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This skill covers Bayesian estimation and inference in quantitative social science. Use when the user is specifying priors, running MCMC, diagnosing chain convergence, or reporting posterior summaries — including hierarchical models, Bayesian structural models, and small-sample settings where priors regularize. Triggers on "Bayesian estimation", "Bayesian inference", "MCMC", "Markov chain Monte Carlo", "Stan", "PyMC", "NumPyro", "prior", "posterior", "credible interval", "Bayesian structural", "Bayesian BLP", "Bayesian DSGE", "hierarchical model", "random effects Bayesian", "posterior predictive check", "Bayes factor", "prior predictive check", "NUTS", "HMC", "Hamiltonian Monte Carlo", "R-hat", "rhat", "effective sample size", "ESS", "Bayesian calibration", "posterior distribution", "prior elicitation", "weakly informative prior", "brms", "rstanarm", "cmdstanpy", "pymc", "arviz".

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Opinionated Bayesian modeling workflow with PyMC and ArviZ. Contains critical guardrails (nutpie sampler, prior/posterior predictive checks, LOO-PIT calibration, prior sensitivity checks, 94% HDI, non-centered parameterizations, reproducible seeds) that agents won't apply unprompted — always consult before writing Bayesian model code. Trigger on: building probabilistic/Bayesian models, prior elicitation, MCMC inference, convergence diagnostics (divergences, R-hat, ESS), model comparison (LOO-CV, ELPD, stacking weights), hierarchical/multilevel models, count regressions, logistic regression with uncertainty, prior sensitivity analysis, reporting Bayesian results, or mentions of PyMC, ArviZ, InferenceData, credible intervals, posterior distributions, shrinkage, uncertainty quantification. Also trigger for model comparison, diagnosing sampling problems, choosing priors, or presenting stats to non-technical audiences.

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Designs Bayesian clinical trials including Phase I dose-finding (BOIN, CRM, EWOC, mTPI-2), meta-analytic-predictive (MAP) priors with robust mixtures for external data borrowing, EXNEX for basket trials, hierarchical models for safety AE (Berry-Berry), Bayesian platform trials (I-SPY 2, GBM AGILE, REMAP-CAP), and posterior probability stopping rules. Covers FDA Bayesian Devices Guidance (2010), FDA Bayesian Methodology in Drugs Draft (January 2026), BOIN Fit-for-Purpose qualification (December 2021), and Project Optimus dose-optimisation. Use when designing dose-finding studies, platform trials, or sensitivity analyses with informative priors.

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Designs Bayesian clinical trials including Phase I dose-finding (BOIN, CRM, EWOC, mTPI-2), meta-analytic-predictive (MAP) priors with robust mixtures for external data borrowing, EXNEX for basket trials, hierarchical models for safety AE (Berry-Berry), Bayesian platform trials (I-SPY 2, GBM AGILE, REMAP-CAP), and posterior probability stopping rules. Covers FDA Bayesian Devices Guidance (2010), FDA Bayesian Methodology in Drugs Draft (January 2026), BOIN Fit-for-Purpose qualification (December 2021), and Project Optimus dose-optimisation. Use when designing dose-finding studies, platform trials, or sensitivity analyses with informative priors.

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Designs Bayesian clinical trials including Phase I dose-finding (BOIN, CRM, EWOC, mTPI-2), meta-analytic-predictive (MAP) priors with robust mixtures for external data borrowing, EXNEX for basket trials, hierarchical models for safety AE (Berry-Berry), Bayesian platform trials (I-SPY 2, GBM AGILE, REMAP-CAP), and posterior probability stopping rules. Covers FDA Bayesian Devices Guidance (2010), FDA Bayesian Methodology in Drugs Draft (January 2026), BOIN Fit-for-Purpose qualification (December 2021), and Project Optimus dose-optimisation. Use when designing dose-finding studies, platform trials, or sensitivity analyses with informative priors.

