{"path":"research/how-independent-reasons-add/real-cases-with-known-outcomes.md","content":"# Literature report: real cases with published numbers and a known combined outcome\n\n*A research helper's report for `../how-independent-reasons-add.md`, returned 2026-10-22 and kept verbatim\nbelow. The brief asked for real-life cases from different fields where each piece of evidence has a\npublished strength and the combined outcome is also published, so that combining rules can be checked\nagainst what happened. Its arithmetic marked [calc] is the helper's own on published numbers. Read by\nClaude before use; the cases Claude recomputed are marked in the note's § 5. Nothing below is a ruling.*\n\n---\n\n# How should several reasons for one claim combine? Real cases with published numbers\n\nScope: ten cases across seven fields, the best five first. No files were written. Tags: [FT] = I read the paper's own text. [FT-part] = I read substantial parts of it. [AB] = abstract only. [SEC] = secondary source. [calc] = my arithmetic on published numbers, not a published result.\n\n## 0. Bottom line\n\n1. **When the sources really are independent, adding evidence works, and adds in the way log-odds or inverse-variance does.** Alais & Burr measured a 1.425x gain against a predicted 1.414x. Four diverse election-forecast methods cut error by 48% against about 50% predicted. D-dimer multiplied cleanly onto the Wells score. Nothing in these cases looks like the Quadratic Energy Model's 0.50 to 0.57 to 0.70 (the 0.9-strength ladder from your brief). Where independence is real, the QEM figure is too low by a wide margin.\n2. **When findings share a cause, naive multiplication overshoots, usually by a moderate amount.** The joint log-evidence came out at roughly 0.6 to 0.9 of the independent sum in the clinical datasets [calc]. Even a damping of 0.6 leaves two 0.9-strength reasons at about 0.93, still far above the QEM's 0.70.\n3. **The disasters come from shared selection or shared error between sources that look independent.**\n   - Seven pooled magnesium trials gave odds ratio 0.45. The 58,050-patient trial gave 1.06.\n   - Eighty-three-study-scale ego-depletion pooling gave d = 0.62. A 23-lab preregistered replication gave 0.04.\n   - Three radiocarbon labs scattered about 3 times more (in variance) than their quoted errors allowed.\n   - Squaring a cot-death probability gave 1 in 73 million.\n   Internal consistency checks did not catch the magnesium case (heterogeneity p > 0.1).\n4. This supports the ruled default's \"best counts until independence is established\" arm as a conservative start. The same data show it costs a lot when independence is genuine.\n5. For the \"weakest premise governs\" arm, I found no dataset with separate premise strengths and an observed conjunction outcome. The nearest support is theoretical. L. Jonathan Cohen's Baconian conjunction takes the minimum (§4).\n\n## 1. Cases at a glance\n\n| # | Field | Separate numbers | Naive independent prediction | Observed or published | Verdict |\n|---|---|---|---|---|---|\n| A1 | Perception (audio + vision) | unimodal localization thresholds, 6 observers | threshold gain sqrt2 = 1.414 | 1.425 | holds |\n| B1 | Radiocarbon, 3 labs, one cloth | 646±31, 750±30, 676±24 BP | 689±16, 95% half-width about 32 yr | scatter-based 691±31, half-width about 81 yr [calc] | fails once, holds on 3 controls |\n| C1 | Paediatric diagnosis, 2 tests, n=93 | LR+ 3.88 and 7.73 | both positive: 96.6%; both negative: 5.0% | 93.3% (28/30); 10.3% (4/39) | overshoots in both directions |\n| C2 | Strep throat, 4 signs | LR+ 1.46, 1.65, 1.65, 2.20 | all four present: 64%, LR 8.7 | 55.7% (Centor); pooled LR 3.85 (CI 2.05 to 7.24) | moderate overshoot at the positive end |\n| C3 | Pulmonary embolism, Wells + D-dimer | prior 