[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6AFKH5S94NTC70AYE6CBE48":3,"skill-same:01M6AFKH5S94NTC70AYE6CBE48":97},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":23,"publishedAt":36,"linkOnly":37,"markdownContent":38,"markdownBody":39,"frontMatter":40,"refName":41,"commitSha":42,"skillDirectory":43,"forksCount":44,"repositoryHtmlUrl":45,"repositoryHomepageUrl":46,"ownerHtmlUrl":47,"ownerBlogUrl":48,"ownerDescription":49,"updatedAt":50,"install":51,"resources":64},"01M6AFKH5S94NTC70AYE6CBE48","pymc",null,"Bayesian modeling with PyMC. Build hierarchical models, MCMC (NUTS), variational inference, LOO\u002FWAIC comparison, posterior checks, for probabilistic programming and inference.","davila7\u002Fclaude-code-templates","davila7","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F6216945?v=4","01M6ADEWWFPS191NFM0Y1EX1JH","Daniel Avila","01M6ADJHGM78PHQRD3XZTFDVKK",33481,"MIT","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fpymc\u002FSKILL.md",[18],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},"01JBSEEDCAT000000000000023","Skill与智能体开发","SCENARIO","使用场景",[5,24,25,26,27,28,29,30,31,32,33,34,35],"inference","programming","models","build","modeling","comparison","with","for","Bayesian","MCMC","Probabilistic Programming","Posterior","2026-11-10 10:12:30",false,"---\nname: pymc\ndescription: \"Bayesian modeling with PyMC. Build hierarchical models, MCMC (NUTS), variational inference, LOO\u002FWAIC comparison, posterior checks, for probabilistic programming and inference.\"\n---\n\n# PyMC Bayesian Modeling\n\n## Overview\n\nPyMC is a Python library for Bayesian modeling and probabilistic programming. Build, fit, validate, and compare Bayesian models using PyMC's modern API (version 5.x+), including hierarchical models, MCMC sampling (NUTS), variational inference, and model comparison (LOO, WAIC).\n\n## When to Use This Skill\n\nThis skill should be used when:\n- Building Bayesian models (linear\u002Flogistic regression, hierarchical models, time series, etc.)\n- Performing MCMC sampling or variational inference\n- Conducting prior\u002Fposterior predictive checks\n- Diagnosing sampling issues (divergences, convergence, ESS)\n- Comparing multiple models using information criteria (LOO, WAIC)\n- Implementing uncertainty quantification through Bayesian methods\n- Working with hierarchical\u002Fmultilevel data structures\n- Handling missing data or measurement error in a principled way\n\n## Standard Bayesian Workflow\n\nFollow this workflow for building and validating Bayesian models:\n\n### 1. Data Preparation\n\n```python\nimport pymc as pm\nimport arviz as az\nimport numpy as np\n\n# Load and prepare data\nX = ...  # Predictors\ny = ...  # Outcomes\n\n# Standardize predictors for better sampling\nX_mean = X.mean(axis=0)\nX_std = X.std(axis=0)\nX_scaled = (X - X_mean) \u002F X_std\n```\n\n**Key practices:**\n- Standardize continuous predictors (improves sampling efficiency)\n- Center outcomes when possible\n- Handle missing data explicitly (treat as parameters)\n- Use named dimensions with `coords` for clarity\n\n### 2. Model Building\n\n```python\ncoords = {\n    'predictors': ['var1', 'var2', 'var3'],\n    'obs_id': np.arange(len(y))\n}\n\nwith pm.Model(coords=coords) as model:\n    # Priors\n    alpha = pm.Normal('alpha', mu=0, sigma=1)\n    beta = pm.Normal('beta', mu=0, sigma=1, dims='predictors')\n    sigma = pm.HalfNormal('sigma', sigma=1)\n\n    # Linear predictor\n    mu = alpha + pm.math.dot(X_scaled, beta)\n\n    # Likelihood\n    y_obs = pm.Normal('y_obs', mu=mu, sigma=sigma, observed=y, dims='obs_id')\n```\n\n**Key practices:**\n- Use weakly informative priors (not flat priors)\n- Use `HalfNormal` or `Exponential` for scale parameters\n- Use named dimensions (`dims`) instead of `shape` when possible\n- Use `pm.Data()` for values that will be updated for predictions\n\n### 3. Prior Predictive Check\n\n**Always validate priors before fitting:**\n\n```python\nwith model:\n    prior_pred = pm.sample_prior_predictive(samples=1000, random_seed=42)\n\n# Visualize\naz.plot_ppc(prior_pred, group='prior')\n```\n\n**Check:**\n- Do prior predictions span reasonable values?\n- Are extreme values plausible given domain knowledge?