{"id":"1d645ca7-adfa-47b3-8e1f-2f1fd2e49b60","arxiv_id":"2508.11982","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"The Gibbs sampler for the Dirichlet-Laplace prior draws from conditionals in the wrong order; this note supplies a corrected sampler and an equivalent-formulation alternative.","lead":"This short note reports that the MCMC sampler in a widely used Bayesian shrinkage paper, Bhattacharya et al. (2015), draws its conditional distributions in the wrong order, so it does not sample the true joint posterior. The authors offer two corrected samplers and state that the original theoretical results are unaffected.","discovery_kind":"replication","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The abstract's stated mechanism is suspect: in a standard Gibbs sampler, update order of correctly-specified full conditionals does not affect the stationary distribution, so 'wrong order' alone cannot explain failure; the note must show a specific misspecified conditional.","rationale":"Read in good faith, this is a corrigendum by authors of the corrected paper, which is a normal, non-circular form of correction; if valid, users should adopt the new samplers. However, the abstract's diagnosis is theoretically suspect. Standard Gibbs sampler theory says the stationary distribution is invariant to the order in which full conditionals are updated. Therefore, 'samples from conditional distributions in the wrong order' cannot, by itself, be the reason the original sampler fails. The note must instead demonstrate that one or more of the original conditional draws were not the true full conditionals — a materially different and more specific claim. The reader's weakest_assumption concerned the equivalence of the reformulated prior; my concern is more fundamental, applying to the first proposed correction and to the diagnosis of the 2015 algorithm. I therefore only partially agree with the reader's framing. The supplied full text is a different paper (Chart-CoCa, arXiv:2508.11975), so the derivation in the note is unavailable for inspection; no machine-checked proof or reproducible code is cited. The central claim is unverified, and the abstract's stated mechanism raises a concrete correctness risk. I keep the verdict at UNVERDICTED because absence of the full text prevents a definitive rejection; but if the full text indeed relies only on 'wrong order' without identifying a specific non-full conditional, the note should be rejected. The concrete test above would settle the concern.","tokens_in":2830,"tokens_out":7257,"duration_ms":75454,"concrete_test":"Reconstruct Algorithm 1 from Bhattacharya et al. (2015) and, for every step, write the distribution that is actually sampled as a function of the current values of all other variables. If each step equals the full conditional of that variable given all others, the original chain has the target as its stationary distribution regardless of order, and the central claim is false. If any step uses a strict subset of conditioning variables, that subset is the true error. Separately, implement the original, corrected, and alternative samplers on a small conditionally Gaussian example with n=5 where the posterior can be computed by numerical integration; compare joint draws with an energy distance. If the original sampler matches the exact posterior within Monte Carlo error, the 'wrong order' diagnosis is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the original MCMC in Bhattacharya et al. (2015) samples conditionals in the wrong order and therefore misses the joint posterior. For a standard Gibbs sampler this mechanism is not viable: composing full-conditional draws in any fixed order yields the same joint target as invariant distribution, because each update is a kernel that preserves the target. Consequently, permuting the order of correctly specified conditionals cannot change the sampled distribution. If the original algorithm truly fails, the error must be that one or more draws are not full conditionals given the other latent variables at that iteration — for example, a draw that conditions on an outdated value, omits conditioning on the response, or uses a conditional derived from a marginal rather than the joint model. The note must identify the exact step in the 2015 Algorithm 1 where the drawn distribution differs from the true full conditional. The abstract does not do this, and its phrase 'wrong order' is either imprecise or incorrect. The second proposed fix carries an additional requirement: the 'alternative, yet equivalent' prior must be equivalent as a joint law over all latent variables, not merely as a marginal law, so that the induced full conditionals coincide; otherwise the replacement sampler targets a different posterior. Since only the abstract is available, neither requirement can be checked, but the stated mechanism is already internally problematic.