerable case: T=64, a candidate grid of 20 frequencies, d=2, one true sinusoid, with the paper's hyperparameters (sigma2_beta=10, a=1, b=10). Enumerate all valid z vectors and compute exact posterior inclusion probabilities via the conjugate Normal/inverse-gamma marginal likelihood, without MCMC. Run the published sampler on the same data for 100,000 iterations (50,000 burn-in) and compare MCMC PPIs to the exact PPIs. If the differences exceed roughly two Monte Carlo standard errors, or if the code's acceptance ratio omits the q(beta_prop|...) term from Eq. (6), then the sampler is not targeting the posterior in Eq. (4) and the reported posterior summaries are not posterior quantities.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 defines a Metropolis-within-Gibbs sampler and gives Eq. (5) as the acceptance probability for adding a frequency. As written, Eq. (5) is a ratio of unnormalized posterior terms only: p(y|z_prop, beta_prop) p(z_prop_j) prod_i p(beta_prop_ji | z_prop_j) in the numerator and p(y|z_curr, beta_curr) p(z_curr_j) in the denominator. But beta_prop is not drawn from the target; it is proposed from the conjugate conditional Normal in Eq. (6). A valid MH ratio must include that proposal density and the reverse move-probability ratio. The text asserts that the chain is irreducible and therefore 'the sampler is valid and converges to the correct target distribution,' but irreducibility alone does not imply detailed balance. Because Eq. (5) is the only acceptance formula supplied, and because every reported PPI, power estimate, and model-size posterior in Sections 4 and 5 is a summary of this chain, an incorrect acceptance function would invalidate the central empirical claim. This is the most load-bearing concern: the applications are only as credible as the posterior they estimate.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes spectralSS, a Bayesian spike-and-slab method for selecting oscillatory components in time series. The model places a spike-and-slab prior on paired sine/cosine Fourier coefficients, enforces a minimum-separation constraint in the prior, and uses a refined grid of candidate frequencies to improve resolution. Inference is carried out with a Metropolis-within-Gibbs sampler using add/delete/swap moves, and posterior inclusion probabilities are used to select frequencies. The framework is extended to multivariate series through a Dirichlet prior over joint inclusion patterns. The paper reports extensive simulations, comparisons with Lasso/EN/SCAD/MCP, and two wearable-data applications. The central claim is that spectralSS recovers the true set of frequencies more accurately and parsimoniously than penalized alternatives and that the multivariate extension identifies shared and component-specific rhythms.","tokens_in":28470,"tokens_out":9862,"duration_ms":112980,"significance":"The modeling framework is attractive and likely useful for chronobiology and wearable-device data. It provides a transparent generative model, explicit uncertainty quantification for selected frequencies, and a flexible multivariate extension. The simulation suite is broad — including closely spaced frequencies, model misspecification, heavy-tailed errors, and correlated bivariate errors — and the authors provide code. However, the manuscript's central empirical claims are currently not fully supported: the only explicit Metropolis–Hastings acceptance formula appears incomplete, the headline comparison confounds the selection mechanism with grid resolution, and the frequency-error metrics are aggregate sums that can mask large per-frequency errors. If these issues are addressed, the paper would be a useful contribution to Bayesian spectral analysis and digital-health applications.","major_comments":[{"comment":"The acceptance probability for the add move is incomplete. β_j^prop is said to be sampled from the conjugate Normal posterior in Eq. (6), but Eq. (5) contains no proposal density q(β_j^prop | z_prop, …) and no ratio of add/delete move probabilities. A valid Metropolis–Hastings ratio for this transdimensional move must include these terms; the denominator should also contain p(β_curr | z_curr) if the joint posterior in Eq. (4) is the target. The assertion that irreducibility implies correctness is not sufficient: irreducibility alone does not imply that the chain has the intended stationary distribution unless detailed balance (or an equivalent stationarity condition) holds. Since every posterior inclusion probability, power estimate, and model-size posterior in Sections 4 and 5 is averaged over this chain, this is a load-bearing issue. The same omission appears in the multivariate accept","section":"Section 3, Eq. (5)"},{"comment":"The comparison between spectralSS and the penalized baselines is not on an equal footing. The paper states that spectralLASSO/EN/SCAD/MCP 'operate on the same set of