\n- If priors generate implausible data, adjust and re-check\n\n### 4. Fit Model\n\n```python\nwith model:\n    # Optional: Quick exploration with ADVI\n    # approx = pm.fit(n=20000)\n\n    # Full MCMC inference\n    idata = pm.sample(\n        draws=2000,\n        tune=1000,\n        chains=4,\n        target_accept=0.9,\n        random_seed=42,\n        idata_kwargs={'log_likelihood': True}  # For model comparison\n    )\n```\n\n**Key parameters:**\n- `draws=2000`: Number of samples per chain\n- `tune=1000`: Warmup samples (discarded)\n- `chains=4`: Run 4 chains for convergence checking\n- `target_accept=0.9`: Higher for difficult posteriors (0.95-0.99)\n- Include `log_likelihood=True` for model comparison\n\n### 5. Check Diagnostics\n\n**Use the diagnostic script:**\n\n```python\nfrom scripts.model_diagnostics import check_diagnostics\n\nresults = check_diagnostics(idata, var_names=['alpha', 'beta', 'sigma'])\n```\n\n**Check:**\n- **R-hat \u003C 1.01**: Chains have converged\n- **ESS > 400**: Sufficient effective samples\n- **No divergences**: NUTS sampled successfully\n- **Trace plots**: Chains should mix well (fuzzy caterpillar)\n\n**If issues arise:**\n- Divergences → Increase `target_accept=0.95`, use non-centered parameterization\n- Low ESS → Sample more draws, reparameterize to reduce correlation\n- High R-hat → Run longer, check for multimodality\n\n### 6. Posterior Predictive Check\n\n**Validate model fit:**\n\n```python\nwith model:\n    pm.sample_posterior_predictive(idata, extend_inferencedata=True, random_seed=42)\n\n# Visualize\naz.plot_ppc(idata)\n```\n\n**Check:**\n- Do posterior predictions capture observed data patterns?\n- Are systematic deviations evident (model misspecification)?\n- Consider alternative models if fit is poor\n\n### 7. Analyze Results\n\n```python\n# Summary statistics\nprint(az.summary(idata, var_names=['alpha', 'beta', 'sigma']))\n\n# Posterior distributions\naz.plot_posterior(idata, var_names=['alpha', 'beta', 'sigma'])\n\n# Coefficient estimates\naz.plot_forest(idata, var_names=['beta'], combined=True)\n```\n\n### 8. Make Predictions\n\n```python\nX_new = ...  # New predictor values\nX_new_scaled = (X_new - X_mean) \u002F X_std\n\nwith model:\n    pm.set_data({'X_scaled': X_new_scaled})\n    post_pred = pm.sample_posterior_predictive(\n        idata.posterior,\n        var_names=['y_obs'],\n        random_seed=42\n    )\n\n# Extract prediction intervals\ny_pred_mean = post_pred.posterior_predictive['y_obs'].mean(dim=['chain', 'draw'])\ny_pred_hdi = az.hdi(post_pred.posterior_predictive, var_names=['y_obs'])\n```\n\n## Common Model Patterns\n\n### Linear Regression\n\nFor continuous outcomes with linear relationships:\n\n```python\nwith pm.Model() as linear_model:\n    alpha = pm.Normal('alpha', mu=0, sigma=10)\n    beta = pm.Normal('beta', mu=0, sigma=10, shape=n_predictors)\n    sigma = pm.HalfNormal('sigma', sigma=1)\n\n    mu = alpha + pm.math.dot(X, beta)\n    y = pm.Normal('y', mu=mu, sigma=sigma, observed=y_obs)\n```\n\n**Use template:** `assets\u002Flinear_regression_template.py`\n\n### Logistic Regression\n\nFor binary outcomes:\n\n```python\nwith pm.Model() as logistic_model:\n    alpha = pm.Normal('alpha', mu=0, sigma=10)\n    beta = pm.Normal('beta', mu=0, sigma=10, shape=n_predictors)\n\n    logit_p = alpha + pm.math.dot(X, beta)\n    y = pm.Bernoulli('y', logit_p=logit_p, observed=y_obs)\n```\n\n### Hierarchical Models\n\nFor grouped data (use non-centered parameterization):\n\n```python\nwith pm.Model(coords={'groups': group_names}) as hierarchical_model:\n    # Hyperpriors\n    mu_alpha = pm.Normal('mu_alpha', mu=0, sigma=10)\n    sigma_alpha = pm.HalfNormal('sigma_alpha', sigma=1)\n\n    # Group-level (non-centered)\n    alpha_offset = pm.Normal('alpha_offset', mu=0, sigma=1, dims='groups')\n    alpha = pm.Deterministic('alpha', mu_alpha + sigma_alpha * alpha_offset, dims='groups')\n\n    # Observation-level\n    mu = alpha[group_idx]\n    sigma = pm.HalfNormal('sigma', sigma=1)\n    y = pm.Normal('y', mu=mu, sigma=sigma, observed=y_obs)\n```\n\n**Use template:** `assets\u002Fhierarchical_model_template.py`\n\n**Critical:** Always use non-centered parameterization for hierarchical models to avoid divergences.\n\n### Poisson Regression\n\nFor count data:\n\n```python\nwith pm.Model() as poisson_model:\n    alpha = pm.Normal('alpha', mu=0, sigma=10)\n    beta = pm.Normal('beta', mu=0, sigma=10, shape=n_predictors)\n\n    log_lambda = alpha + pm.math.dot(X, beta)\n    y = pm.Poisson('y', mu=pm.math.exp(log_lambda), observed=y_obs)\n```\n\nFor overdispersed counts, use `NegativeBinomial` instead.