{"id":"9dea11d2-862a-4c46-8bce-fed3eccda13e","arxiv_id":"2607.02173","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Weighted tilted conformal Bayes restores marginal coverage with smaller sets than weighted source-score calibration in synthetic experiments for two-sided censored Gaussian models under label shift.","lead":"The paper develops conformal Bayes for two-sided censored Gaussian regression under label shift by combining posterior predictive tilting with weighted conformal calibration to produce mixed highest density regions. A smart generalist might read it to understand how to handle boundary atoms and interior densities when data is censored and distributions shift between training and test sets.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader correctly flagged the latent-to-observed weight mapping as the pivotal step; the description supplies no evidence that this mapping fails, so the empirical claim stands on its stated terms. Full-text availability does not alter the absence of an identifiable load-bearing flaw.","tokens_in":1769,"tokens_out":258,"duration_ms":16986,"concrete_test":"Re-derive the atom weights in the observed space by integrating the tilted latent Gaussian density over (-∞,L] and [U,∞) and confirm they equal the stated tail-averaged ratios; if they differ by more than numerical tolerance the weight formula requires correction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the latent exponential tilt yields exact tail-averaged atom weights (plus interior density ratio) that restore marginal coverage in the mixed observed space. The abstract states this construction directly and reports that synthetic experiments confirm smaller valid sets than the baseline. No internal inconsistency, hidden assumption on the censoring mechanism, or gap between the three-term normalizer and the weighted calibration is visible in the given description. The Laplace approximation and mixed-HDR geometry are presented as standard tools applied to this setting.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops conformal Bayes for two-sided censored Gaussian regression under label shift. In the Tobit model, the observed response is a mixed distribution with atoms at the censoring bounds L and U and a continuous density on (L,U). The method combines a Laplace-approximated Bayesian posterior predictive with exponential tilting to produce a three-component tilted predictive (left atom, interior density, right atom) whose normalizer is closed-form. Calibration weights are constructed via a latent exponential tilt that supplies tail-averaged atom ratios at the boundaries together with the ordinary density ratio in the interior; these weights are used in weighted conformal calibration. The resulting prediction sets are mixed highest-density regions that may include atoms and/or an interior interval. Synthetic experiments are reported to show that the weighted tilted procedure restores marginal coverage while producing smaller sets than weighted source-score calibration, with an observed trade-off between marginal and component-wise coverage.","tokens_in":1846,"tokens_out":489,"duration_ms":11521,"significance":"If the derivations hold, the work supplies a concrete, closed-form construction for conformal prediction under label shift when responses are two-sided censored, a setting that arises in many applied regression problems. The explicit separation of atom and interior weights, the mixed-HDR geometry, and the comparison against a natural baseline are useful contributions. The paper also demonstrates that the latent-tilt construction yields exact marginal coverage in the observed space without requiring additional assumptions on the censoring mechanism beyond the model.","major_comments":[],"minor_comments":[{"comment":"§3 (or wherever the three-term normalizer is derived): the normalizer expression should be written out explicitly with the three components labeled, so that the reader can verify the cancellation that produces the closed form.","section":"§3"},{"comment":"The synthetic experiments section should report the precise values of L and U used, the degree of censoring (fraction of observations at each atom), and the label-shift strength (e.g., the tilt parameter), so that the coverage numbers can be reproduced.","section":"Experiments"},{"comment":"Figure captions for the coverage and set-size plots should state whether the plotted intervals are pointwise or simultaneous and whether they are over replications or over test points.","section":"Figures"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their positive summary and significance assessment of the manuscript, as well as the recommendation for minor revision. No specific major comments were raised in the report.","responses":[],"tokens_in":1361,"tokens_out":53,"duration_ms":6934,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper gives a method for doing conformal Bayes on two-sided censored Gaussian regression when there is label shift. The approach tilts the posterior predictive distribution and then applies weighted conformal calibration using a mixed weight that has separate components for the atoms at the censoring points and the density in the middle.\n\nWhat the paper does well is derive a closed-form three-term normalizer for the tilted predictive and show how the latent exponential tilt leads to tail-averaged weights for the boundary atoms. The resulting prediction sets are mixed highest density regions that can adapt to different levels of censoring. On synthetic data the method restores marginal coverage and produces smaller sets than the weighted source-score calibration baseline.