Skip to content
Permalink
Branch: master
Find file Copy path
Find file Copy path
Fetching contributors…
Cannot retrieve contributors at this time
85 lines (60 sloc) 2.6 KB

Tutorials

Independence Tests

The independence testing problem is generalized as follows: consider random variables X and Y that have joint density F_{XY} = F_{X|Y} F_Y. We are testing:

H_0: F_{XY} &= F_X F_Y \\
H_A: F_{XY} &\neq F_X F_Y

These tutorials overview how to use these tests as well as benchmarks comparing the algorithms included against each other.

.. toctree::
    :maxdepth: 1

    tutorials/independence/independence
    tutorials/independence/indep_power
    tutorials/independence/indep_alg_speed


K-sample Tests

The k-sample testing problem is generalized as follows: consider random variables X_1, X_2, \ldots, X_k that have densities F_1, F_2, \ldots, F_k. Then, we are testing

H_0:\ &F_1 = F_2 = \ldots F_k \\
H_A:\ &\exists \ j \neq j' \text{ s.t. } F_j \neq F_{j'}

This tutorial overview how to use k-sample tests in hyppo.

.. toctree::
    :maxdepth: 1

    tutorials/ksample/ksample


Time-Series Tests

Time-series tests of independence consider the following problem: consider random variables X and Y with joint density F_{XY} and marginal densities F_X and F_Y. Let F_{X_t}, F_{Y_s}, and F_{X_t Y_s} represent the marginal and joint distributions of time-indexed random varlables X_t and Y_s at timesteps t and s. Let \{ (X_t, Y_t) \}_{t = -\infty}^\infty be a full jointly-sampled strictly stationary time series with the observed sample \{ (X_1, Y_1), \ldots (X_n, Y_n) \}. Choose some nonnegative integer M as the maximium lag hyperparamater. Then we are testing,

H_0: F_{X_t Y_{t - j}} &= F_{X_t} F_{Y_{t - j}} \text{ for each } j \in \{ 0, 1, \ldots, M \} \\
H_A: F_{X_t Y_{t - j}} &\neq F_{X_t} F_{Y_{t - j}} \text{ for some } j \in \{ 0, 1, \ldots, M \}

This tutorial overview how to use time_series based tests in hyppo.

.. toctree::
    :maxdepth: 1

    tutorials/time_series/time_series


Sims

To evaluate existing implmentations and benchmark against other packages, we have developed a suite of 20 dependency structures. The simulation settings include polynomial (linear, quadratic, cubic), trigonometric (sinusoidal, circular, ellipsoidal, spiral), geometric (square, diamond, w-shaped), and other functions. We also include 3 sample Gaussian simulations as well, which are sampled from multivariate normal distribusions.

.. toctree::
    :maxdepth: 1

    tutorials/sims/indep_simulations
You can’t perform that action at this time.