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Designs Bayesian clinical trials including Phase I dose-finding (BOIN, CRM, EWOC, mTPI-2), meta-analytic-predictive (MAP) priors with robust mixtures for external data borrowing, EXNEX for basket trials, hierarchical models for safety AE (Berry-Berry), Bayesian platform trials (I-SPY 2, GBM AGILE, REMAP-CAP), and posterior probability stopping rules. Covers FDA Bayesian Devices Guidance (2010), FDA Bayesian Methodology in Drugs Draft (January 2026), BOIN Fit-for-Purpose qualification (December 2021), and Project Optimus dose-optimisation. Use when designing dose-finding studies, platform trials, or sensitivity analyses with informative priors.

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Designs Bayesian clinical trials including Phase I dose-finding (BOIN, CRM, EWOC, mTPI-2), meta-analytic-predictive (MAP) priors with robust mixtures for external data borrowing, EXNEX for basket trials, hierarchical models for safety AE (Berry-Berry), Bayesian platform trials (I-SPY 2, GBM AGILE, REMAP-CAP), and posterior probability stopping rules. Covers FDA Bayesian Devices Guidance (2010), FDA Bayesian Methodology in Drugs Draft (January 2026), BOIN Fit-for-Purpose qualification (December 2021), and Project Optimus dose-optimisation. Use when designing dose-finding studies, platform trials, or sensitivity analyses with informative priors.

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Route BayesianOptimization package tasks for black-box Bayesian optimization, HPO, acquisition functions, constraints, typed domains, domain reduction, and checkout maintenance.

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Run Bayesian phylogenetic analysis with MrBayes, BEAST2, RevBayes, and PhyloBayes including MCMC convergence diagnostics and model comparison. Use when needing posterior probability support, Bayesian model averaging, site-heterogeneous models for deep phylogenies, or formal model comparison via stepping-stone sampling.

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Think and work like an expert Bayesian Statistician. Use when a task calls for Bayesian Statistician judgment. Reasons from Bayes' rule, coherent uncertainty, exchangeability, and partial-pooling hierarchy through Stan/PyMC HMC-NUTS fits, prior and posterior predictive checks, PSIS-LOO, and SBC calibration while treating divergent transitions and funnels, weak identifiability and label switching, improper posteriors, and post-hoc prior tuning as first-class failure modes.