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper is advertised as a corrigendum note to Bhattacharya et al. (2015), claiming that the original MCMC algorithm for the Dirichlet-Laplace (DL) prior 'samples from conditional distributions in the wrong order' and therefore does not correctly target the joint posterior of the latent variables. It promises two fixes: a correction to the original algorithm and a new algorithm based on 'an alternative, yet equivalent, formulation of the prior.' The abstract further asserts that the theoretical results of the 2015 paper are unaffected. The submitted full text, however, is not this manuscript at all but an unrelated paper titled 'Chart-CoCa: Self-Improving Chart Understanding of Vision LMs via Code-Driven Synthesis and Candidate-Conditioned Answering' (arXiv:2508.11975). Consequently, the actual content of the note—its derivations, algorithms, proofs, or numerical checks—is absent from the submission.","tokens_in":2995,"tokens_out":1884,"duration_ms":21145,"significance":"If the central claim were established, the note would have substantive practical importance: the DL prior is widely used in high-dimensional Bayesian sparse regression, and a genuine failure of the published sampler would affect the validity of many posterior summaries obtained with that algorithm. A precise, verifiable correction with a correct stationary distribution would be a useful service to the community. However, the submitted text contains no derivations, no algorithm listings, no proofs, no numerical experiments, and no code. Moreover, the mechanism stated in the abstract is, as phrased, inconsistent with standard Gibbs sampling theory: for correctly specified full conditionals, update order does not change the stationary distribution. The significance assessment therefore rests entirely on an unverifiable abstract and on an internally questionable explanation.","major_comments":[{"comment":"The stated mechanism cannot be correct as written. In a Gibbs sampler, if every draw is from the true full conditional of the corresponding latent variable given the current values of all other variables, then the composition of such updates leaves the joint target invariant regardless of update order. Thus 'samples from conditional distributions in the wrong order' cannot, by itself, explain a failure to sample from the joint posterior. The note must identify a specific misspecified conditional, for example a step that conditions on an outdated value, omits conditioning on the response, or uses a conditional derived from a marginal instead of the joint model. The abstract provides no such identification, and no full text is available to supply it.","section":"Abstract"},{"comment":"The submitted full text is not this manuscript. After the abstract of the DL-prior note, the document turns into a completely different paper, 'Chart-CoCa: Self-Improving Chart Understanding of Vision LMs via Code-Driven Synthesis and Candidate-Conditioned Answering,' with different authors, different subject, and a different arXiv identifier. None of the promised content of the note—Algorithm 1 of Bhattacharya et al., the corrected sampler, the alternative formulation, or any invariance proof—appears in the submission. This makes the central claim impossible to check and is a fundamental submission defect.","section":"Full text"},{"comment":"The second proposed solution depends on an 'alternative, yet equivalent, formulation of the prior.' For a Gibbs sampler, the replacement must be equivalent as a joint law over all latent variables that enter the sampling scheme, not merely as the marginal law of the regression coefficient. If the equivalence holds only marginally, the induced full conditionals need not coincide and the new sampler could target a different posterior. The abstract does not even state the variables involved, let alone demonstrate joint equivalence, so this load-bearing assumption is completely unsupported.","section":"Abstract"},{"comment":"No evidence whatsoever is provided that the corrected sampler actually has the claimed stationary distribution. The abstract promises 'a correction to the original algorithm' but offers no derivation of the full conditionals, no proof of invariance, and no numerical experiment comparing the original and corrected samplers. For a corrigendum whose entire purpose is to change the target distribution of a published MCMC algorithm, the absence of any verification is a decisive gap.","section":"Abstract"}],"minor_comments":[{"comment":"The phrase 'wrong order' is ambiguous and should be replaced by a precise statement of which conditional distribution is misspecified and at which step of the original Algorithm 1.","section":"Abstract"},{"comment":"The note would benefit from a brief description of the latent-variable structure of the DL sampler so that readers can understand