\n\n### Time Series\n\nFor autoregressive processes:\n\n```python\nwith pm.Model() as ar_model:\n    sigma = pm.HalfNormal('sigma', sigma=1)\n    rho = pm.Normal('rho', mu=0, sigma=0.5, shape=ar_order)\n    init_dist = pm.Normal.dist(mu=0, sigma=sigma)\n\n    y = pm.AR('y', rho=rho, sigma=sigma, init_dist=init_dist, observed=y_obs)\n```\n\n## Model Comparison\n\n### Comparing Models\n\nUse LOO or WAIC for model comparison:\n\n```python\nfrom scripts.model_comparison import compare_models, check_loo_reliability\n\n# Fit models with log_likelihood\nmodels = {\n    'Model1': idata1,\n    'Model2': idata2,\n    'Model3': idata3\n}\n\n# Compare using LOO\ncomparison = compare_models(models, ic='loo')\n\n# Check reliability\ncheck_loo_reliability(models)\n```\n\n**Interpretation:**\n- **Δloo \u003C 2**: Models are similar, choose simpler model\n- **2 \u003C Δloo \u003C 4**: Weak evidence for better model\n- **4 \u003C Δloo \u003C 10**: Moderate evidence\n- **Δloo > 10**: Strong evidence for better model\n\n**Check Pareto-k values:**\n- k \u003C 0.7: LOO reliable\n- k > 0.7: Consider WAIC or k-fold CV\n\n### Model Averaging\n\nWhen models are similar, average predictions:\n\n```python\nfrom scripts.model_comparison import model_averaging\n\naveraged_pred, weights = model_averaging(models, var_name='y_obs')\n```\n\n## Distribution Selection Guide\n\n### For Priors\n\n**Scale parameters** (σ, τ):\n- `pm.HalfNormal('sigma', sigma=1)` - Default choice\n- `pm.Exponential('sigma', lam=1)` - Alternative\n- `pm.Gamma('sigma', alpha=2, beta=1)` - More informative\n\n**Unbounded parameters**:\n- `pm.Normal('theta', mu=0, sigma=1)` - For standardized data\n- `pm.StudentT('theta', nu=3, mu=0, sigma=1)` - Robust to outliers\n\n**Positive parameters**:\n- `pm.LogNormal('theta', mu=0, sigma=1)`\n- `pm.Gamma('theta', alpha=2, beta=1)`\n\n**Probabilities**:\n- `pm.Beta('p', alpha=2, beta=2)` - Weakly informative\n- `pm.Uniform('p', lower=0, upper=1)` - Non-informative (use sparingly)\n\n**Correlation matrices**:\n- `pm.LKJCorr('corr', n=n_vars, eta=2)` - eta=1 uniform, eta>1 prefers identity\n\n### For Likelihoods\n\n**Continuous outcomes**:\n- `pm.Normal('y', mu=mu, sigma=sigma)` - Default for continuous data\n- `pm.StudentT('y', nu=nu, mu=mu, sigma=sigma)` - Robust to outliers\n\n**Count data**:\n- `pm.Poisson('y', mu=lambda)` - Equidispersed counts\n- `pm.NegativeBinomial('y', mu=mu, alpha=alpha)` - Overdispersed counts\n- `pm.ZeroInflatedPoisson('y', psi=psi, mu=mu)` - Excess zeros\n\n**Binary outcomes**:\n- `pm.Bernoulli('y', p=p)` or `pm.Bernoulli('y', logit_p=logit_p)`\n\n**Categorical outcomes**:\n- `pm.Categorical('y', p=probs)`\n\n**See:** `references\u002Fdistributions.md` for comprehensive distribution reference\n\n## Sampling and Inference\n\n### MCMC with NUTS\n\nDefault and recommended for most models:\n\n```python\nidata = pm.sample(\n    draws=2000,\n    tune=1000,\n    chains=4,\n    target_accept=0.9,\n    random_seed=42\n)\n```\n\n**Adjust when needed:**\n- Divergences → `target_accept=0.95` or higher\n- Slow sampling → Use ADVI for initialization\n- Discrete parameters → Use `pm.Metropolis()` for discrete vars\n\n### Variational Inference\n\nFast approximation for exploration or initialization:\n\n```python\nwith model:\n    approx = pm.fit(n=20000, method='advi')\n\n    # Use for initialization\n    start = approx.sample(return_inferencedata=False)[0]\n    idata = pm.sample(start=start)\n```\n\n**Trade-offs:**\n- Much faster than MCMC\n- Approximate (may underestimate uncertainty)\n- Good for large models or quick exploration\n\n**See:** `references\u002Fsampling_inference.md` for detailed sampling guide\n\n## Diagnostic Scripts\n\n### Comprehensive Diagnostics\n\n```python\nfrom scripts.model_diagnostics import create_diagnostic_report\n\ncreate_diagnostic_report(\n    idata,\n    var_names=['alpha', 'beta', 'sigma'],\n    output_dir='diagnostics\u002F'\n)\n```\n\nCreates:\n- Trace plots\n- Rank plots (mixing check)\n- Autocorrelation plots\n- Energy plots\n- ESS evolution\n- Summary statistics CSV\n\n### Quick Diagnostic Check\n\n```python\nfrom scripts.model_diagnostics import check_diagnostics\n\nresults = check_diagnostics(idata)\n```\n\nChecks R-hat, ESS, divergences, and tree depth.\n\n## Common Issues and Solutions\n\n### Divergences\n\n**Symptom:** `idata.sample_stats.diverging.sum() > 0`\n\n**Solutions:**\n1. Increase `target_accept=0.95` or `0.99`\n2. Use non-centered parameterization (hierarchical models)\n3. Add stronger priors to constrain parameters\n4. Check for model misspecification\n\n### Low Effective Sample Size\n\n**Symptom:** `ESS \u003C 400`\n\n**Solutions:**\n1. Sample more draws: `draws=5000`\n2. Reparameterize to reduce posterior correlation\n3. Use QR decomposition for regression with correlated predictors\n\n### High R-hat\n\n**Symptom:** `R-hat > 1.01`\n\n**Solutions:**\n1. Run longer chains: `tune=2000, draws=5000`\n2. Check for multimodality\n3. Improve initialization with ADVI\n\n### Slow Sampling\n\n**Solutions:**\n1. Use ADVI initialization\n2. Reduce model complexity\n3. Increase parallelization: `cores=8, chains=8`\n4. Use variational inference if appropriate\n\n## Best Practices\n\n### Model Building\n\n1. **Always standardize predictors** for better sampling\n2. **Use weakly informative priors** (not flat)\n3. **Use named dimensions** (`dims`) for clarity\n4. **Non-centered parameterization** for hierarchical models\n5. **Check prior predictive** before fitting\n\n### Sampling\n\n1. **Run multiple chains** (at least 4) for convergence\n2. **Use `target_accept=0.9`** as baseline (higher if needed)\n3. **Include `log_likelihood=True`** for model comparison\n4. **Set random seed** for reproducibility\n\n### Validation\n\n1. **Check diagnostics** before interpretation (R-hat, ESS, divergences)\n2. **Posterior predictive check** for model validation\n3. **Compare multiple models** when appropriate\n4. **Report uncertainty** (HDI intervals, not just point estimates)\n\n### Workflow\n\n1. Start simple, add complexity gradually\n2. Prior predictive check → Fit → Diagnostics → Posterior predictive check\n3. Iterate on model specification based on checks\n4. Document assumptions and prior choices\n\n## Resources\n\nThis skill includes:\n\n### References (`references\u002F`)\n\n- **`distributions.md`**: Comprehensive catalog of PyMC distributions organized by category (continuous, discrete, multivariate, mixture, time series). Use when selecting priors or likelihoods.\n\n- **`sampling_inference.md`**: Detailed guide to sampling algorithms (NUTS, Metropolis, SMC), variational inference (ADVI, SVGD), and handling sampling issues. Use when encountering convergence problems or choosing inference methods.\n\n- **`workflows.md`**: Complete workflow examples and code patterns for common model types, data preparation, prior selection, and model validation. Use as a cookbook for standard Bayesian analyses.\n\n### Scripts (`scripts\u002F`)\n\n- **`model_diagnostics.py`**: Automated diagnostic checking and report generation. Functions: `check_diagnostics()` for quick checks, `create_diagnostic_report()` for comprehensive analysis with plots.\n\n- **`model_comparison.py`**: Model comparison utilities using LOO\u002FWAIC. Functions: `compare_models()`, `check_loo_reliability()`, `model_averaging()`.\n\n### Templates (`assets\u002F`)\n\n- **`linear_regression_template.py`**: Complete template for Bayesian linear regression with full workflow (data prep, prior checks, fitting, diagnostics, predictions).\n\n- **`hierarchical_model_template.py`**: Complete template for hierarchical\u002Fmultilevel models with non-centered parameterization and group-level analysis.\n\n## Quick Reference\n\n### Model Building\n```python\nwith pm.Model(coords={'var': names}) as model:\n    # Priors\n    param = pm.Normal('param', mu=0, sigma=1, dims='var')\n    # Likelihood\n    y = pm.Normal('y', mu=..., sigma=..., observed=data)\n```\n\n### Sampling\n```python\nidata = pm.sample(draws=2000, tune=1000, chains=4, target_accept=0.9)\n```\n\n### Diagnostics\n```python\nfrom scripts.model_diagnostics import check_diagnostics\ncheck_diagnostics(idata)\n```\n\n### Model Comparison\n```python\nfrom scripts.model_comparison import compare_models\ncompare_models({'m1': idata1, 'm2': idata2}, ic='loo')\n```\n\n### Predictions\n```python\nwith model:\n    pm.set_data({'X': X_new})\n    pred = pm.sample_posterior_predictive(idata.posterior)\n```\n\n## Additional Notes\n\n- PyMC integrates with ArviZ for visualization and diagnostics\n- Use `pm.model_to_graphviz(model)` to visualize model structure\n- Save results with `idata.to_netcdf('results.nc')`\n- Load with `az.from_netcdf('results.nc')`\n- For very large models, consider minibatch ADVI or data subsampling\n","# PyMC Bayesian Modeling\n\n## Overview\n\nPyMC is a Python library for Bayesian modeling and probabilistic programming. Build, fit, validate, and compare Bayesian models using PyMC's modern API (version 5.x+), including hierarchical models, MCMC sampling (NUTS), variational inference, and model comparison (LOO, WAIC).\n\n## When to Use This Skill\n\nThis skill should be used when:\n- Building Bayesian models (linear\u002Flogistic regression, hierarchical models, time series, etc.)\n- Performing MCMC sampling or variational inference\n- Conducting prior\u002Fposterior predictive checks\n- Diagnosing sampling issues (divergences, convergence, ESS)\n- Comparing multiple models using information criteria (LOO, WAIC)\n- Implementing uncertainty quantification through Bayesian methods\n- Working with hierarchical\u002Fmultilevel data structures\n- Handling missing data or measurement error in a principled way\n\n## Standard Bayesian Workflow\n\nFollow this workflow for building and validating Bayesian models:\n\n### 1. Data Preparation\n\n```python\nimport pymc as pm\nimport arviz as az\nimport numpy as np\n\n# Load and prepare data\nX = ...  # Predictors\ny = ...  # Outcomes\n\n# Standardize predictors for better sampling\nX_mean = X.mean(axis=0)\nX_std = X.std(axis=0)\nX_scaled = (X - X_mean) \u002F X_std\n```\n\n**Key practices:**\n- Standardize continuous predictors (improves sampling efficiency)\n- Center outcomes when possible\n- Handle missing data explicitly (treat as parameters)\n- Use named dimensions with `coords` for clarity\n\n### 2. Model Building\n\n```python\ncoords = {\n    'predictors': ['var1', 'var2', 'var3'],\n    'obs_id': np.arange(len(y))\n}\n\nwith pm.Model(coords=coords) as model:\n    # Priors\n    alpha = pm.Normal('alpha', mu=0, sigma=1)\n    beta = pm.Normal('beta', mu=0, sigma=1, dims='predictors')\n    sigma = pm.HalfNormal('sigma', sigma=1)\n\n    # Linear predictor\n    mu = alpha + pm.math.dot(X_scaled, beta)\n\n    # Likelihood\n    y_obs = pm.Normal('y_obs', mu=mu, sigma=sigma, observed=y, dims='obs_id')\n```\n\n**Key practices:**\n- Use weakly informative priors (not flat priors)\n- Use `HalfNormal` or `Exponential` for scale parameters\n- Use named dimensions (`dims`) instead of `shape` when possible\n- Use `pm.Data()` for values that will be updated for predictions\n\n### 3. Prior Predictive Check\n\n**Always validate priors before fitting:**\n\n```python\nwith model:\n    prior_pred = pm.sample_prior_predictive(samples=1000, random_seed=42)\n\n# Visualize\naz.plot_ppc(prior_pred, group='prior')\n```\n\n**Check:**\n- Do prior predictions span reasonable values?\n- Are extreme values plausible given domain knowledge?\n- If priors generate implausible data, adjust and re-check\n\n### 4. Fit Model\n\n```python\nwith model:\n    # Optional: Quick exploration with ADVI\n    # approx = pm.fit(n=20000)\n\n    # Full MCMC inference\n    idata = pm.sample(\n        draws=2000,\n        tune=1000,\n        chains=4,\n        target_accept=0.9,\n        random_seed=42,\n        idata_kwargs={'log_likelihood': True}  # For model comparison\n    )\n```\n\n**Key parameters:**\n- `draws=2000`: Number of samples per chain\n- `tune=1000`: Warmup samples (discarded)\n- `chains=4`: Run 4 chains for convergence checking\n- `target_accept=0.9`: Higher for difficult posteriors (0.95-0.99)\n- Include `log_likelihood=True` for model comparison\n\n### 5. Check Diagnostics\n\n**Use the diagnostic script:**\n\n```python\nfrom scripts.model_diagnostics import check_diagnostics\n\nresults = check_diagnostics(idata, var_names=['alpha', 'beta', 'sigma'])\n```\n\n**Check:**\n- **R-hat \u003C 1.01**: Chains have converged\n- **ESS > 400**: Sufficient effective samples\n- **No divergences**: NUTS sampled successfully\n- **Trace plots**: Chains should mix well (fuzzy caterpillar)\n\n**If issues arise:**\n- Divergences → Increase `target_accept=0.95`, use non-centered parameterization\n- Low ESS → Sample more draws, reparameterize to reduce correlation\n- High R-hat → Run longer, check for multimodality\n\n### 6. Posterior Predictive Check\n\n**Validate model fit:**\n\n```python\nwith model:\n    pm.sample_posterior_predictive(idata, extend_inferencedata=True, random_seed=42)\n\n# Visualize\naz.plot_ppc(idata)\n```\n\n**Check:**\n- Do posterior predictions capture observed data patterns?\n- Are systematic deviations evident (model misspecification)?\n- Consider alternative models if fit is poor\n\n### 7. Analyze Results\n\n```python\n# Summary statistics\nprint(az.summary(idata, var_names=['alpha', 'beta', 'sigma']))\n\n# Posterior distributions\naz.plot_posterior(idata, var_names=['alpha', 'beta', 'sigma'])\n\n# Coefficient estimates\naz.plot_forest(idata, var_names=['beta'], combined=True)\n```\n\n### 8. Make Predictions\n\n```python\nX_new = ...  # New predictor values\nX_new_scaled = (X_new - X_mean) \u002F X_std\n\nwith model:\n    pm.set_data({'X_scaled': X_new_scaled})\n    post_pred = pm.sample_posterior_predictive(\n        idata.posterior,\n        var_names=['y_obs'],\n        random_seed=42\n    )\n\n# Extract prediction intervals\ny_pred_mean = post_pred.posterior_predictive['y_obs'].mean(dim=['chain', 'draw'])\ny_pred_hdi = az.hdi(post_pred.posterior_predictive, var_names=['y_obs'])\n```\n\n## Common Model Patterns\n\n### Linear Regression\n\nFor continuous outcomes with linear relationships:\n\n```python\nwith pm.Model() as linear_model:\n    alpha = pm.Normal('alpha', mu=0, sigma=10)\n    beta = pm.Normal('beta', mu=0, sigma=10, shape=n_predictors)\n    sigma = pm.HalfNormal('sigma', sigma=1)\n\n    mu = alpha + pm.math.dot(X, beta)\n    