pymc-distributions

# PyMC Distributions Skill You are an expert in PyMC probability distributions, helping migrate notebook code to work with the current stable PyMC version. ## Distribution Categories ### Continuous Distributions Common distributions include: - `pm.Normal(mu, sigma)` - Gaussian/normal distribution - `pm.Beta(alpha, beta)` - Beta distribution (0, 1) - `pm.Gamma(alpha, beta)` - Gamma distribution - `pm.Exponential(lam)` - Exponential distribution - `pm.StudentT(nu, mu, sigma)` - Student's t-distribution - `pm.Uniform(lower, upper)` - Uniform distribution - `pm.HalfNormal(sigma)` - Half-normal (positive only) - `pm.LogNormal(mu, sigma)` - Log-normal distribution - `pm.Cauchy(alpha, beta)` - Cauchy distribution - `pm.Laplace(mu, b)` - Laplace distribution - `pm.SkewNormal(mu, sigma, alpha)` - Skewed normal ### Discrete Distributions - `pm.Bernoulli(p)` - Binary outcomes - `pm.Binomial(n, p)` - Count of successes - `pm.Poisson(mu)` - Count data - `pm.Categorical(p)` - Categorical outcomes - `pm.NegativeBinomial(mu, alpha)` - Overdispersed count data - `pm.DiscreteUniform(lower, upper)` - Discrete uniform ### Multivariate Distributions - `pm.MvNormal(mu, cov)` - Multivariate normal - `pm.Dirichlet(a)` - Dirichlet distribution - `pm.Wishart(nu, V)` - Wishart distribution - `pm.LKJCorr(n, eta)` - LKJ correlation prior - `pm.LKJCholeskyCov(n, eta, sd_dist)` - Cholesky parameterization ### Mixture Distributions - `pm.Mixture(w, comp_dists)` - General mixture - `pm.NormalMixture(w, mu, sigma)` - Gaussian mixture - `pm.ZeroInflatedPoisson(psi, mu)` - Zero-inflated count - `pm.ZeroInflatedBinomial(psi, n, p)` - Zero-inflated binomial - `pm.HurdleGamma(psi, alpha, beta)` - Hurdle model ### Timeseries Distributions - `pm.AR(rho, sigma)` - Autoregressive - `pm.GaussianRandomWalk(mu, sigma)` - Random walk - `pm.GARCH11(omega, alpha_1, beta_1)` - GARCH model - `pm.EulerMaruyama(dt, sde_fn, sde_pars)` - SDE approximation ## Special Features ### Truncated/Censored Distributions ```python # Truncated distribution pm.Truncated("x", pm.Normal.dist(mu=0, sigma=1), lower=0, upper=10) # Censored distribution pm.Censored("y", pm.Normal.dist(mu=0, sigma=1), lower=None, upper=5) ``` ### Custom Distributions ```python # Define custom distribution def custom_logp(value, mu): return -0.5 * ((value - mu) ** 2) pm.CustomDist("custom", mu, logp=custom_logp, observed=data) ``` ### Simulator Integration ```python pm.Simulator("sim", fn=simulator_function, params=[param1, param2], observed=data) ``` ## Common Parameters Most distributions accept: - `name` - Variable name (required for RVs in model) - Distribution-specific parameters (mu, sigma, alpha, etc.) - `shape` - Shape of the random variable - `dims` - Named dimensions for the variable - `observed` - Observed data (makes it a likelihood) - `transform` - Transformation for parameter constraints ## Key Methods ```python # Log-probability dist.logp(value) # Log cumulative distribution dist.logcdf(value) # Inverse CDF (quantile function) dist.icdf(q) # Random sampling (outside of pm.sample) dist.random(size=100, rng=rng) ``` ## Common Migration Issues ### PyMC3 → latest PyMC version 1. **Import changes** ```python # Old (PyMC3) import pymc3 as pm # New (latest PyMC version) import pymc as pm ``` 2. **Distribution parameters** ```python # Some distributions have parameter renames # Check documentation for specific changes # Old: sd parameter pm.Normal('x', mu=0, sd=1) # PyMC3 # New: sigma parameter pm.Normal('x', mu=0, sigma=1) # latest PyMC version ``` 3. **Shape specification** ```python # Shape handling is more explicit in latest PyMC version # Use dims and coords for cleaner shape management with pm.Model(coords={"subject": subjects, "time": times}) as model: x = pm.Normal("x", mu=0, sigma=1, dims=("subject", "time")) ``` 4. **Distribution creation** ```python # Creating distributions without adding to model # Old dist = pm.Normal.dist(mu=0, sd=1) # New dist = pm.Normal.dist(mu=0, sigma=1) ``` ## Best Practices 1. **Use informative priors** - Weakly informative priors often work better than flat priors 2. **Named dimensions** - Use `dims` and `coords` for better shape management 3. **Vectorization** - Leverage broadcasting for efficient computation 4. **Prior predictive checks** - Always check priors make sense before sampling 5. **Transformations** - Let PyMC handle constraints automatically when possible ## Troubleshooting ### Shape mismatches - Check that observed data shape matches distribution shape - Verify broadcasting rules are applied correctly - Use `pm.model_to_graphviz(model)` to visualize shapes ### Invalid parameter values - Ensure positive constraints (use HalfNormal, Exponential, etc.) - Check bounds for bounded distributions - Verify probability parameters are in (0, 1) ### Sampling issues - Some distributions may need specific step samplers - Consider reparameterization for better geometry - Use `pm.find_MAP()` to check if model is well-specified ## Example Usage ```python import pymc as pm import numpy as np # Generate data true_mu = 5 true_sigma = 2 data = np.random.normal(true_mu, true_sigma, size=100) # Build model with pm.Model() as model: # Priors mu = pm.Normal("mu", mu=0, sigma=10) sigma = pm.HalfNormal("sigma", sigma=5) # Likelihood y = pm.Normal("y", mu=mu, sigma=sigma, observed=data) # Sample trace = pm.sample(1000, tune=1000) ``` ## When to Use This Skill - Converting distribution specifications from old notebooks - Fixing distribution parameter errors - Implementing custom distributions - Troubleshooting likelihood specifications - Choosing appropriate priors - Handling mixture models or zero-inflation