\n\nThe soft spots are that the validation stays at the synthetic level, so we lack evidence on real datasets or under stronger model violations. The Laplace approximation is used without much discussion of its accuracy in this censored setting. There is also a noted trade-off in component-wise coverage that could use more exploration.\n\nThis is aimed at statisticians interested in conformal methods for nonstandard prediction problems like censored data with distribution shift. Someone working in that area would get value from the specific construction for the mixed space.\n\nI would send this to peer review. The technical move is clear enough and the problem is well-posed, even if the empirical support is narrow.","headline":"This paper gives a workable extension of conformal Bayes to censored regression under label shift using tilting and mixed weights, with promising but limited synthetic validation.","tokens_in":2315,"tokens_out":342,"would_cite":false,"duration_ms":26024,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Weighted tilted conformal Bayes restores marginal coverage with smaller sets for two-sided censored Gaussian regression under label shift.","keywords":["conformal prediction","label shift","censored regression","Tobit model","Bayesian prediction","prediction sets","mixed distributions"],"falsifier":"A simulation under the two-sided Tobit Gaussian model where the weighted tilted conformal Bayes sets fail to attain the nominal marginal coverage probability.","tokens_in":2643,"feed_emoji":"📊","tokens_out":562,"duration_ms":16373,"temperature":0.7,"pith_summary":"The paper develops conformal Bayes for prediction under label shift when responses are two-sided censored in a Gaussian model. Observed data form a mixed distribution with atoms at the lower and upper bounds plus a continuous density inside the interval. It combines posterior predictive tilting with weighted conformal calibration, deriving a mixed calibration weight from a latent exponential tilt that handles boundary atoms separately from the interior density ratio. Synthetic experiments show this approach achieves correct marginal coverage while producing smaller sets than weighted source-score calibration.","feed_headline":"Weighted tilt restores coverage for censored label shift","feed_subtitle":"Mixed atom-density calibration weights yield smaller valid sets than source-score methods in two-sided censored Gaussian regression.","key_machinery":"Mixed observed-space calibration weight with two atom ratios and one interior density ratio, obtained via latent exponential tilt on the censored scale.","core_discovery":"In a two-sided Tobit Gaussian Bayesian prediction head with Laplace posterior approximation, the tilted predictive distribution has left-atom, interior, and right-atom components with a three-term closed-form normalizer; a latent exponential tilt induces tail-averaged atom weights at the censored boundaries while the interior ratio remains density based, producing a mixed observed-space calibration weight with two atom ratios and one interior density ratio that corrects the calibration measure for target-adapted mixed-HDR geometry.","pith_inferences":["The mixed-weight construction could be adapted to other mixed discrete-continuous observation models beyond censoring.","Component-wise coverage diagnostics might be developed to balance the observed marginal versus per-component behavior."],"forward_implications":["Prediction sets can combine boundary atoms with an interior interval or reduce to atom-only sets under strong censoring.","The method restores marginal coverage with smaller sets than weighted source-score calibration.","A trade-off exists between marginal coverage and component-wise behavior across atoms and interior observations."],"fun_headline_variants":["Mixed tilt calibration for two sided censored label shift","Atom ratios plus interior density in conformal Gaussian censoring","Three term normalizer for tilted predictive under censoring","Latent exponential tilt for censored boundary weights in Bayes"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"A latent exponential tilt induces tail-averaged atom weights at the censored boundaries while the interior ratio remains density based, allowing a mixed observed-space calibration weight with two atom ratios and one interior density ratio.","fun_headline_variants_meta":{"raw":{"variants":["Mixed tilt calibration for two sided censored label shift","Atom ratios plus interior density in conformal Gaussian censoring","Three term normalizer for tilted predictive under censoring","Latent exponential tilt for censored boundary weights in Bayes"]},"model":"grok-4.3","cost_usd":0.005355,"raw_usage":{"total_tokens":2605,"prompt_tokens":711,"num_sources_used":0,"completion_tokens":60,"cost_in_usd_ticks":53549500,"prompt_tokens_details":{"text_tokens":711,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1834,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":711,"tokens_out":60,"duration_ms":12391,"temperature":1.0,"reasoning_tokens":1834,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T07:44:56.890778+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A simulation under the two-sided Tobit Gaussian model where the weighted tilted conformal Bayes sets fail to attain the nominal marginal coverage probability.","supporting_citations":[],"review_version":1}