Fourier frequencies,' while spectralSS is evaluated on a refined grid with Δω = 0.0001 and L = 5000 candidates. In the simulation of Section 4.1, the true frequencies 1/67, 1/21, and 1/13 are not exactly on the 512-point Fourier grid, so a large portion of the reported AE_F advantage for spectralSS is simply the benefit of being able to place a candidate at (or very near) the true frequency. To support the 'superior performance' claim, either give all methods the same refined grid, or additionally report spectralSS on the Fourier grid, or compare using a nearest-grid baseline. Otherwise the comparison conflates grid resolution with the statistical selection mechanism.","section":"Sections 4.1.1 and 4.1.2"},{"comment":"The two error metrics used in the headline comparisons are aggregate sums: AE_F = |∑_j ω_j − ∑_j ω̂_j| and AE_P = |∑_j P(ω_j) − ∑_j P̂(ω_j)|. These are not per-frequency matching errors. A model that selects a completely wrong set of frequencies can have a small AE_F if the selected frequencies straddle the true ones so that the sums nearly cancel. The metrics also do not define how to handle unequal model sizes. This affects Figures 2 and S1 and the corresponding claims about 'accuracy in frequency estimation.' Please replace these with matching-based metrics (e.g., nearest-neighbor assignment, Hungarian matching, or a comparable F-measure) and report per-frequency power errors under the same matching.","section":"Section 4.1.1, AE_F and AE_P definitions"},{"comment":"The penalized baselines are implemented with glmnet and ncvreg, but the paper does not state how the tuning parameter λ is selected. The number of frequencies selected by Lasso, EN, SCAD, and MCP depends critically on λ; without a reproducible selection rule (cross-validation, BIC, oracle, or a path summary), the claims that EN/LASSO select hundreds of frequencies and are less parsimonious than spectralSS are not reproducible. The real-data claim that spectralLASSO selects on average 322 frequencies and spectralEN 353 frequencies across six subjects needs the same clarification. Please specify the tuning procedure and provide sensitivity of the sparsity comparison to it.","section":"Sections 4.1.1 and 5.1.3"}],"minor_comments":[{"comment":"The notation M_max is imported from the Fourier-frequency setup of Section 2.1 but is then used for the dense grid of Section 2.1.1; L is not defined in Eq. (3). Please define the candidate set once and use consistent notation.","section":"Section 2.2, Eqs. (2)–(3)"},{"comment":"Typo 'PPI ¿ 0.5' should be 'PPI > 0.5'.","section":"Section 4.1"},{"comment":"The labels '(c) PPI (dim 2)' and '(d) PPI (dim 2)' appear to be duplicated; one panel should refer to dimension 1 and the other to dimension 2.","section":"Figure 3"},{"comment":"The text says 'we selected a grid of Fourier frequencies' but the method in Section 2.1.1 uses a refined grid; please clarify whether the real-data grid is the standard Fourier grid or a finer grid, and report its spacing.","section":"Section 5.1.2"},{"comment":"Minor wording: 'a more stricter rule' should be 'a more stringent rule.'","section":"Section 3.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is in scope and likely salvageable, but the missing proposal terms in Eq. (5) are serious: if the implemented sampler is exactly as written, the posterior summaries may not target the stated posterior. Please ask the authors to provide a full derivation of the MH acceptance probabilities and, ideally, to validate the sampler against a known benchmark or an independent implementation. The comparison study should also be redone on a common grid with matching-based metrics. I do not see grounds for rejection, but the central empirical claims need to be re-established after these fixes."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper is a workmanlike contribution to Bayesian spectral analysis. The new part is the multivariate extension — a hierarchical Dirichlet prior over joint inclusion patterns that lets the model learn shared versus component-specific frequencies — plus the use of a dense frequency grid with a minimum-separation constraint. The univariate spike-and-slab on Fourier coefficients is not novel, but the combination is sensible and the simulations are extensive, including misspecification, correlated errors, and closely spaced frequencies. There is also a code link, which deserves credit.\n\nThe soft spots are real, but they are fixable. The largest is Eq. (5). As written, the acceptance ratio for adding a frequency contains only posterior terms; there is no proposal density and no reverse-move probability. If that is all the sampler is doing, detailed balance is not established, and every posterior inclusion probability in the paper rests on an unverified MCMC specification. Perhaps the intended ratio from Savitsky et al. includes the conditional posterior proposal and simplifies, but the text does not show it. This is a load-bearing presentation error that needs a correction, not necessarily a flaw in the underlying algorithm.