y = pm.Normal('y', mu=mu, sigma=sigma, observed=y_obs)\n```\n\n**Use template:** `assets\u002Flinear_regression_template.py`\n\n### Logistic Regression\n\nFor binary outcomes:\n\n```python\nwith pm.Model() as logistic_model:\n    alpha = pm.Normal('alpha', mu=0, sigma=10)\n    beta = pm.Normal('beta', mu=0, sigma=10, shape=n_predictors)\n\n    logit_p = alpha + pm.math.dot(X, beta)\n    y = pm.Bernoulli('y', logit_p=logit_p, observed=y_obs)\n```\n\n### Hierarchical Models\n\nFor grouped data (use non-centered parameterization):\n\n```python\nwith pm.Model(coords={'groups': group_names}) as hierarchical_model:\n    # Hyperpriors\n    mu_alpha = pm.Normal('mu_alpha', mu=0, sigma=10)\n    sigma_alpha = pm.HalfNormal('sigma_alpha', sigma=1)\n\n    # Group-level (non-centered)\n    alpha_offset = pm.Normal('alpha_offset', mu=0, sigma=1, dims='groups')\n    alpha = pm.Deterministic('alpha', mu_alpha + sigma_alpha * alpha_offset, dims='groups')\n\n    # Observation-level\n    mu = alpha[group_idx]\n    sigma = pm.HalfNormal('sigma', sigma=1)\n    y = pm.Normal('y', mu=mu, sigma=sigma, observed=y_obs)\n```\n\n**Use template:** `assets\u002Fhierarchical_model_template.py`\n\n**Critical:** Always use non-centered parameterization for hierarchical models to avoid divergences.\n\n### Poisson Regression\n\nFor count data:\n\n```python\nwith pm.Model() as poisson_model:\n    alpha = pm.Normal('alpha', mu=0, sigma=10)\n    beta = pm.Normal('beta', mu=0, sigma=10, shape=n_predictors)\n\n    log_lambda = alpha + pm.math.dot(X, beta)\n    y = pm.Poisson('y', mu=pm.math.exp(log_lambda), observed=y_obs)\n```\n\nFor overdispersed counts, use `NegativeBinomial` instead.\n\n### Time Series\n\nFor autoregressive processes:\n\n```python\nwith pm.Model() as ar_model:\n    sigma = pm.HalfNormal('sigma', sigma=1)\n    rho = pm.Normal('rho', mu=0, sigma=0.5, shape=ar_order)\n    init_dist = pm.Normal.dist(mu=0, sigma=sigma)\n\n    y = pm.AR('y', rho=rho, sigma=sigma, init_dist=init_dist, observed=y_obs)\n```\n\n## Model Comparison\n\n### Comparing Models\n\nUse LOO or WAIC for model comparison:\n\n```python\nfrom scripts.model_comparison import compare_models, check_loo_reliability\n\n# Fit models with log_likelihood\nmodels = {\n    'Model1': idata1,\n    'Model2': idata2,\n    'Model3': idata3\n}\n\n# Compare using LOO\ncomparison = compare_models(models, ic='loo')\n\n# Check reliability\ncheck_loo_reliability(models)\n```\n\n**Interpretation:**\n- **Δloo \u003C 2**: Models are similar, choose simpler model\n- **2 \u003C Δloo \u003C 4**: Weak evidence for better model\n- **4 \u003C Δloo \u003C 10**: Moderate evidence\n- **Δloo > 10**: Strong evidence for better model\n\n**Check Pareto-k values:**\n- k \u003C 0.7: LOO reliable\n- k > 0.7: Consider WAIC or k-fold CV\n\n### Model Averaging\n\nWhen models are similar, average predictions:\n\n```python\nfrom scripts.model_comparison import model_averaging\n\naveraged_pred, weights = model_averaging(models, var_name='y_obs')\n```\n\n## Distribution Selection Guide\n\n### For Priors\n\n**Scale parameters** (σ, τ):\n- `pm.HalfNormal('sigma', sigma=1)` - Default choice\n- `pm.Exponential('sigma', lam=1)` - Alternative\n- `pm.Gamma('sigma', alpha=2, beta=1)` - More informative\n\n**Unbounded parameters**:\n- `pm.Normal('theta', mu=0, sigma=1)` - For standardized data\n- `pm.StudentT('theta', nu=3, mu=0, sigma=1)` - Robust to outliers\n\n**Positive parameters**:\n- `pm.LogNormal('theta', mu=0, sigma=1)`\n- `pm.Gamma('theta', alpha=2, beta=1)`\n\n**Probabilities**:\n- `pm.Beta('p', alpha=2, beta=2)` - Weakly informative\n- `pm.Uniform('p', lower=0, upper=1)` - Non-informative (use sparingly)\n\n**Correlation matrices**:\n- `pm.LKJCorr('corr', n=n_vars, eta=2)` - eta=1 uniform, eta>1 prefers identity\n\n### For Likelihoods\n\n**Continuous outcomes**:\n- `pm.Normal('y', mu=mu, sigma=sigma)` - Default for continuous data\n- `pm.StudentT('y', nu=nu, mu=mu, sigma=sigma)` - Robust to outliers\n\n**Count data**:\n- `pm.Poisson('y', mu=lambda)` - Equidispersed counts\n- `pm.NegativeBinomial('y', mu=mu, alpha=alpha)` - Overdispersed counts\n- `pm.ZeroInflatedPoisson('y', psi=psi, mu=mu)` - Excess zeros\n\n**Binary outcomes**:\n- `pm.Bernoulli('y', p=p)` or `pm.Bernoulli('y', logit_p=logit_p)`\n\n**Categorical outcomes**:\n- `pm.Categorical('y', p=probs)`\n\n**See:** `references\u002Fdistributions.md` for comprehensive distribution reference\n\n## Sampling and Inference\n\n### MCMC with NUTS\n\nDefault and recommended for most models:\n\n```python\nidata = pm.sample(\n    draws=2000,\n    tune=1000,\n    chains=4,\n    target_accept=0.9,\n    random_seed=42\n)\n```\n\n**Adjust