Pith. sign in

REVIEW 3 major objections 6 minor 16 references

A Bayesian Model of Underreporting for Sexual Assault on College Campuses

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper separates true assault incidence from reporting rates at 1,973 colleges, finding that the 2014-2018 rise in reported campus assaults came mostly from more reporting, not more assaults.

desk verdict A careful, transparent application of underreporting models to campus Clery data, but the headline 'rising reporting rates' result is driven by an untested prior variance ratio, not by the data itself. read the letter →

arxiv 2412.00823 v1 pith:YX3CS2GZ submitted 2024-12-01 stat.AP

Casey Bradshaw , David M. Blei This is my paper · ORCID
classification stat.AP MSC 62F1562P25
keywords sexualassaultunderreportingBayesianhierarchicalmodelcountdatacampuscrimestatisticsinformativepriorsHamiltonianMonteCarloidentifiability
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 tries to separate two quantities hidden inside each college's annual reported sexual assault count: how many assaults actually happen and how likely a student is to report one. Because the reported number alone only fixes the product of these two quantities, the authors add national victimization-survey statistics as informative priors to break the tie, and fit a hierarchical Bayesian model to campus crime data from 2014-2019. Their central finding is that the nationwide rise in reported assaults over this period is better explained by rising reporting rates than by a rise in the true number of assaults. The model also produces school-by-school estimates, and those vary widely: some schools report under 10% of assaults, others around half or more. If the estimates are right, they give administrators a way to read year-over-year changes in their own campus crime numbers instead of taking reported counts at face value.

What carries the argument

The engine is binomial thinning: the observed count $x_{ij}$ is drawn as $\mathrm{Bin}(z_{ij}, p_{ij})$ from a latent Poisson count $z_{ij} \sim \mathrm{Poisson}(\lambda_{ij})$, so marginally $x_{ij} \mid \lambda_{ij}, p_{ij} \sim \mathrm{Poisson}(\lambda_{ij} p_{ij})$. This marginal identity lets the sampler integrate out the discrete latent $z$ and so use gradient-based Hamiltonian Monte Carlo; unreported counts $u_{ij} = z_{ij} - x_{ij}$ are then drawn from $\mathrm{Poisson}(\lambda_{ij}(1-p_{ij}))$ to reconstruct the latent total. The identifiability gap, data fix only $\lambda_{ij} p_{ij}$, is closed by informative priors on $\lambda$ and $p$ calibrated to national victimization survey estimates, with school-level intercepts and covariates providing partial pooling across the 1,973 schools. The paper shows that even this prior information cannot be fully overtaken by data for the absolute levels, only for covariate slopes, which is why its headline trend claim is more stable than its point estimates.

What would settle it

Carry out an anonymous victimization survey at a representative sample of the same campuses, asking about incidents that match the campus crime-report definitions, and compare the implied reporting rate, campus reports divided by survey-estimated victimizations, with the model's posterior median reporting rate; if the survey-based rate is flat or falling from 2014 to 2018, or if true incidence rises while reporting holds steady, the paper's central attribution fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the reported increase in campus sexual assaults from 2014 to 2019 is more likely attributable to an increase in reporting rates than to an increase in the true number of assaults. Under the fitted model, the posterior median reporting rate for the college population rose from 17.3% in 2014 to 24.2% in 2018, while the posterior median incidence stayed roughly flat at 2.6 to 2.8 assaults per 1000 students. This separation comes from a hierarchical binomial-thinning model in which the true assault count at each school-year is Poisson and each assault is reported independently with a school-specific probability; observed counts identify only the product $\lambda p$, so informative priors drawn from national victimization statistics act as the tiebreaker. The same model yields per-school reporting probabilities that range from very low to about 74%, implying that a one-size-fits-all reading of reported campus crime statistics is unreliable. It also associates lower reporting probabilities with junior colleges, religiously oriented institutions, and schools with more need-based aid recipients, and estimates that expected per-capita incidence is higher at smaller schools.