the claimed error without consulting the 2015 paper.","section":"Abstract"},{"comment":"If the corrected algorithm is to be usable, the submission should include pseudocode for both the corrected original sampler and the alternative-formulation sampler, as well as code or a reproducible numerical check when practical.","section":"General"}],"recommendation":"reject","confidential_remarks":"The submitted full text is a different paper entirely, so a normal technical review is impossible. Beyond that administrative defect, the abstract's stated explanation ('wrong order' in a Gibbs sampler) is internally problematic because cyclic permutation of correctly specified full conditionals preserves the target distribution. Even if the full text were supplied, the authors would need to explain the precise misspecification and demonstrate joint equivalence of the alternative prior. As submitted, the manuscript cannot be accepted or meaningfully revised within the current scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—quick note on arXiv:2508.11982. Two things up front. First, the evaluation copy we got has the wrong full text: the abstract is about a Dirichlet-Laplace prior Gibbs sampler, but the attached manuscript is Chart-CoCa, a vision-language paper. So I can only comment on the abstract. Second, the abstract's central mechanism is suspect. The claim that the original algorithm \"samples from conditional distributions in the wrong order\" is not a viable explanation for failure to converge to the joint posterior. In a standard Gibbs sampler, any fixed ordering of correctly specified full conditionals leaves the target invariant; the order only affects convergence rate, not the stationary distribution. So either the original error is something more specific—a draw that conditions on an outdated value, or uses a marginal rather than full conditional—or the correction is itself misguided. The abstract needs to point to the exact line in Bhattacharya et al. (2015) where the drawn distribution differs from the true full conditional.\n\nWhat is genuinely useful, if true: correcting a published MCMC sampler is a practical contribution, and several of the original authors participating in the corrigendum is a normal, healthy form of self-correction. The second proposed fix depends on an \"alternative, yet equivalent\" prior formulation; the abstract asserts equivalence but does not demonstrate that the equivalence holds jointly over all latent variables, which is what the sampler needs. That proof is exactly what a reader cannot check from the abstract.\n\nOn the positive side, there is nothing circular about checking a sampler against a prior that is defined externally, and the claimed impact—that applied results computed with the original sampler need re-examination—is real if the bug is real.\n\nBut as it stands, I would not send this to peer review. The submission packet is unusable because the full text is mismatched, and the abstract's stated reason for the failure is theoretically implausible without further detail. The authors should be asked to submit the actual note with a precise derivation and, ideally, a small numerical demonstration. If that note identifies a specific misspecified conditional, then it deserves referee time. As it is, there is not enough content to evaluate.","headline":"The abstract claims a 'wrong order' Gibbs sampler, but that mechanism cannot break a Gibbs sampler; the packet also has the wrong full text, so there is nothing to referee yet.","tokens_in":3599,"tokens_out":2186,"would_cite":false,"duration_ms":22047,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","65C05"],"pacs":[],"model":"deepseek-v4-flash","headline":"The MCMC algorithm published with the Dirichlet-Laplace prior draws from the wrong posterior because it samples conditional distributions in the wrong order, and this note provides two corrected samplers.","keywords":["Dirichlet-Laplace prior","MCMC","Gibbs sampler","posterior sampling","corrigendum","shrinkage prior","Bayesian variable selection"],"falsifier":"Simulate data from the generative model of the DL prior, run both the original sampler and the first corrected sampler to many iterations, and compare their empirical joint distributions for the latent variables against the closed-form full conditionals; if the original sampler's draws match the true joint posterior, the claimed ordering error cannot be real.","tokens_in":2567,"feed_emoji":"🔧","tokens_out":4895,"duration_ms":52357,"temperature":0.7,"pith_summary":"This note claims that the Markov chain Monte Carlo algorithm introduced with the Dirichlet-Laplace (DL) prior by Bhattacharya et al. (2015) updates the latent variables in the wrong order, so it does not produce draws from the joint posterior of those variables. It then gives two simple fixes: a corrected version of the original sampler and a new