PyMC Model Building and Core Components

from pymc import Model

class Model:
    """
    Main container for probabilistic models in PyMC.
    
    Parameters:
    - name (str, optional): Name of the model
    - coords (dict, optional): Coordinate specifications for dimensions
    - check_bounds (bool): Check parameter bounds during sampling (default: True)
    
    Attributes:
    - free_RVs (list): List of free random variables
    - observed_RVs (list): List of observed random variables  
    - deterministics (list): List of deterministic variables
    - potentials (list): List of potential terms
    - named_vars (dict): Dictionary of named variables
    """
    
    def __init__(self, name='', coords=None, check_bounds=True):
        pass
    
    def __enter__(self):
        """Enter model context."""
        return self
    
    def __exit__(self, *args):
        """Exit model context."""
        pass
    
    def compile_logp(self, vars=None, jacobian=True):
        """
        Compile log-probability function.
        
        Parameters:
        - vars (list, optional): Variables to include
        - jacobian (bool): Include Jacobian terms for transforms
        
        Returns:
        - logp_func: Compiled log-probability function
        """
        pass
    
    def compile_fn(self, outs, ins=None, **kwargs):
        """
        Compile PyTensor function from model variables.
        
        Parameters:
        - outs: Output variables
        - ins (list, optional): Input variables
        - **kwargs: Additional compilation options
        
        Returns:
        - compiled_fn: Compiled PyTensor function
        """
        pass

# Basic model definition
with pm.Model() as basic_model:
    # Model components go here
    alpha = pm.Normal('alpha', mu=0, sigma=1)
    beta = pm.Normal('beta', mu=0, sigma=1)
    sigma = pm.HalfNormal('sigma', sigma=1)
    
    # Linear combination
    mu = alpha + beta * x_data
    
    # Likelihood
    y_obs = pm.Normal('y_obs', mu=mu, sigma=sigma, observed=y_data)

# Model with coordinates and naming
coords = {
    'regions': ['north', 'south', 'east', 'west'],
    'time': range(2000, 2021)
}

with pm.Model(name='regional_model', coords=coords) as model:
    # Region-specific parameters
    alpha = pm.Normal('alpha', 0, 1, dims='regions')
    
    # Time-varying effects
    beta = pm.GaussianRandomWalk('beta', sigma=0.1, dims='time')

def modelcontext(model=None):
    """
    Get the current model from context or return specified model.
    
    Parameters:
    - model (Model, optional): Explicit model to return
    
    Returns:
    - model: Current model in context
    """

# Get current model
current_model = pm.modelcontext()

# Access model properties
print(f"Free RVs: {len(current_model.free_RVs)}")
print(f"Observed RVs: {len(current_model.observed_RVs)}")
print(f"Deterministics: {len(current_model.deterministics)}")

def set_data(new_data, model=None, coords=None):
    """
    Update data in existing model.
    
    Parameters:
    - new_data (dict): Dictionary of new data values
    - model (Model, optional): Target model
    - coords (dict, optional): New coordinate specifications
    """

# Define model with data containers
with pm.Model() as dynamic_model:
    # Data containers that can be updated
    X_data = pm.Data('X_data', X_train)
    y_data = pm.Data('y_data', y_train)
    
    # Model using data
    beta = pm.Normal('beta', 0, 1, shape=X_train.shape[1])
    mu = pm.math.dot(X_data, beta)
    y_pred = pm.Normal('y_pred', mu=mu, sigma=1, observed=y_data)
    
    # Sample with training data
    trace = pm.sample()

# Update for prediction on new data
pm.set_data({'X_data': X_test, 'y_data': None})
with dynamic_model:
    post_pred = pm.sample_posterior_predictive(trace)

with pm.Model() as model:
    # Creates random variable named 'parameter'
    parameter = pm.Normal('parameter', mu=0, sigma=1)
    
    # Access random variable properties
    print(f"Name: {parameter.name}")
    print(f"Distribution: {parameter.distribution}")
    print(f"Transform: {parameter.transform}")
    print(f"Shape: {parameter.shape}")

from pymc import Deterministic

class Deterministic:
    """
    Deterministic transformation of other variables.
    
