otter

A lightweight pandas-based framework for research workflows. It manages datasets and working subsets, tracks dependent/independent/control variables, provides clean interfaces for transforming columns, and includes a full Monte Carlo simulation module for uncertainty analysis. Installs and imports as otter.

Name clash, known and accepted. otter-grader, the Berkeley autograder, also ships a top-level otter package. The two cannot share an environment. Use a separate virtualenv if you need both.

The vocabulary. A Pond holds your dataset and tracks which columns are dependent, independent and control. A pool is a working subset you carve off it with create_pool(), and every variable call takes full=True or full=False to say which one it reads from. Note Pool here is a pandas subset, not multiprocessing.Pool.

Installation

Core dependencies:

pip install pandas numpy geopandas

For the simulation module:

pip install scipy matplotlib

For running the example workflows:

pip install statsmodels scikit-learn

For running the tests:

pip install pytest

Or install everything at once:

pip install -r requirements.txt

Quick Start

import numpy as np
from otter import Pond
from otter import mean_center, log_transform, z_score

def clean(df):
    df.columns = df.columns.str.lower().str.strip()
    df = df.dropna(subset=["income", "age", "education"])
    df["female"] = (df["gender"] == "F").astype(int)
    return df

# Initialize from a CSV with a cleaning function
pond = Pond("survey_data.csv", clean)

# Transform with named functions from transforms.py
pond.normalize_and_attach("income", log_transform, "log_income")
pond.normalize_and_attach("age", mean_center, "age_centered")

# Create a working subset
pond.create_pool(lambda df: (df["age"] >= 18) & (df["employed"] == 1))

# Set up variables from the subset
pond.set_dependent("log_income", full=False)
pond.add_independents("age_centered", "education", full=False)
pond.add_controls("female", full=False)

# Retrieve design matrix and outcome vector
X = pond.get_X()
y = pond.get_y()

# Or get a frozen snapshot with full metadata
spec = pond.get_spec()

Simulation module

simulation.py provides a Monte Carlo simulation framework for running models under uncertainty. The primary integration path is get_spec() + Simulation.from_spec(): it fits distributions from your observed data, infers the correlation structure, and returns a ready-to-run simulation, no manual wiring needed.

from otter import Pond
from otter import Simulation

pond = Pond("labor_data.csv", clean)
pond.normalize_and_attach("income", log_transform, "log_income")
pond.set_dependent("log_income")
pond.add_independents("education", "experience")
pond.add_controls("female")

spec = pond.get_spec()

sim = Simulation.from_spec(
    spec,
    model=lambda row: 8.0 + 0.08 * row["education"] + 0.02 * row["experience"],
    n_iterations=10_000,
    seed=42,
)
result = sim.run()

The module also covers sensitivity analysis (tornado, one-at-a-time, Sobol indices), named scenario comparison, convergence diagnostics, and plotting. Full API below.

Experiment module

Sizing an experiment before it runs, and measuring it after.

from otter.experiment import sample_size_for_mean, assign_groups, compare_groups

# How many units to detect a 2% lift on a metric averaging 120, sd 300?
size = sample_size_for_mean(baseline_mean=120, baseline_sd=300, min_lift_pct=2)
size.treatment_n, size.control_n, size.total_n

# Randomise reproducibly, then measure.
assign_groups(user_ids, {"control": 0.5, "treatment": 0.5}, seed=1)
compare_groups(data, group_col="group", metric_cols=["revenue", "orders"],
               control="control", treatment="treatment")

Comparisons use Welch's t-test (unequal variances are handled, not assumed away) with Benjamini-Hochberg correction across metrics. Two things worth knowing:

• cuped_pre= reduces variance using a pre-period covariate, so the same sample detects a smaller effect. The covariate must be measured before assignment.
• pretest_balance() checks the randomisation actually worked by testing the pre-period metrics. A pre-period that is empty (new units, no history) is reported as uninformative rather than tested, because a degenerate t-test returns a confident answer built on nothing.

detectable_lift_for_mean() and detectable_lift_for_proportion() run the other direction: the sample is fixed, so what can it actually see?