1.3% / 16.2% / 37.5% | D-dimer LR- constant across strata | implied LR- 0.38 / 0.34 / 0.22 [calc] | roughly holds |\n| D1 | Cardiology, 7 pooled trials | OR 0.45 (0.28 to 0.71) | the pooled OR | ISIS-4 OR about 1.06 | wrong, wrong sign |\n| D2 | Psychology | d = 0.62 pooled | the pooled d | 23-lab replication d = 0.04 | wrong |\n| E1 | Cot deaths, forensic | P(SIDS) 1/8543 | squared: 1/73 million | not independent | wrong by orders of magnitude |\n| E2 | Forensic DNA, 13 loci | per-locus match 1/13.66 | 68.3 pairs match at 9 loci | 122 observed | holds to a factor of 1.8 at 9 loci |\n| F1 | Election forecasts, 4 methods | typical error of each method | error falls by 29 / 42 / 50% for 2 / 3 / 4 methods | 23 / 37 / 48% | holds, slightly under |\n\n## 2. Cases in detail\n\n### A. Measurement and perception: independence holds\n\n**A1. Alais & Burr 2004 [FT-part]**\n- Task: locate a light blob or a sound click, alone and together. Six observers, with the blob blurred until visual and auditory precision matched.\n- Prediction: for independent noise, combined variance is the product over the sum of the two variances. At equal precision the threshold falls by sqrt2.\n- Result: bimodal thresholds were lower than the average unimodal threshold by 1.425, against 1.414 predicted. Against the best unimodal threshold the group test was t5 = 3.69, p < 0.01. No individual observer's bimodal threshold differed from prediction (all p > 0.2). Only two of six were individually significant against the best single cue.\n- The authors list correlated noise between modalities as one reason for individual deviations, citing Gepshtein & Banks 2003 and Oruç, Maloney & Landy 2003.\n\n**A2. Ernst & Banks 2002 [FT]**\n- Four observers judged the height of a ridge by sight, by touch, and by both.\n- Haptic threshold was about 0.085 of the 55 mm mean height. Visual threshold rose from 0.04 to 0.2 of it as stimulus noise went from 0% to 200%.\n- The model has no free parameters. The paper states that predicted and observed combined thresholds, and the weights, \"are similar\". The exact values appear only in Fig. 3c and 3d; the text gives none.\n\n### B. Measurement: independence fails or is overclaimed\n\n**B1. Shroud of Turin, Damon et al. 1989 [FT]**\n- Table 2: Arizona 646±31, Oxford 750±30, Zurich 676±24 BP. The inverse-variance mean is 689±16.\n- Ward & Wilson χ² test: 6.4 on 2 df, significance level 5%. The three controls (samples 2 to 4) gave χ² of 0.1, 1.3 and 2.4 (90%, 50%, 30%).\n- The paper concluded the quoted errors for sample 1 do not fully reflect the scatter. It switched to an unweighted mean of 691±31 with t5 multipliers 1.1 (68%) and 2.6 (95%). The 95% half-width is therefore about 81 years against 32 for the naive combination, a factor of 2.5 [calc].\n- Caveats:\n  - The Shroud itself is contested. Di Lazzaro et al. 2020 (PMC7597180) argue the three results cannot be pooled because of a spatial age gradient; I saw only a snippet.\n  - The lesson from the controls is that the same procedure worked three times in four.\n\n**B2. Henrion & Fischhoff 1986 [FT]**\n- Quoted uncertainties in physical constants show \"a consistent bias towards underestimating the actual errors\".\n- Measurements of c, 1875 to 1958 (27 values): Birge ratio 1.42 (P < 0.005), interquartile index 41% against 50% ideal, surprise index 11% against 2% ideal.\n- 306 particle-property results: Birge ratio 1.24, surprise index about 6%.\n- Recommended values 1928 to 1973: surprise index 57%.\n- Their suggested cause is early values anchoring later experiments, which makes errors correlated.\n- The Particle Data Group's rule for discrepant data (S = sqrt(χ²/(N−1)), applied when the ratio exceeds 1) is the working fix [FT, 2006 edition text]. Applied to B1, S = 1.78 and the error becomes ±28.6 [calc]. That is close to the ±31 the Shroud team chose.