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        "author": "Andrew Ross",
        "author_email": "andrewslavinross@gmail.com",
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        "description": "Sample Space\n============\n\n...is a very lightweight Python API for simulating sample spaces,\nevents, random variables, and (conditional) distributions.\n\nExample\n-------\n\nCheck out the `iPython notebook <./example.ipynb>`__ or read the\nfollowing:\n\n.. code:: python\n\n    from sample_space import *\n\n    class NCoinTosses(Experiment):\n        def __init__(self, n, p):\n            self.n = n\n            self.p = p\n\n        def rerun(self):\n            self.tosses = [Bern(self.p) for _ in range(self.n)]\n\n        def heads(self):\n            return sum(self.tosses)\n\n        def there_are_at_least_two_heads(self):\n            return self.heads() >= 2\n\n        def first_toss_heads(self):\n            return self.tosses[0]\n\n    space = SampleSpace(NCoinTosses(10, 0.5), iters=20000)\n\n    # ask for probability of any truthy method\n    print('        P(#H>=2):', space.probability_that('there_are_at_least_two_heads'))\n\n    # alias for the above, if it's more grammatical\n    print('           P(H1):', space.probability_of('first_toss_heads'))\n\n    # change the number of iterations\n    print(' P(H1), 1K iters:', space.probability_of('first_toss_heads', iters=1000))\n\n    # ask for probabilities of functions of random variables\n    print('         P(#H>5):', space.probability_that(['heads', is_greater_than(5)]))\n\n    # ask for conditional probabilities\n    print('      P(#H>5|H1):', space.probability_that(['heads', is_greater_than(5)], given=['first_toss_heads']))\n    print('      P(H1|#H>5):', space.probability_of('first_toss_heads', given=[['heads', is_greater_than(5)]]))\n    print(' P(#H>5|H1,H>=2):', space.probability_that(['heads', is_greater_than(5)],\n        given=['first_toss_heads', 'there_are_at_least_two_heads']))\n\n    # ask for expectations, variances, and moments, conditionally or absolutely\n    print('           E(#H):', space.expected_value_of('heads'))\n    print('        E(#H|H1):', space.expected_value_of('heads', given=['first_toss_heads']))\n    print('         Var(#H):', space.variance_of('heads'))\n    print('      Var(#H|H1):', space.variance_of('heads', given=['first_toss_heads']))\n    print('1st moment of #H:', space.nth_moment_of('heads', 1))\n    print('2nd moment of #H:', space.nth_moment_of('heads', 2))\n    print('3rd moment of #H:', space.nth_moment_of('heads', 3))\n    print('4th moment of #H:', space.nth_moment_of('heads', 4))\n    print('  Skewness of #H:', space.nth_moment_of('heads', 3, central=True, normalized=True), '(using nth_moment_of w/ central=True, normalized=True)')\n    print('  Skewness of #H:', space.skewness_of('heads'), '(using skewness_of)')\n    print('  Kurtosis of #H:', space.kurtosis_of('heads'))\n\n    # some plots\n    fig = plt.figure(figsize=(14,3))\n\n    # plot distribution histograms\n    fig.add_subplot(121)\n    space.plot_distribution_of('heads') # pass kwargs\n    plt.legend()\n\n    # plot conditional distribution histograms\n    fig.add_subplot(122)\n    space.plot_distribution_of('heads', given=['first_toss_heads'], bins=10) # can pass kwargs\n    plt.legend()\n    plt.show()\n\nWhich should output (plus some plots):\n\n::\n\n            P(#H>=2): 0.98975\n               P(H1): 0.502\n     P(H1), 1K iters: 0.48\n             P(#H>5): 0.37665\n          P(#H>5|H1): 0.5076294006183305\n          P(H1|#H>5): 0.6580109757729888\n     P(#H>5|H1,H>=2): 0.49361831442463533\n               E(#H): 4.9983\n            E(#H|H1): 5.48924623116\n             Var(#H): 2.4486457975\n          Var(#H|H1): 2.31806506582\n    1st moment of #H: 4.99245\n    2nd moment of #H: 27.5097\n    3rd moment of #H: 163.13055\n    4th moment of #H: 1015.54155\n      Skewness of #H: -0.00454435802967 (using nth_moment_of w/ central=True, normalized=True)\n      Skewness of #H: 0.00414054522343 (using skewness_of)\n      Kurtosis of #H: 2.78225928171\n\nWhy?