Example Workflows

All examples in examples/ generate their own synthetic data so you can clone and run immediately:

python examples/ols_mincer.py
python examples/random_forest_churn.py
python examples/heckman_selection.py
python examples/monte_carlo_test.py

Running Tests

From the repo root:

pytest tests/test_pond.py -v

The test suite covers the full Pond class and every function in transforms.py, using synthetic data with no external dependencies.

pytest tests/test_pond.py::TestSubset -v
pytest tests/test_pond.py::TestTransforms::test_z_score -v

Start here

Run one of the example workflows in examples/: ols_mincer.py is the shortest path to seeing the framework end to end.

---

Reference

The rest of this file is the full API reference and design notes.

Repository Structure

otter/
├── pyproject.toml         # Package metadata (pip install .)
├── requirements.txt       # Dependencies (core + optional)
├── LICENSE                # MIT
├── .gitignore
├── README.md
├── src/otter/
│   ├── __init__.py        # public API re-exports
│   ├── pond.py              # Core data handling class + ModelSpec
│   ├── experiment.py      # Power, assignment, lift, CUPED, balance checks
│   ├── transforms.py      # Reusable single- and multi-column transforms
│   ├── simulation.py      # Monte Carlo simulation module
│   └── plotter.py         # Plotly plotting for simulation results
├── tests/
│   ├── test_pond.py       # Pond and transforms, on synthetic data
│   └── test_experiment.py # design, assignment, lift, CUPED, balance
└── examples/
    ├── data/
    │   └── startup_portfolio.csv      # generated on first run, not committed
    ├── ols_mincer.py                  # OLS Mincer wage equation
    ├── random_forest_churn.py         # Random forest churn prediction
    ├── heckman_selection.py           # Heckman two-step selection model
    └── monte_carlo_test.py            # Monte Carlo portfolio valuation

Pond API

Pond(source, handler=None, *, shapefile=False)

Constructor. Accepts a CSV filepath, shapefile path, DataFrame, or GeoDataFrame. The optional handler function transforms the data after loading.

# From a CSV with a cleaning function
def clean(df):
    df.columns = df.columns.str.lower()
    df["married"] = (df["marital_status"] == "married").astype(int)
    df = df.drop_duplicates()
    return df.dropna()

pond = Pond("data.csv", clean)

# From a CSV without cleaning
pond = Pond("data.csv")

# From a shapefile
pond = Pond("regions.shp", shapefile=True)

# From an existing DataFrame or GeoDataFrame
pond = Pond(existing_df)
pond = Pond(existing_df, clean)

The handler function receives a pd.DataFrame (or gpd.GeoDataFrame for shapefiles) and must return one. If the source type is unsupported, a TypeError is raised. The shapefile parameter is keyword-only.

create_pool(condition)

Creates a working subset of the full dataset based on a boolean condition.

pond.create_pool(lambda df: df["age"] > 30)
pond.create_pool(lambda df: (df["income"] > 20000) & (df["employed"] == 1))
pond.create_pool(lambda df: df["country"].isin(["US", "UK", "CA"]))

reset_pool()

Clears the working subset back to None.

set_dependent(col, full=True)

Sets the dependent (outcome) variable. Locks the source mode (see Design Notes).

pond.set_dependent("log_income")
pond.set_dependent("log_income", full=False)

add_independents(*cols, full=True)

Adds one or more independent (predictor) variables.

pond.add_independents("education", "experience", "tenure")
pond.add_independents("education", "experience", full=False)

add_controls(*cols, full=True)

Adds one or more control variables.

pond.add_controls("female", "married", "region_code")
pond.add_controls("female", "married", full=False)

get_X() / get_y()

Returns the design matrix as a pd.DataFrame or the dependent variable as a pd.Series.

get_spec()

Returns a frozen ModelSpec snapshot of the current variable specification. Contains copies of the design matrix, dependent variable, column name metadata, and the source DataFrame. Nothing mutates after creation.

spec = pond.get_spec()

spec.X              # DataFrame: same as get_X()
spec.y              # Series: same as get_y()
spec.independents   # ("education", "experience")
spec.controls       # ("female",)
spec.dependent      # "log_income"
spec.columns        # ("education", "experience", "female")
spec.all_columns    # ("log_income", "education", "experience", "female")
spec.source_label   # "full" or "subset"
spec.n              # number of observations
spec.data           # copy of the source DataFrame (for distribution fitting)

ModelSpec is the bridge between Pond and the simulation module: pass it to Simulation.from_spec() to build a data-driven Monte Carlo simulation.

attach(col_name, series, to_full=True, quiet=False)

Attaches a precomputed Series to the full dataset or subset.