\n\n### C. Clinical diagnosis\n\n**C1. Two tests for biliary obstruction in 93 children [FT]**\n- Source: Cruz & Pericchi 2018, reproducing the Pereira & Pericchi 1990 data. Table 1: disease (n=45) ++28, +-12, -+1, --4; no disease (n=48) ++2, +-9, -+2, --35. Seven further children lacked the second test.\n- Derived strengths [calc]: test 1 sensitivity 0.889, specificity 0.771 (LR+ 3.88, LR- 0.144). Test 2 sensitivity 0.644, specificity 0.917 (LR+ 7.73, LR- 0.388). Prior 48.4%.\n- Naive versus observed:\n\n| Result | Naive | Observed | 95% CI of observed |\n|---|---|---|---|\n| ++ | 96.6% (odds 28.1) | 93.3% (odds 14.0) | 77.9 to 99.2% |\n| -- | 5.0% | 10.3% | 2.9 to 24.2% |\n| +- | 58.5% | 57.1% (12/21) | 34.0 to 78.2% |\n| -+ | 51.1% | 33.3% (1/3) | too few |\n\n- The authors give a Bayes factor of 0.62, \"mild evidence\" against independence, and conclude that independence overstates two positives and two negatives. In joint log-LR terms, the observed values are 0.80 (++) and 0.73 (--) of the naive sum [calc].\n- Caution: counts are tiny, and every naive figure lies inside the observed confidence interval.\n\n**C2. Strep throat: Centor score against pooled LRs [FT via fetch tool]**\n- Aalbers et al. 2011, pooled LRs: absence of cough LR+ 1.46 (LR- 0.53); fever 1.65 (0.71); tender anterior nodes 1.65 (0.56); any exudate 2.20 (0.58). Centor probabilities by score 0 to 4: 2.5, 6.5, 15.4, 31.6, 55.7%. The paper uses a derivation prevalence of 17.1%.\n- Naive products [calc]: all four present gives LR 8.74, which is 64% at the 17.1% prior. All four absent gives LR 0.122, which is 2.5%. The second matches the published 2.5% exactly. The first overshoots the published 55.7%.\n- Pooled validation LR for a score of exactly 4 is 3.85 (CI 2.05 to 7.24). That puts about 44% at the same prior, and the naive 8.74 lies outside that interval.\n- Across the whole 0 to 4 span the Centor-implied odds ratio is about 49, against a naive product of about 72. The log ratio is 0.91 [calc].\n- Centor calibration in validation: relative risks of 0.72 (0.49 to 1.06), 0.93 (0.73 to 1.17) and 1.14 (0.95 to 1.37) for scores 0 to 1, 2 to 3 and 4.\n- Caveats: the pooled LRs come from 9 to 21 studies each, with different definitions. Treat this as rough.\n\n**C3. Wells score + D-dimer for pulmonary embolism [FT-part]**\n- Wells 2001, 930 patients. Prevalence by pretest class: 1.3% (n=527), 16.2% (n=339), 37.5% (n=64). NPV of a negative D-dimer by class: 99.5%, 93.9%, 88.5%.\n- Implied D-dimer LR- by class [calc]: 0.38, 0.34, 0.22. Roughly constant across a 30-fold range of prior, which is what multiplication needs. The high-class CI is wide (NPV 69.9 to 97.6).\n- Combined strategy, low pretest probability plus negative D-dimer: 437 patients, 1 event.\n- Why it works: a clinical score and a blood assay have different mechanisms. The strep signs are all symptoms of one throat.\n\n**C4. Accuracy versus calibration [mixed]**\n- Weintraub 1984 [AB], 147 patients: ECG stress test and thallium scan against angiography. Sensitivity (not specificity) of each test depended partly on the other, yet sequential Bayes was \"remarkably close\" to the tabulated data.\n- de Dombal 1972 [FT]: 304 patients, system 91.8% accurate against 79.6% for the senior clinician. The system is widely described as independence Bayes; I did not verify that in this paper.\n- Seymour, Green & Vaz 1990 [FT-part]: independence Bayes \"may lead to overconfident estimates\" when several risk factors contribute.\n- Zadrozny & Elkan 2001 [FT-part]: naive Bayes scores are \"typically too extreme\" but rank well. On the KDD'98 test set, MSE for naive Bayes is 0.1011, worse than predicting the base rate (0.0960) and worse than monotone-binned naive Bayes (0.0953). On CoIL the figures are 0.1341, 0.1119 and 0.1074. Niculescu-Mizil & Caruana 2005 [FT-part] report the same over-extremity across eight datasets, in figures only.