expectation

Sequential hypothesis testing with e-values and e-processes. Optional Rust acceleration for massively parallel testing (300K+ simultaneous tests at ~24 ns/test).

v0.6.1 — the public API may still evolve before 1.0.

What this does

E-values replace p-values with a framework where you can monitor data continuously, stop whenever you want, and still have valid inference. No sample size calculations, no correction for peeking.

The library covers:

• Sequential testing — mean, proportion, quantile, variance tests with anytime-valid guarantees
• Parallel engine — Rust + rayon backend for 300K+ simultaneous tests (brain voxels, genomics, A/B tests at scale)
• Multiple testing — e-Bonferroni (FWER), e-BH (FDR), e-Holm (FWER) for cross-test error control
• Confidence sequences — time-uniform confidence intervals that are valid at every sample size
• Calibration — convert between p-values and e-values

Install

pip install expectation

Prebuilt wheels bundle the Rust parallel engine, so no Rust toolchain is required.

From source (development)

git clone https://github.com/jakorostami/expectation.git
cd expectation
pip install -e ".[dev]"
maturin develop --release

Usage

Single sequential test

from expectation.seqtest import SequentialTesting

test = SequentialTesting(test_type="mean", null_value=0, alternative="greater")

result = test.update([0.5, 1.2, 0.8])
print(f"e-value: {result.e_value:.2f}, reject: {result.reject_null}")

result = test.update([1.5, 1.1])
print(f"cumulative e-process: {result.e_process.cumulative_value:.2f}")

Massively parallel testing (Rust)

import numpy as np
from expectation.par_seqtest import ParallelSequentialTest, ParallelTestConfig

config = ParallelTestConfig(
    n_tests=300_000,
    alpha=0.05,
    alternative="greater",
    combiner="empirically_adaptive",
)
engine = ParallelSequentialTest(config=config, null_values=0.0, variance=1.0)

for t in range(100):
    obs = np.random.randn(300_000)
    obs[:1000] += 0.5  # signal in first 1000
    result = engine.step(obs)

# Cross-test error control
bh = engine.e_bh()          # FDR control
bonf = engine.e_bonferroni() # FWER control

# Per-test state
log_ep = engine.log_e_processes()   # log e-process values
pvals = engine.p_values()           # calibrated p-values
stops = engine.stopping_times()     # when each test rejected

References

• Ramdas, Wang (2025). Hypothesis testing with e-values
• Howard, Ramdas, McAuliffe, Sekhon (2022). Time-uniform, nonparametric, nonasymptotic confidence sequences
• Waudby-Smith, Ramdas (2024). Estimating means of bounded random variables by betting
• Vovk, Wang (2021). E-values: calibration, combination, and applications

Citation

BibTeX

@software{rostami2024expectation,
  author = {Rostami, Jako},
  title = {expectation: Sequential testing with e-values and e-processes},
  year = {2024},
  url = {https://github.com/jakorostami/expectation},
  version = {0.6.1}
}

APA

Rostami, J. (2024). expectation: Python library for sequential testing and e-processes (Version 0.6.1) [Computer software]. https://github.com/jakorostami/expectation