from otter import square

pond.attach("age_sq", square(pond.data["age"]))
pond.attach("age_sq", square(pond.pool["age"]), to_full=False)

normalize_and_attach(source_col, normalizing_function, new_colname, full=True)

Applies a single-column transformation and attaches the result.

from otter import log_transform, z_score, mean_center, min_max_scale

pond.normalize_and_attach("income", log_transform, "log_income")
pond.normalize_and_attach("gpa", z_score, "gpa_z")
pond.normalize_and_attach("age", mean_center, "age_centered")
pond.normalize_and_attach("score", min_max_scale, "score_scaled")
pond.normalize_and_attach("wage", log_transform, "log_wage", full=False)

calculate_and_attach(source_cols, func, new_colname, full=True)

Applies a multi-column transformation and attaches the result. The function receives a DataFrame subset of the specified columns.

from otter import interaction, row_mean, row_sum, safe_ratio

pond.calculate_and_attach(["education", "experience"], interaction, "edu_x_exp")
pond.calculate_and_attach(["math", "reading", "science"], row_mean, "avg_score")
pond.calculate_and_attach(["q1", "q2", "q3", "q4"], row_sum, "annual_total")
pond.calculate_and_attach(
    ["revenue", "visits"],
    safe_ratio("revenue", "visits"),
    "rev_per_visit",
    full=False
)

clear_caches()

Clears the dependent, independents, controls, and source mode lock so you can set up a new specification without reinitializing.

Transforms Reference

transforms.py provides reusable functions so you don't have to write lambdas inline every time.

Single-column transforms (Series → Series)

For use with normalize_and_attach:

Function	Description	Example
mean_center	x - mean(x)	pond.normalize_and_attach("age", mean_center, "age_c")
z_score	(x - mean) / std	pond.normalize_and_attach("gpa", z_score, "gpa_z")
min_max_scale	Scale to [0, 1]	pond.normalize_and_attach("score", min_max_scale, "score_01")
log_transform	ln(x)	pond.normalize_and_attach("income", log_transform, "log_inc")
log1p_transform	ln(1 + x), safe for zeros	pond.normalize_and_attach("tickets", log1p_transform, "log_tix")
square	x²	pond.normalize_and_attach("exp", square, "exp_sq")
rank_transform	Replace with rank	pond.normalize_and_attach("score", rank_transform, "score_rank")

Factory transforms (return a callable)

Function	Description	Example
winsorize(lower, upper)	Clip at quantiles	pond.normalize_and_attach("income", winsorize(0.01, 0.99), "inc_wins")
demean_by_group(group_col)	Subtract group means	pond.normalize_and_attach("income", demean_by_group(pond.data["industry"]), "inc_dm")

Multi-column transforms (DataFrame → Series)

For use with calculate_and_attach:

Function	Description	Example
interaction	Product of first two columns	pond.calculate_and_attach(["edu", "exp"], interaction, "edu_x_exp")
row_mean	Row-wise average	pond.calculate_and_attach(["m", "r", "s"], row_mean, "avg")
row_sum	Row-wise sum	pond.calculate_and_attach(["q1", "q2"], row_sum, "total")
safe_ratio(num, denom)	Division, 0 → NaN	pond.calculate_and_attach(["rev", "vis"], safe_ratio("rev", "vis"), "rpv")

Simulation Module API

DistributionSpec(name, dist_type, params, empirical_data=None)

Defines an uncertain variable and its probability distribution. Validation happens on construction: missing params or unknown distribution types raise immediately.

dist_type	Required params
"normal"	{"mean": ..., "std": ...}
"uniform"	{"low": ..., "high": ...}
"lognormal"	{"mean": ..., "sigma": ...}
"beta"	{"a": ..., "b": ...}
"triangular"	{"left": ..., "mode": ..., "right": ...}
"exponential"	{"scale": ...}
"empirical"	empirical_data=np.array([...])