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临床诊断思维 (临床诊断思维 / 临床推理 (Clinical Diagnostic Reasoning) — 医生『怎么想病』的元学科:从症状/体征/检查到诊断结论的认知操作系统,从业者(临床医生/住院医/规培生,尤其全科/急诊/大内科等以未分化主诉为生的科室)、医学生与医学教育者、诊断安全与质量改进研究者、以及做医疗 AI 辅助诊断产品的人的视角。覆盖: (a) 第一性张力 — **直觉模式识别 (System 1: illness scripts 疾病脚本 / pattern recognition / gestalt, 『资深人一眼认出 aunt Minnie』) ⇄ 分析性推理 (System 2: hypothetico-deductive 假设演绎 / Bayesian 概率更新)** 的 dual-process 双过程理论 (Kahneman→Croskerry/Norman 谱系), 资深≠更会分析而是『脚本库更大+校准更好』; 更深层论战 — **『认知去偏可教 (Croskerry: bias awareness / cognitive forcing strategies / diagnostic timeout) ⇄ 偏倚标签是马后炮、知识结构才是主因 (Norman/Sherbino/Monteiro: debiasing 干预 transfer 证据弱, bias 是 hindsight 标签)』** — 本行最核心学术对垒; 『概率思维 (验前概率 × 似然比 → 验后概率, Pauker-Kassirer test/treatment threshold 阈值模型) ⇄ 穷尽式排查 (rule-out everything / 防御性医疗 / VOMIT)』; 『临床 gestalt ⇄ 结构化临床决策规则 (Wells/PERC/HEART)』; 『诊断简约 Occam's razor ⇄ Hickam's dictum (病人可以同时得 N 个病)』; 『床旁体格检查复兴 (Verghese Stanford 25 / McGee 循证体检) ⇄ 影像检验替代床旁』; (b) 方法论正典 — illness script theory (Schmidt/Boshuizen: enabling conditions/fault/consequences 三段结构), problem representation + semantic qualifiers 问题表征与语义限定词 (Bowen NEJM 2006, 把病人翻成 one-liner), hypothetico-deductive model (Elstein 1978《Medical Problem Solving》: 早期假设生成+定向检验), Bayesian 工具箱 (sensitivity/specificity/LR/Fagan nomogram/SnNout-SpPin), threshold model (Pauker-Kassirer NEJM 1975/1980), 认知偏倚分类学 (anchoring/premature closure/availability/confirmation/base-rate neglect/search satisficing/diagnostic momentum — Croskerry 偏倚清单), 去偏与元认知策略 (diagnostic timeout/cognitive forcing/Ely checklist/calibration), schema-based reasoning (Clinical Problem Solvers schemas: 按 pivot 症状走分支), reflective practice 结构化反思 (Mamede/Schmidt), 诊断错误科学 (NAM 2015 报告定义 / Newman-Toker Big Three / Hardeep Singh e-triggers / SAFER Dx 框架); (c) 行业结构与角色 — 医学生→实习/住院医 (晨会 morning report/查房被 pimping/汇报训练)→主治 attending→master clinician (NEJM CPC discussant/晨会大师如 Dhaliwal); 配套生态: 医学教育者 (clinical reasoning curriculum + 评估: script concordance test/key features exam/OSCE), 诊断安全研究者 (SIDM/AHRQ), 诊断辅助与 CDS 工具开发者 (DDx generator/AI); (d) 核心工作流 — 数据采集 (病史为王 + 循证体检 + 针对性检验影像) → 问题表征 (one-liner + semantic qualifiers) → 鉴别诊断生成 (schema / 解剖定位法 / VINDICATE-M 病因筛, 按『常见可能 × 致命不能漏 can't-miss』双轴排序) → 假设定向检验 (按 LR 选检查 / 阈值决策) → working diagnosis + 安全网 (red flags 交代 / test of time / test of treatment) → 反馈校准 (follow-up / M&M / diagnostic timeout); 教学工作流: 晨会渐进披露汇报 / CPC / SNAPPS / one-minute preceptor / virtual morning report; AI 增强工作流 (2023-2026: LLM 鉴别诊断头脑风暴 / OpenEvidence 检索 / ambient scribe 释放认知带宽 + 自动化偏倚 guardrails); (e) 产出物 — one-liner, problem list, prioritized DDx, assessment & plan (按问题分层), 晨会/CPC 汇报, M&M 复盘, 诊断不确定性沟通 (『最可能是 X, 但出现 Y 红旗立刻回来』); (f) 教育与评估 — script concordance test / key feature exam / EPA / 里程碑; 中国语境: 人卫《诊断学》教材 / 执业医师考试 / 规培结业临床思维考核; (g) 争议/批判 — debiasing 之争 (Croskerry vs Norman-Sherbino『knowledge is the cure』, 去偏 RCT 效果弱 / bias 标签不可证伪), 诊断错误率数字之争 (『10-15%』经典估计 / Newman-Toker 79.5 万美国年严重伤害外推方法被质疑 / 尸检符合率), dual-process 二分被批过度简化 (连续谱 / 难以实证分离), 决策规则 vs gestalt (资深 gestalt 常不输 Wells 类规则 / 算法厌恶), vignette 研究外推性 + context/case specificity (推理高度内容绑定不可通用迁移 [Norman/Eva] — 对『教推理通用课』产业的根本批判), AI 辅助诊断 2023-2026 (GPT-4 在 NEJM CPC/vignette 追平或超医生 [Kanjee 2023 JAMA / Goh 2024 JAMA Netw Open『AI alone > physician+AI』悖论] / Google AMIE / OpenEvidence 爆发 vs 自动化偏倚 / 去技能化 / 真实环境验证缺失), 防御性医疗与过度检查 (incidentaloma 瀑布 / VOMIT), 体检衰亡之争, pimping 教学法争议; (h) 流派/思想谱系 — 决策科学/Bayesian 派 (Ledley-Lusted 1959 → Elstein/Kassirer/Sox/Pauker/Eddy → Brush) vs 认知心理/双过程派 (Kahneman-Tversky → Croskerry/Graber) vs 教育认知派 (Schmidt/Boshuizen illness scripts → Norman/Eva/Mamede/Durning 情境认知) vs 诊断安全/系统派 (NAM 2015 / Newman-Toker / Hardeep Singh / Graber-SIDM: 错误=系统×认知共因) vs 床旁临床派 (Osler 传统 → Tierney aphorisms / Verghese / McGee / Dhaliwal / Saint: 病史体检为王 + 刻意练习) vs AI/计算派 (INTERNIST-1/DXplain 专家系统 → Isabel → LLM 世代 Rodman/Topol)。不含: 具体专科治疗方案与手术决策深度 (足踝外科/种植牙等另有 skill), 中医辨证 (另有 skill), EBM 文献批判性评价方法学 (相关但本 skill 聚焦诊断推理本身), 护理诊断体系 (NANDA), 影像/病理知觉型读片训练 (相邻但独立), 精神科 DSM 结构化访谈细节, 医患沟通技巧全集 (只覆盖诊断不确定性沟通), 患者自查/自我诊断指