Load-bearing premise

The load-bearing assumption is that the national victimization-survey statistics used to set the priors give an unbiased picture of true assault incidence and reporting behavior on college campuses; because the observed data pin down only the product of these two quantities, any bias in those priors shifts the absolute estimates.

Editorial extensions

If this is right

  • The 2014-2018 rise in national reported totals is more plausibly a sign that victims are coming forward than a sign that more assaults are occurring.
  • For a school with a low estimated reporting rate, a year-over-year increase in reports can plausibly come from reporting-rate variation alone; for a high-reporting school, the same increase is harder to explain without an incidence change.
  • Schools with the lowest estimated reporting probabilities, such as junior colleges, religiously oriented institutions, and schools with many need-based aid recipients, have reported counts that understate their true incidence by the most.
  • Expected per-capita assault incidence is higher at smaller schools, so comparing raw reported counts across schools of different sizes is misleading.

Reading between the lines

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

  • The same marginal-Poisson augmentation could be reused in any underreported-count setting where an external source anchors either the event rate or the reporting probability; the independence-of-reporting assumption is the main thing that would have to be checked.
  • If the upward reporting trend has continued since 2019, reported counts and true incidence could move in opposite directions in coming years, so administrators who use raw reports as a success metric will get the sign wrong.
  • Because the paper's sensitivity analysis keeps the rising-reporting conclusion even under a 75% downward shift in the prior reporting rate, the direction of the national trend is more trustworthy than the absolute posterior levels.
  • A direct validation would compare the model's school-level reporting rates with reporting rates measured from a redesigned national victimization survey once campus-specific estimates become available; mismatches would show exactly where the prior transfer breaks down.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript proposes a hierarchical Bayesian model for Clery Act campus sexual assault counts, treating observed reports x_ij as binomial thinnings of latent true counts z_ij with reporting probability p_ij and Poisson incidence rate lambda_ij. After marginalizing out z_ij, the observed counts follow Poisson(lambda_ij p_ij), so the data identify only the product of incidence and reporting probability; informative priors based on NCVS statistics are used to separate the two components. The model is fitted with HMC/Stan to 1,973 institutions over 2014-2019, with held-out predictive checks, a comparison of pooling schemes, and posterior estimates of incidence and reporting rates. The headline result is that true incidence was roughly flat while reporting rates rose from about 17% in 2014 to about 24% in 2018, making rising reporting rates the more likely explanation for the observed increase in reported assaults.

Significance. The paper is a serious and mostly careful contribution to the underreported-count-data literature: the marginalization derivation in Appendix B is correct, the split predictive checks are methodologically appropriate, and Appendices C-E contain unusually thorough model comparison and sensitivity analyses. The use of external NCVS statistics to set informative priors is legitimate and does not involve circular reasoning. However, the central substantive claim about the temporal trend in reporting rates is not empirically identified; it depends on the relative prior variances of the year-level noise terms, and the reported sensitivity analysis does not vary that ratio. Consequently, the paper's headline conclusion is a conditional modeling outcome rather than an established empirical finding. The framework and software are valuable, but the claims need reframing or additional robustness analysis.