\n\nThe second soft spot is the comparison in Section 4.1.1. spectralSS is run on a refined grid with about 10,000 candidate frequencies, while the penalized baselines are restricted to the Fourier grid (around 250 candidates). That is not a fair test, and it inflates the apparent advantage. The baselines should be run on the same refined grid.\n\nMinor points: the clinical claims in the epilepsy application are exploratory — the sample is six individuals, and the \"clinically relevant\" language overreaches. The sensitivity analysis for the sparsity hyperparameter b is helpful, and the Discussion appropriately notes the limitations of the fixed separation parameter and the exponential cost in multivariate dimension.\n\nAll in all, the paper deserves a serious referee. The core method is plausible, the simulations are thorough, and the multivariate coupling idea is worth discussing. I would send it to review, but with a clear request to rewrite Eq. (5) with all proposal terms, rerun the benchmark on the fine grid, and tone down the clinical claims.","headline":"Useful Bayesian frequency-selection method with a solid simulation study and a real multivariate twist, but the MCMC acceptance probability as written is incomplete and the main comparison is unfairly stacked.","tokens_in":28931,"tokens_out":2938,"would_cite":true,"duration_ms":112699,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","62M10","62P10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A Bayesian spike-and-slab prior over Fourier coefficients can select true periodicities from dense frequency grids while remaining sparse enough for wearable-device time series.","keywords":["Bayesian frequency selection","spike-and-slab prior","spectral analysis","time series","multivariate spectral modeling","wearable actigraphy","circadian rhythms","stochastic search MCMC"],"falsifier":"Take a short time series with a small number of candidate frequencies, enumerate the exact posterior over inclusion configurations (small enough to compute directly), then compare it with the empirical inclusion frequencies from the MCMC sampler; any systematic discrepancy would indicate the sampler is not targeting the stated posterior. Alternatively, simulate two frequencies separated by less than d times the grid spacing and check whether the procedure ever places posterior mass on both, revealing how the separation constraint rather than the data governs resolution.","tokens_in":28032,"feed_emoji":"📈","tokens_out":4171,"duration_ms":47504,"temperature":0.7,"pith_summary":"The paper introduces spectralSS, a Bayesian method that treats a time series as a sum of sines and cosines at many candidate frequencies and uses a spike-and-slab prior to decide which frequencies are actually present. It claims this approach recovers the true number, locations, and power of oscillatory components more accurately and more parsimoniously than penalized alternatives like LASSO, Elastic Net, SCAD, and MCP, especially when the candidate grid is finer than the classical Fourier grid. For multivariate signals, a hierarchical prior over joint inclusion patterns lets the model learn which rhythms are shared across series and which are component-specific. Applied to wrist actigraphy from people with partial-onset seizures, the univariate model finds circadian and ultradian rhythms; applied jointly to activity and skin temperature, the multivariate model finds overlapping components consistent with physiological coupling. A sympathetic reader would care because automatic, quantified selection of periodicities is a bottleneck in chronobiology and wearable-device monitoring.","feed_headline":"A spike-and-slab prior recovers true signal frequencies","feed_subtitle":"Selection stays sparse and beats LASSO-style penalties while finding shared rhythms across wearable signals.","key_machinery":"The load-bearing object is the bivariate spike-and-slab prior on each frequency's sine-cosine coefficient pair, together with the minimum-separation constraint that gives zero prior mass to configurations with two active frequencies closer than d grid bins. The refined frequency grid (spacing smaller than the standard Fourier spacing) is what buys resolution beyond Fourier bins. The sampler couples these pieces: add/delete/swap proposals are restricted to valid configurations, coefficients are drawn from the conjugate Gaussian conditional, and the multivariate version places a Dirichlet prior over joint inclusion patterns so that shared rhythms are encouraged only when the data support them.","core_discovery":"The central discovery is that frequency selection can be formulated as a sparse regression problem over a dense grid of candidate frequencies and solved