\n----\n\nMostly to avoid bugs / reduce boilerplate in statistical simulations for\nsanity-checking homework solutions. But also to get a better\nunderstanding of probability theory.\n\n`Sample spaces <https://en.wikipedia.org/wiki/Sample_space>`__ are a\ncore concept in probability theory. They encapsulate the idea of\nrepeatedly running an experiment with random results. Almost every\nimportant statistical quantity -- the probability of an event, or any\nmoment of a random variable -- is always defined relative to a sample\nspace. So if you're trying to program meaningful simulations (and if\nyou're more concerned with expressiveness than performance), you might\nas well organize your code by explicitly defining one.\n\nInstallation / Usage\n--------------------\n\nFirst run\n\n::\n\n    pip install sample_space\n\nand ``import`` the library. Then define a subclass of ``Experiment``\nthat responds to ``rerun(self)``. ``rerun`` should perform a random\nexperiment and store one or more basic results as instance variables. If\nyou want to define more complex events or random variables, you can\nexpress them as instance methods.\n\nThen, initialize a ``SampleSpace`` with an instance of your\n``Experiment``. You can query your sample space for the\n``probability_that``/``probability_of`` an event, or you can query it\nfor the ``distribution_of``, ``expected_value_of``, ``variance_of``,\n``skewness_of``, ``kurtosis_of``, or ``nth_moment_of`` of random\nvariable (which can also just be an event, in which case it will be\ninterpreted as an indicator). Finally, for any of these methods, you can\npass a ``given`` keyword argument with a list of events, which will make\nany results you obtain conditional on all of those events occurring.\nBehind the scenes, ``SampleSpace`` will just ``rerun`` your experiment\n10000 times and average your random variable or count how often an event\noccurs (conditionally). You can pass an ``iters`` keyword argument to\nany method or to ``SampleSpace.__init__`` to increase the number of\niterations.\n\nTo reference events or random variable, pass the string name of an\ninstance variable or instance method of your experiment, or pass an\narray with a variable/method name and a lambda function. For example:\n\n.. code:: python\n\n    space = SampleSpace(CoinTossExperiment(10))\n    space.probability_that('first_toss_is_heads')\n    space.probability_that(['n_heads', lambda h: h > 5])\n    space.expected_value_of('n_heads')\n    space.expected_value_of('n_heads', given=['first_toss_is_heads'])\n    space.probability_that('first_toss_is_heads, given=[['n_heads', lambda h: h > 3], 'last_toss_is_heads'])\n\nAdditionally, ``sample_space`` defines a few helpful lambda-returning\nmethods (``is_greater_than(x)``, ``is_less_than(x)``,\n``is_at_least(x)``, ``is_at_most(x)``, ``equals(x)``) for convenience.\nOf course, you could also define instance methods on your ``Experiment``\nto accomplish the same goal.\n\nThe library also exposes a few basic sampling functions (``Bern(p)``,\n``Bin(n,p)``, ``RandomSign(p)``, and ``Categ(categories, weights)``) to\nassist with defining experiments.\n\nLite Version\n------------\n\nIf you'd prefer not to define a full ``Experiment`` class, you can also\njust define a random event / random variable function that returns\neither a boolean or a number, and call\n``probability_that``/``expected_value_of``:\n\n.. code:: python\n\n    import sample_space as ss\n\n    def weighted_coin_flip_is_heads(p=0.4):\n      return ss.Bern(p)\n\n    def n_weighted_heads(n=100, p=0.4):\n      return sum(weighted_coin_flip_is_heads(p) for _ in range(n))\n\n    print(ss.probability_that(weighted_coin_flip_is_heads))\n    print(ss.probability_that(lambda: weighted_coin_flip_is_heads(0.5))\n    print(ss.expected_value_of(n_weighted_heads))\n    print(ss.expected_value_of(lambda: n_weighted_heads(200, 0.3)))\n\nLicense\n-------\n\n`MIT <http://opensource.org/licenses/MIT>`__",
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