\n- Reading: summing log-odds ranks well, and the scale needs a calibration map. The QEM is, in effect, a fixed saturating one.\n- What the textbooks say [SEC, via de Souza & de Alencar 2026, partial text]:\n  - McGee 2002: combine no more than three findings.\n  - The Rational Clinical Examination: use 3 to 4 findings.\n  - Newman & Kohn: multiply only if conditionally independent.\n- I found no published numeric comparison of product-of-LRs against logistic regression. The Centor score is the nearest thing, a summed-points rule. I could not read Ebell's strep review (JAMA 2000), Fryback 1978 or the Rational Clinical Examination itself.\n\n### D. Pooling many apparently independent studies\n\n**D1. Intravenous magnesium after myocardial infarction [FT-part]**\n- Teo et al. 1991: seven trials, 1,301 patients, 25/657 (3.8%) against 53/644 (8.2%) deaths. Typical odds ratio 0.45 (0.28 to 0.71); the heterogeneity test passed (χ² = 7.6, df 6, p > 0.1).\n- ISIS-4 1995: 58,050 patients, 2,216 (7.64%) against 2,103 (7.24%) deaths at 35 days. The odds ratio is about 1.06 [calc]; the CI of 0.99 to 1.13 is from a secondary summary.\n- The pooled estimate and the large trial differ by a factor of 2.4 in odds ratio [calc], with opposite sign.\n- Egger & Smith 1995 [first paragraph only] call it a false-positive meta-analysis. They note seven small trials sufficed to reach P < 0.001.\n- LeLorier et al. 1997 [FT-part]: 12 large trials against 19 prior meta-analyses, 40 outcomes. Kappa 0.35 (0.06 to 0.64); the large trials' outcomes were not predicted 35% of the time.\n\n**D2. Ego depletion and replication [FT-part]**\n- Hagger 2016: an earlier meta-analysis found d = 0.62 across 198 tests. A 23-lab preregistered replication (N = 2,141) found d = 0.04 (95% CI −0.07 to 0.15). The authors also report bias-corrected estimates of g = 0.24 (trim-and-fill) and 0.003 (PEESE).\n- Open Science Collaboration 2015 [AB]: 100 studies. Mean effect fell from r = 0.403 to 0.197; 97% significant originally against 36% on replication. Naively combining original with replication, assuming no bias, left 68% significant.\n\n### E. Law and forensics\n\n**E1. Sally Clark: squaring a probability [FT]**\n- CESDI risk of one SIDS death for a low-risk family was 1/8543. Squaring gives 1 in 73 million.\n- The Royal Statistical Society (2001) said this is valid only if cases arise independently, and the error is \"very large, and in one particular direction\".\n- Hill 2004: after one cot death the risk of a second is much higher. He estimates second cot deaths occur about 4 to 5 times a year in the UK, against the roughly one per century the 73 million figure implied.\n- CESDI counts: 5 of 323 SIDS families had a previous SIDS death against 2 of 1,288 controls, about 10 times [calc, SEC via a Hill BMJ response].\n- Counterpoint, Sesardić 2007 [FT-part]: the direction of dependence is empirical; careful parents after a first death could lower it. The sign of the error is not guaranteed.\n- This is about events, not evidence for a claim, but it shows the cost of independence over a shared cause.\n\n**E2. Arizona offender database [SEC]**\n- 65,493 profiles give 2.14 billion pairs. Per-locus match probability is 1/13.66. Brenner's web page tabulates expected against observed partial matches under the product rule; observed counts come from the court-ordered report.\n\n| Matching loci | Expected | Observed |\n|---|---|---|\n| 9 | 68.3 | 122 (1.8x) |\n| 10 | 2.2 | 20 (9x) |\n| 11 | 0.05 | 1 |\n| 12 | 1/1600 | 1 |\n\n- Brenner argues 40 multiplied factors err by only one factor of 1.8 at nine loci. The tail excess is most likely relatives, a hidden common cause. The 11- and 12-locus matches were reportedly relatives.