when needed:**\n- Divergences → `target_accept=0.95` or higher\n- Slow sampling → Use ADVI for initialization\n- Discrete parameters → Use `pm.Metropolis()` for discrete vars\n\n### Variational Inference\n\nFast approximation for exploration or initialization:\n\n```python\nwith model:\n    approx = pm.fit(n=20000, method='advi')\n\n    # Use for initialization\n    start = approx.sample(return_inferencedata=False)[0]\n    idata = pm.sample(start=start)\n```\n\n**Trade-offs:**\n- Much faster than MCMC\n- Approximate (may underestimate uncertainty)\n- Good for large models or quick exploration\n\n**See:** `references\u002Fsampling_inference.md` for detailed sampling guide\n\n## Diagnostic Scripts\n\n### Comprehensive Diagnostics\n\n```python\nfrom scripts.model_diagnostics import create_diagnostic_report\n\ncreate_diagnostic_report(\n    idata,\n    var_names=['alpha', 'beta', 'sigma'],\n    output_dir='diagnostics\u002F'\n)\n```\n\nCreates:\n- Trace plots\n- Rank plots (mixing check)\n- Autocorrelation plots\n- Energy plots\n- ESS evolution\n- Summary statistics CSV\n\n### Quick Diagnostic Check\n\n```python\nfrom scripts.model_diagnostics import check_diagnostics\n\nresults = check_diagnostics(idata)\n```\n\nChecks R-hat, ESS, divergences, and tree depth.\n\n## Common Issues and Solutions\n\n### Divergences\n\n**Symptom:** `idata.sample_stats.diverging.sum() > 0`\n\n**Solutions:**\n1. Increase `target_accept=0.95` or `0.99`\n2. Use non-centered parameterization (hierarchical models)\n3. Add stronger priors to constrain parameters\n4. Check for model misspecification\n\n### Low Effective Sample Size\n\n**Symptom:** `ESS \u003C 400`\n\n**Solutions:**\n1. Sample more draws: `draws=5000`\n2. Reparameterize to reduce posterior correlation\n3. Use QR decomposition for regression with correlated predictors\n\n### High R-hat\n\n**Symptom:** `R-hat > 1.01`\n\n**Solutions:**\n1. Run longer chains: `tune=2000, draws=5000`\n2. Check for multimodality\n3. Improve initialization with ADVI\n\n### Slow Sampling\n\n**Solutions:**\n1. Use ADVI initialization\n2. Reduce model complexity\n3. Increase parallelization: `cores=8, chains=8`\n4. Use variational inference if appropriate\n\n## Best Practices\n\n### Model Building\n\n1. **Always standardize predictors** for better sampling\n2. **Use weakly informative priors** (not flat)\n3. **Use named dimensions** (`dims`) for clarity\n4. **Non-centered parameterization** for hierarchical models\n5. **Check prior predictive** before fitting\n\n### Sampling\n\n1. **Run multiple chains** (at least 4) for convergence\n2. **Use `target_accept=0.9`** as baseline (higher if needed)\n3. **Include `log_likelihood=True`** for model comparison\n4. **Set random seed** for reproducibility\n\n### Validation\n\n1. **Check diagnostics** before interpretation (R-hat, ESS, divergences)\n2. **Posterior predictive check** for model validation\n3. **Compare multiple models** when appropriate\n4. **Report uncertainty** (HDI intervals, not just point estimates)\n\n### Workflow\n\n1. Start simple, add complexity gradually\n2. Prior predictive check → Fit → Diagnostics → Posterior predictive check\n3. Iterate on model specification based on checks\n4. Document assumptions and prior choices\n\n## Resources\n\nThis skill includes:\n\n### References (`references\u002F`)\n\n- **`distributions.md`**: Comprehensive catalog of PyMC distributions organized by category (continuous, discrete, multivariate, mixture, time series). Use when selecting priors or likelihoods.\n\n- **`sampling_inference.md`**: Detailed guide to sampling algorithms (NUTS, Metropolis, SMC), variational inference (ADVI, SVGD), and handling sampling issues. Use when encountering convergence problems or choosing inference methods.\n\n- **`workflows.md`**: Complete workflow examples and code patterns for common model types, data preparation, prior selection, and model validation. Use as a cookbook for standard Bayesian analyses.\n\n### Scripts (`scripts\u002F`)\n\n- **`model_diagnostics.py`**: Automated diagnostic checking and report generation. Functions: `check_diagnostics()` for quick checks, `create_diagnostic_report()` for comprehensive analysis with plots.\n\n- **`model_comparison.py`**: Model comparison utilities using LOO\u002FWAIC. Functions: `compare_models()`, `check_loo_reliability()`, `model_averaging()`.\n\n### Templates (`assets\u002F`)\n\n- **`linear_regression_template.py`**: Complete template for Bayesian linear regression with full workflow (data prep, prior checks, fitting, diagnostics, predictions).\n\n- **`hierarchical_model_template.py`**: Complete template for hierarchical\u002Fmultilevel models with non-centered parameterization and group-level analysis.