major comments (3)
  1. [Section 5.2; Section 4.5; Eqs. (3) and (5)] The central claim that the 2014-2019 increase in reported assaults is attributable to rising reporting rates is not identified by the data. Because the likelihood is Poisson(lambda_ij p_ij), and Section 4.5 correctly explains that posterior estimates of lambda and p approach their prior conditional on the identified product, the decomposition of year-to-year changes in observed reports between incidence and reporting probability is governed by the priors on the per-year noise terms. Equation (3) sets eta_ij ~ N(0, 0.1) on log(lambda_ij), while Equation (5) sets delta_ij ~ N(0, 0.5) on logit(p_ij); on the log scale relevant to the observed count, this makes p roughly five times more mobile year-to-year than lambda. The upward trend in Figure 2 can be represented either by rising incidence or by rising reporting probability, and the much smaller prior variance on eta strongly steers the posterior toward the latter. Appendix E varies prior means (scenarios a-e) but never the relative variances of eta and delta, so the sensitivity analysis does not probe the assumption that drives the headline result. The authors should provide external empirical justification for these variance scales or report the posterior trend under a range of eta/delta variance ratios; if the reporting-rate trend reverses under plausible ratios, Section 5.2 should be substantially softened.
  2. [Appendix A] The post hoc data modifications are material and are not subjected to sensitivity analysis. Collapsing the 104 Nebraska-Lincoln reports from 2017 to a single report reduces that year's reported total by 103 (from 119 to 16); the Ohio State Strauss exclusion removes 30 reports in 2018 and 97 in 2019; Michigan State University is dropped entirely; and similar collapses are applied to Wells College and Genesee Community College. These choices can affect both systemwide and school-level estimates, yet no analysis reports results on the unmodified data or under less aggressive treatments (for example, excluding one affected school at a time or modeling the repeat-victim counts as a separate category). Given that Appendix D shows the model is sensitive to correlated reporting decisions, the treatment of these extreme records deserves the same scrutiny as the prior specifications.
  3. [Sections 4.1-4.2 and Appendix E] The mapping from NCVS statistics to the Clery-reportable sexual assault construct is not established. Clery Act counts use specific offense definitions and require reports to campus authorities or local police, while NCVS measures victimization that may not be reported to any authority. Because the likelihood identifies only the product lambda p, the absolute posterior levels of incidence and reporting rate inherit the prior means. Appendix E varies the prior means over a plausible range of underreporting, but it does not address definitional mismatch or the possibility that the bias in NCVS self-reports varies over time. The paper should either provide an explicit argument that NCVS estimates are commensurate with Clery-reportable campus assaults or add a scenario in which the prior means shift over time; this is relevant to the absolute estimates in Figures 10-11 even if the variance-ratio issue in the previous comment is the more direct threat to the trend conclusion.
minor comments (6)
  1. [Section 4.2] The sentence describing the priors for the reporting-probability model says "priors on epsilon, eta, and intercepts beta_0 are chosen," which repeats the incidence-model description; it should refer to gamma, delta, and alpha_0.
  2. [Algorithm 2] The predictive sampling draws eta_ij ~ N(0, 0.2) and, for new schools, gamma_i ~ N(0, 1) and epsilon_i ~ N(0, 0.5), which do not match the prior variances stated in Eqs. (3) and (5) (0.1, 1.25, and 0.75 respectively). Please clarify whether these are deliberate prior-predictive choices or typographical errors.
  3. [Section 3] The phrase "on the behalf of the behalf of the US Bureau of Justice Statistics" contains a duplicated phrase and should be corrected.
  4. [Section 5.1] In the sentence beginning "The proposed the power law relationship," the word "the" is repeated.
  5. [Appendix C] The word "distributioin" is misspelled in the model-comparison subsection.
  6. [Section 5.2] The sentence "the true trend in incidence could conceivably be flat or even increasing" appears to express uncertainty about whether incidence is flat or decreasing; please rephrase to say what the posterior intervals actually permit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model's non-identifiability is disclosed and broken by external NCVS priors, not by the paper's own conclusions.