\n- Weir (PMC2585748) and Mueller 2008 [AB] discuss population structure and kinship.\n\n**E3. A false-positive ceiling on a DNA match [FT excerpt, course copy]**\n- Thompson et al.: random match probability 1 in 10⁹ and prior odds 1:1000 give posterior odds of 10⁶:1 with no error. With a false-positive probability of 1 in 10,000, posterior odds fall to 10:1.\n- A shared failure route, lab error, caps the combined strength. Their example: two independent tests each at 1 in 100 give 1 in 10,000 on both, so independence of errors is what makes a repeat count.\n\n**E4. Eyewitnesses**\n- I found no published dataset with numeric ground truth for multi-witness corroboration.\n- Clark & Wells 2008 [AB] compute multi-witness diagnosticity from a signal-detection model, not from observed data.\n- Gabbert, Memon & Allan 2003 [AB]: 71% of witnesses who discussed an event went on to recall items they never saw. Talking witnesses are not independent.\n\n**E5. Schum, Cohen, Fenton**\n- Schum [FT-part, 2009 and 2000 papers; the book unread]:\n  - Corroboration (the same event reported by several sources) is redundant. If the first source were perfectly credible, a second adds nothing; it \"springs to life\" only as the first is doubted.\n  - Convergence (different events pointing at one conclusion) can be redundant or synergistic.\n  - Ignoring redundancy overstates joint force; ignoring synergy understates it.\n  - Worked likelihood-ratio chains exist for the Sacco and Vanzetti witnesses, with no ground-truth outcome.\n- Cohen, via Wagner's 1979 Duke Law Journal review and Schum's Michigan Law Review review [SEC]:\n  - Baconian support is ordinal, with no arithmetic.\n  - The conjunction of propositions on the same subject matter takes the smallest component. Where subject matter differs, the components are incommensurable and each stands alone.\n  - Convergent or corroborative independent evidence raises support strictly, with no magnitude given.\n  - The min-rule matches your \"weakest premise governs\".\n- Fenton, Neil & Berger 2016 [FT-part]: Collins and Clark both failed to model dependence. They offer no numeric ground-truth example.\n\n### F. Forecast combination\n\n**F1. Graefe et al. 2014 [FT, preprint]**\n- Four methods (poll projections, experts, models, Iowa Electronic Markets), 2004 to 2012 elections, error reduction against the typical component:\n  - Two methods: 23% on average (17% models + polls, 29% IEM + experts). Independent equal-error prediction is 29% [calc].\n  - Three methods: 37%, against 42% predicted [calc].\n  - Four methods: 48%, against 50% predicted [calc].\n- The authors attribute the weak models-plus-polls gain to models already using poll data.\n- Caveat: only three elections underlie that table.\n- Batchelor & Dua (via Graefe): the most similar forecasters gave a 2% error reduction, the most diverse 21%. In the economic GNP comparison the corresponding figures are 11% and 23%.\n\n**F2. Clemen & Winkler 1985 [FT excerpt]**\n- Equivalent independent sources: n = k / (1 + (k−1)ρ), with limit 1/ρ.\n- At ρ = 0.8, which they say fits their football and economic forecast data, the limit is 1.25.\n\n## 3. Cross-case quantities\n\nJoint log-evidence as a fraction of the independent sum [calc, small samples]:\n- Alais & Burr, precision: about 1.0.\n- Wells + D-dimer: roughly 1.\n- Graefe: 0.84 / 0.84 / 0.92 for 2 / 3 / 4 methods, expressed as effective sources over actual.\n- Strep, full span: 0.91. Strep, all four signs present: 0.62.\n- Biliary: 0.73 to 0.80.\n- Clemen & Winkler at ρ = 0.8: a ceiling of 1.25 sources.