DistributionSpec("revenue",  "normal",   {"mean": 1e6, "std": 2e5})
DistributionSpec("cost",     "uniform",  {"low": 4e5, "high": 7e5})
DistributionSpec("duration", "empirical", empirical_data=observed_array)

InputManager

Collects uncertain variables, fits distributions from data, manages correlation, and draws samples.

mgr = InputManager()

# Register manually
mgr.add_variable(DistributionSpec("x", "normal", {"mean": 0, "std": 1}))
mgr.add_variables([...])
mgr.remove_variable("x")

# Fit from observed data
mgr.fit_from_data(df, ["col_a", "col_b"], dist_type="normal")
mgr.fit_from_data(df, ["col_c"], dist_type="empirical")

# Correlation
mgr.set_correlation_matrix(np.array([[1.0, 0.6], [0.6, 1.0]]))
mgr.infer_correlation_from_data(df)

# Draw samples: returns DataFrame of shape (n, n_variables)
draws = mgr.draw(10_000, seed=42)

When a correlation matrix is set, draws use a Gaussian copula (Cholesky decomposition + inverse-CDF transform) to produce correlated samples with the correct marginal distributions. Without a correlation matrix, draws are independent.

ModelFunction(func, vectorized=False)

Wraps the user-supplied model function.

# Row-wise: receives a pd.Series per iteration
model = ModelFunction(lambda row: row["revenue"] - row["cost"])

# Vectorized: receives the full DataFrame, returns an array (faster)
model = ModelFunction(
    lambda df: (df["revenue"] - df["cost"]).values,
    vectorized=True,
)

# Multi-output: return a dict per row
def multi(row):
    profit = row["revenue"] - row["cost"]
    return {"profit": profit, "margin": profit / row["revenue"]}
model = ModelFunction(multi)

MonteCarloEngine(inputs, model, n_iterations=10_000, seed=None)

Runs the simulation loop.

engine = MonteCarloEngine(mgr, model, n_iterations=10_000, seed=42)
result = engine.run()
result = engine.run(store_draws=False)  # save memory on large runs

SimulationResult

Container for outcomes and summary statistics.

result.outcomes         # np.ndarray of model outputs
result.draws            # DataFrame of input draws (if stored)

result.summarize()      # compute and cache all stats, returns dict
result.mean             # cached after summarize()
result.median
result.std
result.ci_lower         # 95% CI by default
result.ci_upper
result.percentiles      # {1: ..., 5: ..., 10: ..., 25: ..., 50: ..., 75: ..., 90: ..., 95: ..., 99: ...}

result.to_dataframe()   # draws + outcomes in one exportable DataFrame

Simulation(variables, model, *, n_iterations=10_000, seed=None, ...)

Top-level facade that wires everything together. Use this with manual DistributionSpec lists, or use Simulation.from_spec() with a ModelSpec from Pond.

sim = Simulation(
    variables=[
        DistributionSpec("growth",   "normal",     {"mean": 0.4, "std": 0.15}),
        DistributionSpec("churn",    "beta",        {"a": 2, "b": 30}),
        DistributionSpec("multiple", "triangular",  {"left": 3, "mode": 8, "right": 20}),
    ],
    model=portfolio_value,
    n_iterations=10_000,
    seed=42,
    correlation_matrix=corr_matrix,  # optional
)

result = sim.run()

The facade exposes sub-components directly:

sim.engine                  # MonteCarloEngine
sim.input_manager           # InputManager
sim.sensitivity             # SensitivityAnalyzer
sim.convergence             # ConvergenceDiagnostics (class reference)
sim.plot                    # SimulationPlotter

Simulation.from_spec(spec, model, *, dist_type, overrides, include_dependent, ...)

Builds a Simulation from a ModelSpec. Fits distributions from the spec's observed data, infers the correlation matrix, and returns a ready-to-run simulation.

Two modes:

• Standard (default): model provided, include_dependent=False. Fits distributions on independents + controls. The model function produces outcomes from simulated inputs.
• Joint distribution: model=None, include_dependent=True. Fits distributions on all variables including dependent. Returns correlated draws with no model applied.

Passing both model and include_dependent=True raises ValueError.

# Standard mode
sim = Simulation.from_spec(spec, model=my_func, seed=42)

# With per-column overrides
sim = Simulation.from_spec(
    spec, model=my_func,
    overrides={"income": {"dist_type": "lognormal"}},
)

# Joint distribution mode
sim = Simulation.from_spec(spec, include_dependent=True, dist_type="empirical")

Sensitivity Analysis

Accessed via sim.sensitivity or by constructing SensitivityAnalyzer(engine) directly.