full rationale

The paper's derivation chain is transparent about its core identifiability limitation rather than hiding it. The likelihood marginalizes to x|λ,p ∼ Poisson(λp), so the data identify only the product of incidence and reporting probability; Section 4.5 explicitly states that the posterior distributions of λ0 and p0 approach p(λ0|λ0p0) and p(p0|λ0p0), i.e., the split is prior-conditional. This is a prior-sensitivity issue, not circularity, because the informative priors are elicited from external NCVS statistics (Section 4.1 and 4.2), not from the Clery data or from the paper's own conclusions. The central claim that reporting rates rose is therefore not identified from the Clery counts alone, but the paper discloses this dependence and conducts sensitivity analysis in Appendix E. One can question whether Appendix E varies the right feature of the prior, since it changes prior means under scenarios (a)-(e) but leaves the relative scales of the year-level noise terms η and δ fixed; however, that is an incomplete robustness analysis, not a circular argument. The only self-citation, Moran, Blei and Ranganath (2019) for split predictive checks, is methodological and not load-bearing for the substantive estimates. No equation is defined in terms of the conclusion, no fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' prior work. The paper is honest that external assumptions are doing real work, and that honesty is the opposite of circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The model rests on a small set of hand-set hyperparameters and domain assumptions. The most consequential are the NCVS-derived priors for incidence and reporting, which are load-bearing because only lambda times p is identified by the data (Section 4.5). The post hoc data edits in Appendix A are an additional unmodeled assumption. No new physical entities are introduced; the latent variables z and u are standard inference targets.

free parameters (5)
  • Prior intercept for log incidence (beta0 = -5.5, sd 0.5) = -5.5
    Hand-set so the prior predictive incidence is centered at 4.1 per 1000, matching NCVS rates for 18-24 year olds. Because only lambda times p is identified, this prior mean is load-bearing for absolute incidence estimates.
  • Prior intercept for logit reporting (alpha0 = -1.25, sd 0.5) = -1.25
    Hand-set so the prior reporting probability is centered at 22%, matching NCVS reporting rates. This prior level directly anchors the reported underreporting estimates.
  • Random effect standard deviations (epsilon=0.866, eta=0.316, gamma=1.118, delta=0.707) = 0.866, 0.316, 1.118, 0.707
    Chosen to make prior predictive distributions match NCVS incidence and reporting variability. These scales control the amount of school heterogeneity and shrinkage.
  • Prior mean for population scaling coefficient (beta1 = 1, sd 0.1) = 1
    An informative prior that assaults scale roughly linearly with student population. The posterior estimate of 0.82 is pulled toward 1 by this prior.
  • Weakly informative prior means for covariate slopes (beta2, alpha1, alpha2, alpha3, alpha4 = 0) = 0
    Standard weakly informative choices with standard deviations 2 to 4. The central trend claim is less sensitive to these, but they are part of the model specification.
assumptions (5)
  • standard math Poisson thinning marginalization: x given lambda and p follows Poisson(lambda*p), and u given x, lambda, p follows Poisson((1-p)*lambda)
    Relied on to marginalize the discrete latent counts and enable HMC. The derivation in Appendix B is correct.
  • domain assumption NCVS estimates are unbiased for campus sexual assault incidence and reporting rates
    Informative priors are set to match NCVS values in Sections 4.1 and 4.2. If NCVS undercounts due to nondisclosure or definitional mismatch, absolute posterior levels shift, as Appendix E shows.
  • domain assumption Reporting decisions are independent conditional on p (binomial thinning)
    Needed for the Poisson marginal in Section 4. Appendix D shows that correlated reporting causes the model to overestimate true counts.
  • domain assumption Clery reported sexual assault counts correspond to the same construct as NCVS sexual assault victimization
    The model treats Clery reports and NCVS estimates as measurements of the same latent process. This mapping is not directly checked in the paper.
  • domain assumption The post hoc data edits in Appendix A do not bias the central trend
    The model is fit to edited counts, including collapsed repeat-victim events and excluded Ohio State historical assaults, with no sensitivity analysis around these edits.
invented entities (2)
  • Latent true assault count z_ij
    purpose: Target of inference; the unobserved total number of assaults at school i in year j
    Postulated as a Poisson latent variable. It is identifiable only through the product lambda times p plus the informative priors, with no direct validation data.
  • Unreported assault count u_ij
    purpose: Augments the observed count x_ij to reconstruct z_ij in posterior sampling
    Derived as Poisson((1-p)*lambda) in Appendix B. It is not directly observed and inherits the same identifiability limitations as z_ij.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Bayesian Model of Underreporting for Sexual Assault on College Campuses." pith.science (2026). https://pith.science/paper/YX3CS2GZ