with a structured spike-and-slab prior. Each candidate frequency has two coefficients (sine and cosine) that are included or excluded jointly through a latent indicator; a minimum-separation constraint embedded in the prior forbids nearby active frequencies, which keeps the selected set parsimonious and identifiable. A Metropolis-within-Gibbs sampler with add/delete/swap moves explores the posterior, and posterior inclusion probabilities quantify each frequency's relevance. In simulations the method identifies the true frequencies and their","pith_inferences":["The minimum-separation distance d acts as a resolution parameter; treating it as random would require handling a combinatorial normalizing constant, so a systematic sensitivity analysis over d, as the paper's simulations partially provide, is the practical way to learn how many distinct rhythms the data can actually support.","Because the multivariate sampler evaluates likelihood ratios only for affected components, the machinery could scale beyond two channels if the joint inclusion-pattern prior were compressed; as written, the 2^D configuration space is the main bottleneck.","The line-spectrum model is a deliberate simplification, so on broad-band or non-stationary signals the method will interpret spectral mass as discrete peaks; it may be best used as a screening tool before smooth-spectrum or time-varying spectral analysis.","The real-data results generate testable clinical hypotheses, such as whether ultradian components near 8 or 12 hours differ systematically across epilepsy patients or track seizure frequency; these could be checked in larger cohorts.","The paper's mechanism for selecting frequencies, if valid, could be adapted to other settings where a sparse set of sinusoidal components is sought, such as detecting oscillatory structure in neural, financial, or environmental time series."],"forward_implications":["If the central claim holds, researchers can replace manual periodogram peak-picking with automatically selected frequencies that come with posterior probabilities of inclusion.","A dense grid rather than the standard Fourier grid becomes a practical default, since the paper shows the extra computational cost buys better frequency localization and power estimates.","Joint modeling of multiple wearable signals can separate rhythms that are genuinely shared across modalities from those specific to one signal, useful for connecting thermoregulation, activity, and other physiological rhythms.","The method offers a parsimony check on penalized alternatives: in the real actigraphy data, LASSO and Elastic Net selected hundreds of frequencies while spectralSS selected a handful of interpretable components.","Frequency-specific inclusion probabilities and the posterior distribution over model size give a principled, interpretable measure of uncertainty about which periodicities matter."],"fun_headline_variants":["Spike-and-slab prior exposes true frequencies in wearables","Bayesian search filters noise to find real rhythms","Sparse spectral model reveals shared rhythms across sensors","Posterior probability flags key frequencies in time series"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The stochastic-search MCMC is assumed to converge to the correct constrained posterior, but the paper asserts irreducibility without proof and the acceptance ratio in Eq. (5) is written without explicit proposal or Jacobian terms; if the chain does not mix over the dense candidate grid, every posterior inclusion probability and power estimate is unreliable.","fun_headline_variants_meta":{"raw":{"variants":["Spike-and-slab prior exposes true frequencies in wearables","Bayesian search filters noise to find real rhythms","Sparse spectral model reveals shared rhythms across sensors","Posterior probability flags key frequencies in time series"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1236,"prompt_tokens":700,"completion_tokens":536,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":444,"completion_tokens_details":{"reasoning_tokens":486}},"tokens_in":444,"tokens_out":536,"duration_ms":5815,"temperature":1.0,"reasoning_tokens":486,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T23:58:04.211209+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a short time series with a small number of candidate frequencies, enumerate the exact posterior over inclusion configurations (small enough to compute directly), then compare it with the empirical inclusion frequencies from the MCMC sampler; any systematic discrepancy would indicate the sampler is not targeting the stated posterior. Alternatively, simulate two frequencies separated by less than d times the grid spacing and check whether the procedure ever places posterior mass on both, revealing how the separation constraint rather than the data governs resolution.","supporting_citations":[],"review_version":1}