# Tornado: which variable drives the most swing?
tornado = sim.sensitivity.tornado()
# Returns DataFrame: variable, low_value, high_value, low_outcome, high_outcome, swing
# Sorted by swing descending

# One-at-a-time: sweep a single variable across its range
oat = sim.sensitivity.one_at_a_time("revenue", n_steps=20)
# Returns DataFrame: variable_value, outcome

# Sobol indices: variance-based global sensitivity
sobol = sim.sensitivity.sobol_indices(n_samples=5_000, seed=99)
# Returns DataFrame: variable, S1, S1_conf, sorted by S1 descending

Scenario Comparison

Define named scenarios with distribution parameter overrides, then compare outcomes against baseline:

from otter import Scenario

scenarios = [
    Scenario("bull_market", overrides={
        "multiple": {"left": 8, "mode": 15, "right": 30},
    }),
    Scenario("bear_market", overrides={
        "multiple": {"left": 2, "mode": 4, "right": 8},
        "growth": {"mean": 0.20},
    }),
]

# Full results
results = sim.compare_scenarios(scenarios)
# Returns {"baseline": SimulationResult, "bull_market": ..., "bear_market": ...}

# Summary table
summary = sim.compare_scenarios_summary(scenarios)
# Returns DataFrame: scenario, mean, median, std, ci_lower, ci_upper, min, max

Only the parameters that differ need to be specified: everything else stays at the base case.

Convergence Diagnostics

Check whether the simulation ran enough iterations:

# Quick report
report = sim.check_convergence(result)
# {"is_converged": True, "relative_se": 0.0051, "current_n": 10000, "suggested_n": 39261}

# Detailed: running statistics
running = ConvergenceDiagnostics.running_statistics(result.outcomes)
# DataFrame: iteration, cumulative_mean, cumulative_std

# Did it converge?
ConvergenceDiagnostics.is_converged(result.outcomes, window=1000, tolerance=0.01)

# How many iterations do I need for 0.5% precision?
ConvergenceDiagnostics.suggest_n(result.outcomes, target_tolerance=0.005)

# Snapshots at increasing N
snapshots = sim.engine.run_convergence()
# [SimulationResult(n=100), ..., SimulationResult(n=10000)], all pre-summarized

Plotting

All plot methods return matplotlib Figure objects. Accessed via sim.plot or SimulationPlotter directly.

fig = sim.plot.histogram(result)                        # distribution with CI shading
fig = sim.plot.cumulative_density(result)               # empirical CDF with percentile markers
fig = sim.plot.convergence_plot(result.outcomes)         # running mean ± SE
fig = sim.plot.tornado_chart(tornado_data)               # sensitivity swings
fig = sim.plot.scenario_comparison(scenario_results)     # overlaid KDE curves

fig.savefig("output.png", dpi=150)

Supported Distributions

New distributions can be added by inserting an entry into _DISTRIBUTION_REGISTRY at the top of simulation.py. Each entry defines how to draw samples, validate parameters, fit from data, and transform through the inverse-CDF for correlated draws. No other code changes are required.

Example Workflows (full)

OLS Regression with statsmodels

A standard Mincer wage equation with log wages, centered experience, and a squared term.

import numpy as np
import statsmodels.api as sm
from otter import Pond, log_transform, mean_center, square

def clean(df):
    df.columns = df.columns.str.lower()
    df["female"] = (df["gender"] == "F").astype(int)
    return df.dropna(subset=["wage", "education", "experience", "age", "gender"])

pond = Pond("labor_data.csv", clean)

pond.normalize_and_attach("wage", log_transform, "log_wage")
pond.normalize_and_attach("experience", mean_center, "exp_centered")
pond.attach("exp_centered_sq", square(pond.data["exp_centered"]))

pond.set_dependent("log_wage")
pond.add_independents("education", "exp_centered", "exp_centered_sq")
pond.add_controls("female")

X = sm.add_constant(pond.get_X())
y = pond.get_y()

model = sm.OLS(y, X).fit()
print(model.summary())

Random Forest with scikit-learn

Predicting customer churn with engineered features and standardized inputs.

from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report
from otter import Pond, z_score, log1p_transform, safe_ratio

pond = Pond("customer_data.csv", clean)

pond.calculate_and_attach(["revenue", "visits"], safe_ratio("revenue", "visits"), "rev_per_visit")
pond.normalize_and_attach("tenure", z_score, "tenure_z")
pond.normalize_and_attach("support_tickets", log1p_transform, "log_tickets")

pond.set_dependent("churned")
pond.add_independents("rev_per_visit", "tenure_z", "log_tickets")
pond.add_controls("gender_code", "region_code")