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Bayesian parameter estimation with MCMC (emcee) and probabilistic programming (PyMC). Posterior distributions, corner plots, model evidence, convergence diagnostics. Use when you need full posterior distributions, not just point estimates.

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Guided statistical analysis for research data - test selection, assumption checking, effect sizes, power analysis, Bayesian alternatives, and APA-formatted reporting. Use whenever a user wants to compare groups, test a hypothesis, analyze experimental or survey data, check statistical assumptions, compute required sample sizes, or write up results - even if they never name a specific test. Covers t-tests, ANOVA, chi-square, correlation, regression, non-parametric and Bayesian methods. For low-level model APIs, see the statsmodels and pymc skills.

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Guided statistical analysis for research data - test selection, assumption checking, effect sizes, power analysis, Bayesian alternatives, and APA-formatted reporting. Use whenever a user wants to compare groups, test a hypothesis, analyze experimental or survey data, check statistical assumptions, compute required sample sizes, or write up results - even if they never name a specific test. Covers t-tests, ANOVA, chi-square, correlation, regression, non-parametric and Bayesian methods. For low-level model APIs, see the statsmodels and pymc skills.

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Bayesian modeling with PyMC. Build hierarchical models, MCMC (NUTS), variational inference, LOO/WAIC comparison, posterior checks, for probabilistic programming and inference.

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Estimates time-scaled phylogenies, molecular-clock rates, effective reproduction number R_e, and population dynamics from dated pathogen genomes using TreeTime (maximum-likelihood) and BEAST2 (Bayesian; strict/relaxed clocks; coalescent, Bayesian-Skyline, Skygrid, Birth-Death-Skyline, and sampled-ancestor priors; structured coalescent via MASCOT). Covers root-to-tip clock QC via TempEst, date-randomisation tests, recombination masking via Gubbins/ClonalFrameML before clock inference for recombining bacteria, BDSKY origin-vs-rootHeight pitfalls, sampling-bias correction, multi-chain convergence diagnostics, and reconciling phylodynamic R_e with case-based R_t. Use when dating outbreak origins, estimating substitution rates, inferring R_e through time, building time-calibrated Nextstrain Augur trees, choosing between strict and relaxed clocks, fitting Birth-Death-Skyline models, diagnosing temporal-signal failure, running MASCOT for structured-population analyses, or using UShER for pandemic-scale placement.