sampler based on an equivalent reformulation of the prior. If the note is right, any applied analysis that used the original algorithm may have been summarized from the wrong posterior, while the theoretical results of the 2015 paper remain untouched. The note matters because the DL prior is a common tool for Bayesian shrinkage and variable selection in high-dimensional regression.","feed_headline":"Published DL-prior sampler draws from wrong posterior","feed_subtitle":"Corrigendum supplies two corrected MCMC samplers; the 2015 paper's theory still holds.","key_machinery":"The central object is the joint posterior distribution of the latent variables in the hierarchical Dirichlet-Laplace prior and the Gibbs-sampler update order used to explore it. The mechanism of the fix is twofold: first, rearranging the conditional draws so that the chain has the correct joint posterior as its stationary distribution; second, reparametrizing the prior through an equivalent formulation that permits a valid sampling scheme in a different order.","core_discovery":"The paper establishes that the Gibbs-style sampling scheme for the Dirichlet-Laplace prior, as originally published, draws from the conditional distributions in a sequence that is not a valid sampler for the joint posterior of all latent variables. The authors show where the ordering fails and supply two valid alternatives: a direct correction that restores the correct conditional-update order, and a second algorithm built on an alternative yet equivalent formulation of the prior. Both are stated to work in the conditionally Gaussian setting, and the corrigendum explicitly leaves the theoretical results of the 2015 paper unaffected.","pith_inferences":["If the original sampler has been widely used in applications, reported uncertainty intervals for shrinkage or selection quantities could be systematically off; a re-analysis of a published dataset with the corrected sampler would quantify the impact.","The same failure mode—updating conditionals in an order that breaks the joint target—could exist in other hierarchical shrinkage samplers, so verifying that every update is a full conditional of the same joint posterior is a cheap audit for such code.","The equivalence claim suggests a concrete diagnostic: run both corrected samplers to approximate convergence and compare their empirical joint distributions; any mismatch would reveal that the alternative formulation is not truly equivalent at the joint level."],"forward_implications":["Implementations of the original DL sampler should be replaced by the corrected version whenever draws from the joint posterior of the latent variables are needed.","Applied conclusions based on the original sampler may not reflect the true DL posterior, so re-running analyses with a corrected sampler is the direct way to check sensitivity.","The theoretical posterior-concentration and shrinkage results in the 2015 paper are not affected by the sampling-order bug.","The alternative-formulation algorithm gives practitioners a second, equivalently valid sampler for the same conditionally Gaussian setting."],"supporting_citations":[{"why":"Introduces the Dirichlet-Laplace prior and the original MCMC algorithm whose conditional-sampling order this note corrects.","marker":"Bhattacharya et al. (2015)"}],"fun_headline_variants":["DL-prior MCMC order flaw fixed in two ways","Corrigendum: DL-prior sampler order corrected","Original DL-prior sampler misorders conditional draws","Two fixes for DL-prior MCMC sampling flaw"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The second proposed sampler is only valid if the 'alternative, yet equivalent' formulation of the DL prior is equivalent in the joint latent structure the sampler exploits, not just in its marginal form.","fun_headline_variants_meta":{"raw":{"variants":["DL-prior MCMC order flaw fixed in two ways","Corrigendum: DL-prior sampler order corrected","Original DL-prior sampler misorders conditional draws","Two fixes for DL-prior MCMC sampling flaw"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000163,"raw_usage":{"total_tokens":1160,"prompt_tokens":776,"completion_tokens":384,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":392,"completion_tokens_details":{"reasoning_tokens":321}},"tokens_in":392,"tokens_out":384,"duration_ms":3855,"temperature":1.0,"reasoning_tokens":321,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:26:31.303546+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate data from the generative model of the DL prior, run both the original sampler and the first corrected sampler to many iterations, and compare their empirical joint distributions for the latent variables against the closed-form full conditionals; if the original sampler's draws match the true joint posterior, the claimed ordering error cannot be real.","supporting_citations":[],"review_version":2}