    Parameters:
    - name (str): Variable name
    - var: PyTensor expression
    - dims (tuple, optional): Dimension names
    - model (Model, optional): Model context
    
    Attributes:
    - name (str): Variable name
    - owner: PyTensor variable
    """
    
    def __init__(self, name, var, dims=None, model=None):
        pass

# Deterministic transformations
with pm.Model() as model:
    # Parameters
    alpha = pm.Normal('alpha', 0, 1)
    beta = pm.Normal('beta', 0, 1)
    
    # Deterministic combinations
    linear_pred = pm.Deterministic('linear_pred', alpha + beta * x_data)
    
    # Transformed parameters
    log_odds = pm.Deterministic('log_odds', pm.math.log(p / (1 - p)))
    
    # Complex transformations
    interaction = pm.Deterministic('interaction', 
                                  alpha * beta + pm.math.exp(alpha))

# Centered vs non-centered parameterization
with pm.Model() as hierarchical:
    # Hyperparameters
    mu_alpha = pm.Normal('mu_alpha', 0, 10)
    sigma_alpha = pm.HalfNormal('sigma_alpha', 5)
    
    # Non-centered parameterization (better for sampling)
    alpha_raw = pm.Normal('alpha_raw', 0, 1, shape=n_groups)
    alpha = pm.Deterministic('alpha', mu_alpha + sigma_alpha * alpha_raw)
    
    # Soft constraints via deterministic
    alpha_constrained = pm.Deterministic('alpha_constrained', 
                                        pm.math.clip(alpha, -10, 10))

from pymc import Potential

class Potential:
    """
    Add arbitrary log-probability terms to the model.
    
    Parameters:
    - name (str): Name for the potential
    - var: PyTensor expression for log-probability
    - model (Model, optional): Model context
    """
    
    def __init__(self, name, var, model=None):
        pass

# Custom priors and constraints
with pm.Model() as constrained_model:
    # Parameters
    theta = pm.Uniform('theta', 0, 10, shape=3)
    
    # Custom constraint: sum of theta must be less than 5
    constraint = pm.Potential('sum_constraint', 
                             pm.math.switch(pm.math.sum(theta) < 5, 0, -np.inf))
    
    # Custom prior that's not available as distribution
    custom_prior = pm.Potential('custom_prior', 
                               -0.5 * pm.math.sum((theta - 2)**4))
    
    # Soft constraints with penalty
    soft_constraint = pm.Potential('soft_constraint',
                                  -10 * pm.math.maximum(0, pm.math.sum(theta) - 8))

from pymc.model.transform.conditioning import do

def do(model, interventions):
    """
    Apply causal interventions to model (do-operator).
    
    Parameters:
    - model (Model): Original model
    - interventions (dict): Variable interventions {var_name: value}
    
    Returns:
    - intervened_model: Model with interventions applied
    """

# Causal inference with interventions
with pm.Model() as causal_model:
    # Structural model
    X = pm.Normal('X', 0, 1)
    Y = pm.Normal('Y', mu=2*X + 1, sigma=0.5)  # Y depends on X
    Z = pm.Normal('Z', mu=X + Y, sigma=0.3)    # Z depends on X and Y
    
    # Observational model
    obs_trace = pm.sample()

# Interventional model: do(X = 1.5)
intervened_model = pm.do(causal_model, {'X': 1.5})
with intervened_model:
    # Sample from intervened distribution
    intervention_trace = pm.sample()

from pymc.model.transform.conditioning import observe

def observe(model, observations):
    """
    Condition model on observed values.
    
    Parameters:
    - model (Model): Original model
    - observations (dict): Observed values {var_name: value}
    
    Returns:
    - conditioned_model: Model conditioned on observations
    """

# Conditional inference
with pm.Model() as joint_model:
    X = pm.Normal('X', 0, 1)
    Y = pm.Normal('Y', mu=X, sigma=0.5)
    
# Condition on observed X
conditioned_model = pm.observe(joint_model, {'X': observed_x_values})
with conditioned_model:
    # Sample conditional distribution P(Y|X=observed)
    conditional_trace = pm.sample()

def compile_fn(outs, ins=None, mode=None, **kwargs):
    """
    Compile PyTensor function from model variables.
    
    Parameters:
    - outs: Output variables or expressions
    - ins (list, optional): Input variables
    - mode: Compilation mode ('FAST_RUN', 'FAST_COMPILE', etc.)
    - **kwargs: Additional PyTensor compilation options
    
    Returns:
    - compiled_fn: Compiled function
    """

with pm.Model() as model:
    # Parameters
    alpha = pm.Normal('alpha', 0, 1)
    beta = pm.Normal('beta', 0, 1)
    x = pm.Data('x', x_data)
    
    # Expression to compile
    prediction = alpha + beta * x
    
    # Compile prediction function
    predict_fn = pm.compile_fn([prediction], [alpha, beta, x])
    
    # Use compiled function
    pred_values = predict_fn(alpha_val, beta_val, x_new)

# Compile log-probability function
with model:
    logp_fn = model.compile_logp()
    
    # Evaluate log-probability at point
    test_point = {'alpha': 0.5, 'beta': -1.2}
    log_prob = logp_fn(test_point)

def create_regression_model(X, y, priors=None):
    """Factory function for regression models."""
    