\n\n## Quick Reference\n\n### Model Building\n```python\nwith pm.Model(coords={'var': names}) as model:\n    # Priors\n    param = pm.Normal('param', mu=0, sigma=1, dims='var')\n    # Likelihood\n    y = pm.Normal('y', mu=..., sigma=..., observed=data)\n```\n\n### Sampling\n```python\nidata = pm.sample(draws=2000, tune=1000, chains=4, target_accept=0.9)\n```\n\n### Diagnostics\n```python\nfrom scripts.model_diagnostics import check_diagnostics\ncheck_diagnostics(idata)\n```\n\n### Model Comparison\n```python\nfrom scripts.model_comparison import compare_models\ncompare_models({'m1': idata1, 'm2': idata2}, ic='loo')\n```\n\n### Predictions\n```python\nwith model:\n    pm.set_data({'X': X_new})\n    pred = pm.sample_posterior_predictive(idata.posterior)\n```\n\n## Additional Notes\n\n- PyMC integrates with ArviZ for visualization and diagnostics\n- Use `pm.model_to_graphviz(model)` to visualize model structure\n- Save results with `idata.to_netcdf('results.nc')`\n- Load with `az.from_netcdf('results.nc')`\n- For very large models, consider minibatch ADVI or data subsampling\n",{"name":5,"description":7},"main","2b749c82b5d11fac39d9a6e021ce3f5b8a541bd1","cli-tool\u002Fcomponents\u002Fskills\u002Fscientific\u002Fpymc",3931,"https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates","https:\u002F\u002Faitmpl.com","https:\u002F\u002Fgithub.com\u002Fdavila7","https:\u002F\u002Fdanielavila.me","Building AI dev tools with LLMs","2026-11-14 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DeFi liquidity pools before providing liquidity. Returns a 0-100 pool score and an Enter\u002FHold\u002FExit\u002FReduce\u002FAvoid verdict with calibrated confidence for ~68,800 Solana pools and 575 EVM pools, plus a public miss-inclusive track record. Use when asked whether a pool is worth LPing into, which pools look best right now, or how accurate the scores have actually been.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fweb-data\u002Fwealthville-pool-scoring\u002FSKILL.md",[104],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},[106,107,108,109,110,31,111,112,113,114,115,30,116,117,118,119,120,121,122,123],"scoring","pool","wealthville pool scoring","liquidity","which","exit","now","use","when","reduce","record","track","verdict","evm","solana","how","public","look",{"skillNo":125,"name":126,"nameZh":6,"description":127,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":128,"categories":129,"keywords":131,"publishedAt":36},"01M70MB6VR8ERJ4EM8D5KHBMEV","technical-debt-auditor","Scans a codebase and produces a quantified technical debt report with a prioritized remediation plan. Analyzes dead code, TODO\u002FFIXME\u002FHACK markers, dependency staleness, complexity hotspots, code duplication signals, test coverage gaps, unused exports, and outdated patterns. Use this skill when the user asks to audit their codebase for tech debt, wants a health check of their code quality, says things like \"where should I focus refactoring\", \"find code smells\", \"audit my codebase\", \"what technical debt do we have\", \"prioritize cleanup work\", or asks about code quality metrics. Also trigger when the user mentions \"code rot\", \"legacy cleanup\", \"refactoring priorities\", or wants to understand the overall health of a project before a major effort. Trigger even if the user doesn't say \"technical debt\" explicitly — any request to systematically assess code quality and identify improvement priorities belongs here.","https:\u002F\u002Fgithub.com\u002Fdavila7\u002Fclaude-code-templates\u002Fblob\u002Fmain\u002Fcli-tool\u002Fcomponents\u002Fskills\u002Fdevelopment\u002Ftechnical-debt-auditor\u002FSKILL.md",[130],{"categoryNo":19,"categoryName":20,"taxonomyType":21,"taxonomyTypeDesc":22},[132,133,134,135,136,137,138,139,140,141,142,114,143,144,145,146,147,148,149,150],"technical debt","debt","technical","technical debt auditor","auditor","coverage","complexity","markers","project","cleanup","unused","code","todo","work","plan","focus","signals","audit","dependency",{"skillNo":152,"name":153,"nameZh":6,"description":154,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":155,"categories":156,"keywords":166,"publishedAt":36},"01M70KPYH9QNHCNME5GJQGE22K","readonly-sql-guard","Make an agent's database access provably read-only. Use when an agent runs caller-supplied SQL against a production\u002FERP\u002Fanalytics database (a \"query\" MCP tool, text-to-SQL, an admin console), or when reviewing DB-access code for write\u002FDDL\u002Fside-effect\u002Ftransaction-escape risks. 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