\n\nFor two 0.9-strength reasons, and assuming 0.9 maps to a likelihood ratio of 9 from a 0.5 prior, a fraction f of the summed log-odds gives:\n- f = 1.0: 0.988\n- f = 0.75: 0.964\n- f = 0.6: 0.933\n- QEM: 0.70\n\nConsistent with your ruled default (my inference):\n- \"Best counts until independence\" fits the shared-bias disasters in D1, D2, B1 and E1.\n- It would understate genuinely independent sources such as A1 and F1.\n- A damping such as effective sources = k / (1 + (k−1)ρ), once independence is partly established, is the pattern the data support.\n\n## 4. Not found or not read\n\n- No multi-witness ground-truth dataset; no numeric product-of-LRs versus logistic-regression comparison; no premise-conjunction dataset.\n- Not retrieved: Many Labs (Klein 2014) and the Ottawa ankle rules. The Ottawa rules were not pursued because they are a decision rule rather than combined strengths.\n- Unread beyond abstract or snippet: Ebell 2000, Fryback 1978, Weintraub 1984, Clark & Wells 2008, Gabbert 2003, Mueller 2008, Hand & Yu 2001, Di Lazzaro 2020, OSC 2015. Not read at all: the Schum and Cohen books.\n- Egger & Smith's table was paywalled. The ISIS-4 CI of 0.99 to 1.13 is from a secondary summary.\n\n## 5. References\n\n- Aalbers J, et al. (2011). Predicting streptococcal pharyngitis in adults in primary care: a systematic review of the diagnostic accuracy of symptoms and signs and validation of the Centor score. BMC Med 9:67. doi:10.1186/1741-7015-9-67; https://pmc.ncbi.nlm.nih.gov/articles/PMC3127779 [FT via fetch tool; Table 4 arithmetic cross-checked]\n- Alais D, Burr D (2004). The ventriloquist effect results from near-optimal bimodal integration. Curr Biol. doi:10.1016/j.cub.2004.01.029; https://www.cell.com/current-biology/fulltext/S0960-9822(04)00043-0 [FT-part]\n- Batchelor R, Dua P (1995), via Graefe et al. [SEC]\n- Brenner C. Arizona DNA databases \"matches\". http://www.dna-view.com/ArizonaMatch.htm [SEC]\n- Clark SE, Wells GL (2008). On the diagnosticity of multiple-witness identifications. Law Hum Behav. doi:10.1007/s10979-007-9115-7 [AB]\n- Clemen RT, Winkler RL (1985). Limits for the precision and value of information from dependent sources. Oper Res 33(2):427-442. doi:10.1287/opre.33.2.427; https://people.duke.edu/~clemen/bio/Published%20Papers/01.Limits-Clemen&Winkler-OR-85.pdf [FT excerpt]\n- Cohen LJ (1977). The Probable and the Provable. Oxford: Clarendon. https://academic.oup.com/book/3708 [AB]; via Wagner, Duke Law J 1979, https://scholarship.law.duke.edu/dlj/vol28/iss4/6, and Schum, Mich Law Rev 77:446 (1979), https://repository.law.umich.edu/cgi/viewcontent.cgi?article=3673&context=mlr [SEC]\n- Cruz J, Pericchi LR (2018). Sequential Bayesian tests and the hypothesis of independent or naive Bayes. Rev Fac Cienc 7(1):112-123. doi:10.15446/rev.fac.cienc.v7n1.67107 [FT]; data from Pereira CAB, Pericchi LR (1990), Analysis of diagnosability, Applied Statistics, pp. 189-204\n- Damon PE, et al. (1989). Radiocarbon dating of the Shroud of Turin. Nature 337:611-615. doi:10.1038/337611a0; reprint https://www.shroud.com/nature.htm [FT]\n- de Dombal FT, et al. (1972). Computer-aided diagnosis of acute abdominal pain. BMJ 2:9-13. doi:10.1136/bmj.2.5804.9 [FT-part]\n- de Souza MB, de Alencar JN (2026). Likelihood ratios and the dependence of clinical evidence. Theor Med Bioeth. doi:10.1007/s11017-026-09770-5 [FT-part; source of the McGee, Rational Clinical Examination and Newman & Kohn statements]\n- Di Lazzaro P, et al. (2020). Statistical and proactive analysis of an inter-laboratory comparison: the radiocarbon dating of the Shroud of Turin. https://pmc.ncbi.nlm.nih.gov/articles/PMC7597180 [snippet only]\n- Egger M, Davey Smith G (1995). Misleading meta-analysis. BMJ 310:752. doi:10.1136/bmj.310.6982.752 [first paragraph only]\n- Ernst MO, Banks MS (2002). Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415:429-433. doi:10.1038/415429a [FT]\n- Fenton N, Neil M, Berger D (2016). Bayes and the law. Annu Rev Stat Appl 3:51-77. doi:10.1146/annurev-statistics-041715-033428; PMC4934658 [FT-part]\n- Fryback DG (1978). Bayes' theorem and conditional nonindependence of data in medical diagnosis. Comput Biomed Res 11:423-434. doi:10.1016/0010-4809(78)90001-0 [summary only]\n- Gabbert F, Memon A, Allan K (2003). Memory conformity. Appl Cogn Psychol 17:533-543. doi:10.1002/acp.885 [AB]\n- Graefe A, Armstrong JS, Jones RJ, Cuzán AG (2014). Combining forecasts: an application to elections. Int J Forecast 30(1):43-54. doi:10.1016/j.ijforecast.2013.02.005; https://faculty.wharton.upenn.edu/wp-content/uploads/2014/03/16.-JSA.-Combining-forecasts-An-application-to-elections.pdf [FT, preprint]\n- Hagger MS, et al. (2016). A multilab preregistered replication of the ego-depletion effect. Perspect Psychol Sci. doi:10.1177/1745691616652873 [FT-part]\n- Henrion M, Fischhoff B (1986). Assessing uncertainty in physical constants. Am J Phys 54(9):791-798. https://www.gwern.net/doc/statistics/bias/1986-henrion.pdf [FT]\n- Hill R (2004). Multiple sudden infant deaths: coincidence or beyond coincidence? Paediatr Perinat Epidemiol 18:320-326. doi:10.1111/j.1365-3016.2004.00560.x [FT-part]\n- ISIS-4 Collaborative Group (1995). Lancet 345:669-685. doi:10.1016/S0140-6736(95)90865-X [AB]\n- LeLorier J, et al. (1997). Discrepancies between meta-analyses and subsequent large randomized, controlled trials. N Engl J Med. doi:10.1056/NEJM199708213370806 [FT-part]\n- Mueller LD (2008). Can simple population genetic models reconcile partial match frequencies observed in large forensic databases? J Genet 87(2):101-108 [AB]\n- Niculescu-Mizil A, Caruana R (2005). Predicting good probabilities with supervised learning. ICML. doi:10.1145/1102351.1102430 [FT-part]\n- Open Science Collaboration (2015). Estimating the reproducibility of psychological science. Science 349:aac4716. doi:10.1126/science.aac4716 [AB]\n- Particle Data Group, Review of Particle Physics (2006 edition), §5.2.2 unconstrained averaging, https://archive.org/stream/Review_of_Particle_Physics/rpp-2006-book_djvu.txt [FT excerpt]\n- Royal Statistical Society (2001). Statement on the Sally Clark case. https://rss.org.uk/RSS/media/File-library/Membership/Sections/2020/Sally-Clark-RSS-statement-2001.pdf [FT]\n- Schum DA (1994/2001). The Evidential Foundations of Probabilistic Reasoning. Wiley / Northwestern UP [not read]; Schum (2009), A science of evidence, Law Probab Risk, https://scispace.com/pdf/a-science-of-evidence-contributions-from-law-and-probability-5bfzdxdsp7.pdf; Schum (2000), Alternative views of argument construction, Cardozo L Rev 22:1461 [FT excerpts]\n- Sesardić N (2007). Sudden infant death or murder? Br J Philos Sci. doi:10.1093/bjps/axm015 [FT-part]\n- Seymour DG, Green M, Vaz FG (1990). BMJ 300:223-226. doi:10.1136/bmj.300.6719.223 [FT-part]\n- Teo KK, Yusuf S, Collins R, Held PH, Peto R (1991). BMJ 303:1499-1503. doi:10.1136/bmj.303.6816.1499 [FT-part]\n- Thompson WC, et al. (2003). How the probability of a false positive affects the value of DNA evidence. J Forensic Sci 48(1):47-54; copy read: https://www.site.uottawa.ca/~gvj/Courses/CSI4539-OLD/lectures/JFSFalsePos.pdf [FT excerpt; co-authors from memory]\n- Weintraub WS, et al. (1984). Am J Cardiol 54:43-49. doi:10.1016/0002-9149(84)90301-1 [AB]\n- Weir BS, The rarity of DNA profiles. https://pmc.ncbi.nlm.nih.gov/articles/PMC2585748 [snippet only]\n- Wells PS, et al. (2001). Excluding pulmonary embolism at the bedside without diagnostic imaging. Ann Intern Med 135:98-107. doi:10.7326/0003-4819-135-2-200107170-00010 [FT-part]\n- Zadrozny B, Elkan C (2001). Obtaining calibrated probability estimates from decision trees and naive Bayesian classifiers. ICML. https://cseweb.ucsd.edu/~elkan/calibrated.pdf [FT-part]\n"}