@misc{pith2026241200823,
  author       = {Pith},
  title        = {Pith review of: A Bayesian Model of Underreporting for Sexual Assault on College Campuses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YX3CS2GZ}},
  note         = {Machine review of arXiv:2412.00823}
}
read the original abstract

In an effort to quantify and combat sexual assault, US colleges and universities are required to disclose the number of reported sexual assaults on their campuses each year. However, many instances of sexual assault are never reported to authorities, and consequently the number of reported assaults does not fully reflect the true total number of assaults that occurred; the reported values could arise from many combinations of reporting rate and true incidence. In this paper we estimate these underlying quantities via a hierarchical Bayesian model of the reported number of assaults. We use informative priors, based on national crime statistics, to act as a tiebreaker to help distinguish between reporting rates and incidence. We outline a Hamiltonian Monte Carlo (HMC) sampling scheme for posterior inference regarding reporting rates and assault incidence at each school, and apply this method to campus sexual assault data from 2014-2019. Results suggest an increasing trend in reporting rates for the overall college population during this time. However, the extent of underreporting varies widely across schools. That variation has implications for how individual schools should interpret their reported crime statistics.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 15 canonical work pages

  1. [1]

    AXELSON , B. (2019). These are the 45 Upstate NY college campuses that reported the most rapes, ranked. NewYorkUpstate.com. 14 May 2019, https://www.newyorkupstate.com/news/g66l-2019/05/b1452bae03654/ these-are-the-45-ny-college-campuses-that-reported-the-most-rapes-ranked.html. Accessed: 3 Aug

    work page 2019

  2. [3]

    GUTTMAN , I. (1967). The use of the concept of a future observation in goodness-of-fit problems. Journal of the Royal Statistical Society: Series B (Methodological) 29 83–100. JAYNES , E. T. (1968). Prior probabilities. IEEE Transactions on Systems Science and Cybernetics 4 227–241. JEFFREYS , H. (1946). An invariant form for the prior probability in esti...

    arXiv 1967

  3. [6]

    Quantifying disparities in intimate partner violence: a machine learning method to correct for underreporting

    POWERS , S., G ERLACH , R. and S TAMEY, J. (2010). Bayesian variable selection for Poisson regression with underreported responses. Computational statistics & data analysis 54 3289–3299. RUBIN , D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. An- nals of Statistics 1151–1172. SABINA , C. and H O, L. Y...

    work page Pith review arXiv 2010

  4. [7]

    and D RUMMOND MARQUES DA SILVA, G

    STONER , O., E CONOMOU , T. and D RUMMOND MARQUES DA SILVA, G. (2019). A hierarchical framework for correcting under-reporting in count data. Journal of the American Statistical Association 114 1481–1492. STAN DEVELOPMENT TEAM (2023). RStan: the R interface to Stan. R package version 2.21.8. TRUMAN , J. L. and B ROTSOS , H. (2021). Update on the NCVS Inst...

    work page 2019

  5. [10]

    One of its campuses is co- located with the main Stillwater, OK campus of Oklahoma State University (OSU), a large flagship public university

    • Northern Oklahoma College (NOC) is a community college. One of its campuses is co- located with the main Stillwater, OK campus of Oklahoma State University (OSU), a large flagship public university. Beginning in 2019, campus crime statistics for NOC include crimes on the shared OSU Stillwater campus. Consequently, these assaults are double counted in th...

    work page 2019

  6. [19]

    Prior distributions on the reporting probability p under scenarios (a) - (e) (with model coefficients α1, α2, α3, and α4 set to zero). In line with the discussion in Section 4.5, we find that inferences about the role of co- variates are relatively more stable across scenarios (as depicted in Figures 20 and 21), while inferences about the true incidence a...