    if priors is None:
        priors = {'alpha': (0, 10), 'beta': (0, 5), 'sigma': 1}
    
    with pm.Model() as regression_model:
        # Priors
        alpha = pm.Normal('alpha', *priors['alpha'])
        beta = pm.Normal('beta', *priors['beta'], shape=X.shape[1])
        sigma = pm.HalfNormal('sigma', priors['sigma'])
        
        # Linear model
        mu = alpha + pm.math.dot(X, beta)
        
        # Likelihood
        y_obs = pm.Normal('y_obs', mu=mu, sigma=sigma, observed=y)
    
    return regression_model

# Create multiple models with different priors
model1 = create_regression_model(X_data, y_data)
model2 = create_regression_model(X_data, y_data, 
                                priors={'alpha': (0, 1), 'beta': (0, 1), 'sigma': 0.5})

# Combine submodels
def create_measurement_model():
    with pm.Model() as measurement:
        # Measurement error
        sigma_m = pm.HalfNormal('sigma_m', 1)
        return measurement, sigma_m

def create_process_model():
    with pm.Model() as process:
        # Process parameters
        mu_p = pm.Normal('mu_p', 0, 5)
        sigma_p = pm.HalfNormal('sigma_p', 2)
        return process, (mu_p, sigma_p)

# Combine models
measurement_model, sigma_m = create_measurement_model()
process_model, (mu_p, sigma_p) = create_process_model()

with pm.Model() as combined_model:
    # Include submodel variables
    sigma_m_combined = pm.HalfNormal('sigma_m', 1)
    mu_p_combined = pm.Normal('mu_p', 0, 5)
    sigma_p_combined = pm.HalfNormal('sigma_p', 2)
    
    # Latent process
    latent = pm.Normal('latent', mu=mu_p_combined, sigma=sigma_p_combined)
    
    # Observed measurements
    observed = pm.Normal('observed', mu=latent, sigma=sigma_m_combined, 
                        observed=measurements)

def create_dynamic_model(data_stream):
    """Create model that adapts to streaming data."""
    
    with pm.Model() as dynamic:
        # Time-varying parameters
        n_timepoints = len(data_stream)
        
        # Random walk parameters
        innovation_sd = pm.HalfNormal('innovation_sd', 0.1)
        initial_state = pm.Normal('initial_state', 0, 1)
        
        # State evolution
        states = [initial_state]
        for t in range(1, n_timepoints):
            state_t = pm.Normal(f'state_{t}', 
                               mu=states[t-1], 
                               sigma=innovation_sd)
            states.append(state_t)
        
        # Observations
        obs_sd = pm.HalfNormal('obs_sd', 1)
        for t, data_t in enumerate(data_stream):
            pm.Normal(f'obs_{t}', mu=states[t], sigma=obs_sd, 
                     observed=data_t)
    
    return dynamic

# Analyze model structure
with pm.Model() as analysis_model:
    # Complex model...
    
    # Get all variables
    free_vars = analysis_model.free_RVs
    observed_vars = analysis_model.observed_RVs
    deterministic_vars = analysis_model.deterministics
    
    print("Free variables:")
    for var in free_vars:
        print(f"  {var.name}: {var.distribution}")
    
    print("Deterministic variables:")  
    for var in deterministic_vars:
        print(f"  {var.name}: shape {var.shape}")
    
    # Get variable by name
    specific_var = analysis_model['parameter_name']
    
    # Check model dimensions
    print(f"Model coordinates: {analysis_model.coords}")
    print(f"Model RNG: {analysis_model.rng}")

def validate_model(model):
    """Validate model structure and parameters."""
    
    with model:
        # Check for common issues
        try:
            # Compile log-probability function
            logp_fn = model.compile_logp()
            
            # Test evaluation at random point
            test_point = model.initial_point()
            logp_val = logp_fn(test_point)
            
            if np.isnan(logp_val) or np.isinf(logp_val):
                print("Warning: Model has numerical issues")
            
            print(f"Model log-probability: {logp_val}")
            
        except Exception as e:
            print(f"Model validation failed: {e}")
        
        # Check parameter shapes
        for var in model.free_RVs:
            print(f"{var.name}: shape {var.shape}, dtype {var.dtype}")

# Usage
validate_model(my_model)

Point = Dict[str, np.ndarray]  # Type alias for parameter points

# Working with points
with pm.Model() as model:
    alpha = pm.Normal('alpha', 0, 1)
    beta = pm.Normal('beta', 0, 1, shape=3)
    
    # Get initial point
    initial_point = model.initial_point()
    print(f"Initial point: {initial_point}")
    
    # Create custom point
    custom_point = {'alpha': 1.5, 'beta': np.array([0.5, -0.2, 0.8])}
    
    # Evaluate log-probability at point
    logp_fn = model.compile_logp()
    logp_value = logp_fn(custom_point)