X = pond.get_X().fillna(0)
y = pond.get_y()

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
rf = RandomForestClassifier(n_estimators=200, random_state=42)
rf.fit(X_train, y_train)
print(classification_report(y_test, rf.predict(X_test)))

Heckman Selection Model (Two-Step)

Correct for selection bias in observed wages using the inverse Mills ratio.

import statsmodels.api as sm
from scipy.stats import norm
from otter import Pond, mean_center, log_transform

pond = Pond("labor_survey.csv", clean)
pond.normalize_and_attach("age", mean_center, "age_centered")

# Step 1: Probit on full sample
pond.set_dependent("employed")
pond.add_independents("age_centered", "education")
pond.add_controls("married", "children")

probit = sm.Probit(pond.get_y(), sm.add_constant(pond.get_X())).fit(disp=0)
pond.attach("imr", norm.pdf(probit.fittedvalues) / norm.cdf(probit.fittedvalues))

# Step 2: OLS on employed subset with IMR correction
pond.clear_caches()
pond.create_pool(lambda df: df["employed"] == 1)
pond.normalize_and_attach("wage", log_transform, "log_wage", full=False)

pond.set_dependent("log_wage", full=False)
pond.add_independents("age_centered", "education", full=False)
pond.add_controls("imr", full=False)

ols = sm.OLS(pond.get_y(), sm.add_constant(pond.get_X())).fit()
print(ols.summary())

Monte Carlo Portfolio Simulation

Simulate a VC portfolio's 3-year value under uncertainty about growth, churn, market multiples, and discount rates.

from otter import Simulation, DistributionSpec, Scenario

def portfolio_value(row):
    base_arr = 33.0 * 12
    net_growth = row["growth_rate"] - row["churn_rate"]
    projected_arr = base_arr * (1 + net_growth) ** 3
    terminal = projected_arr * row["revenue_multiple"]
    return terminal / (1 + row["discount_rate"]) ** 3

sim = Simulation(
    variables=[
        DistributionSpec("growth_rate",       "normal",     {"mean": 0.40, "std": 0.15}),
        DistributionSpec("churn_rate",        "beta",        {"a": 2, "b": 30}),
        DistributionSpec("revenue_multiple",  "triangular",  {"left": 3, "mode": 8, "right": 20}),
        DistributionSpec("discount_rate",     "normal",     {"mean": 0.12, "std": 0.03}),
    ],
    model=portfolio_value,
    n_iterations=10_000,
    seed=42,
)

result = sim.run()
tornado = sim.sensitivity.tornado()

results = sim.compare_scenarios([
    Scenario("bull", overrides={"revenue_multiple": {"left": 8, "mode": 15, "right": 30}}),
    Scenario("bear", overrides={"revenue_multiple": {"left": 2, "mode": 4, "right": 8}}),
])

sim.plot.histogram(result).savefig("distribution.png")
sim.plot.tornado_chart(tornado).savefig("tornado.png")
sim.plot.scenario_comparison(results).savefig("scenarios.png")

Design Notes

Source mode locking. The set_dependent, add_independents, and add_controls methods all accept a full parameter. The first call locks the source mode to either "full" or "subset". Subsequent calls that use a different mode raise ValueError immediately rather than silently mixing columns from different DataFrames. clear_caches() resets the lock.

Guard pattern. Every method that accesses data checks is not None (not bare truthiness, which raises ValueError on DataFrames), handles both full=True and full=False branches explicitly, and bails early with a printed message when the needed dataset isn't available.

ModelSpec as bridge. Pond produces a frozen ModelSpec dataclass via get_spec(). The simulation module consumes it via Simulation.from_spec(). The dependency flows one direction: simulation.py can accept a ModelSpec, but does not import from pond.py. pond.py knows nothing about simulations.

Distribution registry. _DISTRIBUTION_REGISTRY maps string names to draw functions, scipy distributions, and parameter translation maps. Adding a new distribution is a single dictionary insertion: no other code changes needed. Correlated draws use a Gaussian copula (Cholesky decomposition of the correlation matrix applied to standard normal draws, then transformed through each variable's inverse-CDF).

Sensitivity analysis. Includes one-at-a-time sweeps, tornado charts, and variance-based Sobol indices via the Saltelli sampling scheme.