    work page 2018

  7. [21]

    Panel (i) depicts α1, the coefficient corresponding to whether a school is a junior college

    Estimates of coefficients relating covariates to the reporting probability remain similar under moderate changes to the prior distributions, and begin to shrink toward zero under more extreme changes to the prior distribution. Panel (i) depicts α1, the coefficient corresponding to whether a school is a junior college. Panel (ii) depicts α2, the coefficien...

    work page 2014

  8. [22]

    0.00 0.10 0.20 0.30 Assaults per 1000 Persons 2014 2015 2016 2017 2018 2019 a b c d e FIG

    Prior belief in a higher incidence of sexual assault produces higher posterior estimates of the total number of assaults occurring. 0.00 0.10 0.20 0.30 Assaults per 1000 Persons 2014 2015 2016 2017 2018 2019 a b c d e FIG

    work page 2014

Show all 16 references
  1. [23]

    Prior belief in a lower probability of reporting sexual assault produces lower posterior estimates of the reporting rate. BAYESIAN MODEL OF UNDERREPORTING FOR SEXUAL ASSAULT 33 8 10 12 14 16 18 Assaults per 1000 Persons 2014 2015 2016 2017 2018 2019 e 0.02 0.04 0.06 0.08 Assau...

    2014

  2. [24]

    Panel (i) depicts the posterior distribution of the incidence rate; panel (ii) depicts the posterior distribution of the reporting rate

    Under scenario (e), posterior estimates of the incidence rate do not exhibit a clear increasing or de- creasing trend, while posterior estimates of the reporting rate are more suggestive of an increase over 2014-2018. Panel (i) depicts the posterior distribution of the inciden...

    2021

  3. [1998]

    (Note: Strauss died in 2005.) 22 • In 2017 University of Nebraska-Lincoln had a total of 119 reported assaults

    We exclude these assaults from our analysis (30 in 2018 and 97 in 2019), as they occurred long before the relevant reporting period. (Note: Strauss died in 2005.) 22 • In 2017 University of Nebraska-Lincoln had a total of 119 reported assaults. Of those 119 reported assaults, ...

    2018

  4. [2014]

    TRUMAN , J

    Bureau of Justice Statistics NCJ 248973. TRUMAN , J. L. and M ORGAN , R. E. (2016). Criminal Victimization,

    2016

  5. [2015]

    Private not-for-profit (religious affiliation)

    Bureau of Justice Statistics NCJ 250180. WINKELMANN , R. (1996). Markov chain Monte Carlo analysis of underreported count data with an application to worker absenteeism. Empirical Economics 21 575–587. WU, K., D AHLEM , D., H ANE , C., H ALPERIN , E. and Z OU, J. (2023). Colle...

    1996

  6. [2017]

    OBAMA , B

    Bureau of Justice Statistics NCJ 252472. OBAMA , B. (2014). Memorandum – Establishing a White House Task Force to Protect Students from Sexual Assault. The White House Office of the Press Secretary . 22 Jan 2014, https://obamawhitehouse.archives.gov/ the-press-office/2014/01/2...

    2014

  7. [2019]

    20 MORGAN , R

    Bureau of Justice Statistics NCJ 255113. 20 MORGAN , R. E. and T RUMAN , J. L. (2018). Criminal Victimization,

    2018

  8. [2023]

    C., C ARVALHO , M

    BAILEY , T. C., C ARVALHO , M. S., L APA, T. M., S OUZA , W. V. and B REWER , M. J. (2005). Modeling of under-detection of cases in disease surveillance. Annals of Epidemiology 15 335–343. BETTENCOURT , L. M. A., L OBO , J., H ELBING , D., K ÜHNERT , C. and W EST, G. B. (2007)...

    2005

Pith tools

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