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Bayesian modeling with PyMC 5: priors, likelihood, NUTS/ADVI sampling, diagnostics (R-hat, ESS), LOO/WAIC comparison, prediction. Hierarchical, logistic, GP variants; predictive checks.

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Guided statistical analysis: test choice, assumption checks, effect sizes, power, APA reporting. Pick tests, verify assumptions, or format results for publication. Covers frequentist (t-test, ANOVA, chi-square, regression, correlation, survival, count, reliability) and Bayesian. Use statsmodels or pymc-bayesian-modeling to fit.

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"Apply Bayesian averaging to rank items by combining observed ratings with prior expectations. Use this skill when the user needs to rank items with varying review counts, build a 'top rated' list that handles low-sample items fairly, or implement IMDB-style weighted rating — even if they say 'weighted average rating', 'IMDB formula', or 'ranking with prior'.".

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Estimates time-scaled phylogenies, molecular-clock rates, effective reproduction number R_e, and population dynamics from dated pathogen genomes using TreeTime (maximum-likelihood) and BEAST2 (Bayesian; strict/relaxed clocks; coalescent, Bayesian-Skyline, Skygrid, Birth-Death-Skyline, and sampled-ancestor priors; structured coalescent via MASCOT). Covers root-to-tip clock QC via TempEst, date-randomisation tests, recombination masking via Gubbins/ClonalFrameML before clock inference for recombining bacteria, BDSKY origin-vs-rootHeight pitfalls, sampling-bias correction, multi-chain convergence diagnostics, and reconciling phylodynamic R_e with case-based R_t. Use when dating outbreak origins, estimating substitution rates, inferring R_e through time, building time-calibrated Nextstrain Augur trees, choosing between strict and relaxed clocks, fitting Birth-Death-Skyline models, diagnosing temporal-signal failure, running MASCOT for structured-population analyses, or using UShER for pandemic-scale placement.

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Bayesian data analysis — priors, likelihoods, posterior computation, model comparison, and honest reporting.

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Expert-level statistics knowledge. Use when working with probability distributions, hypothesis testing, regression, Bayesian statistics, statistical inference, experimental design, ANOVA, or statistical modeling. Also use when the user mentions 'p-value', 'confidence interval', 'hypothesis test', 'regression', 'ANOVA', 'chi-square', 't-test', 'Bayesian', 'maximum likelihood', 'statistical significance', 'correlation', 'normal distribution', or 'sampling distribution'.

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METAINFORMANT rules for directory src/metainformant/math/bayesian. Use when editing, adding tests, or reviewing code under this path. Read the linked AGENTS.md first; use uv only, write outputs to output/, real implementations.

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Knowledge base from the NIST/SEMATECH e-Handbook of Statistical Methods (NIST HB 151) — the practical statistics reference for engineering, metrology, and quality. Use for: exploratory data analysis and the four univariate assumptions (4-plot); measurement process characterization including bias/precision, calibration designs, gauge R&R, and ISO/GUM uncertainty budgets; production process characterization (stability vs. capability); process modeling and regression (LS/WLS/NLS/LOESS); design of experiments (screening, fractional/factorial, response-surface, Taguchi); statistical process control (Shewhart/CUSUM/EWMA charts, capability indices, acceptance sampling); product/process comparisons (hypothesis tests and confidence intervals for 1/2/3+ groups, ANOVA, multiple comparisons); and reliability (lifetime & repair-rate models, accelerated testing, reliability growth). Scope limits: this is applied frequentist statistics for measurement and quality — it does NOT reproduce the per-distribution formula galleries, worked case studies, datasets, plot images, or Dataplot/R code of the original web Handbook (those are described, not copied); it is thin on modern machine learning, Bayesian methods beyond conjugate reliability priors, time-series/forecasting, and Bayesian experimental design.

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