예제 #1
0
def model_best(y1, y2, samples=1000):
    """Bayesian Estimation Supersedes the T-Test

    This model runs a Bayesian hypothesis comparing if y1 and y2 come
    from the same distribution. Returns are assumed to be T-distributed.

    In addition, computes annual volatility and Sharpe of in and
    out-of-sample periods.

    This model replicates the example used in:
    Kruschke, John. (2012) Bayesian estimation supersedes the t
    test. Journal of Experimental Psychology: General.

    Parameters
    ----------
    y1 : array-like
        Array of returns (e.g. in-sample)
    y2 : array-like
        Array of returns (e.g. out-of-sample)
    samples : int, optional
        Number of posterior samples to draw.

    Returns
    -------
    pymc3.sampling.BaseTrace object
        A PyMC3 trace object that contains samples for each parameter
        of the posterior.

    See Also
    --------
    plot_stoch_vol : plotting of tochastic volatility model
    """

    y = np.concatenate((y1, y2))

    mu_m = np.mean(y)
    mu_p = 0.000001 * 1 / np.std(y)**2

    sigma_low = np.std(y)/1000
    sigma_high = np.std(y)*1000
    with pm.Model():
        group1_mean = pm.Normal('group1_mean', mu=mu_m, tau=mu_p,
                                testval=y1.mean())
        group2_mean = pm.Normal('group2_mean', mu=mu_m, tau=mu_p,
                                testval=y2.mean())
        group1_std = pm.Uniform('group1_std', lower=sigma_low,
                                upper=sigma_high, testval=y1.std())
        group2_std = pm.Uniform('group2_std', lower=sigma_low,
                                upper=sigma_high, testval=y2.std())
        nu = pm.Exponential('nu_minus_two', 1/29., testval=4.) + 2.

        returns_group1 = pm.T('group1', nu=nu, mu=group1_mean,
                              lam=group1_std**-2, observed=y1)
        returns_group2 = pm.T('group2', nu=nu, mu=group2_mean,
                              lam=group2_std**-2, observed=y2)

        diff_of_means = pm.Deterministic('difference of means',
                                         group2_mean - group1_mean)
        pm.Deterministic('difference of stds',
                         group2_std - group1_std)
        pm.Deterministic('effect size', diff_of_means /
                         pm.sqrt((group1_std**2 +
                                  group2_std**2) / 2))

        pm.Deterministic('group1_annual_volatility',
                         returns_group1.distribution.variance**.5 *
                         np.sqrt(252))
        pm.Deterministic('group2_annual_volatility',
                         returns_group2.distribution.variance**.5 *
                         np.sqrt(252))

        pm.Deterministic('group1_sharpe', returns_group1.distribution.mean /
                         returns_group1.distribution.variance**.5 *
                         np.sqrt(252))
        pm.Deterministic('group2_sharpe', returns_group2.distribution.mean /
                         returns_group2.distribution.variance**.5 *
                         np.sqrt(252))

        step = pm.NUTS()

        trace = pm.sample(samples, step)
    return trace
예제 #2
0
파일: bayesian.py 프로젝트: lib3r/pyfolio
def model_best(y1, y2, samples=1000):
    """Bayesian Estimation Supersedes the T-Test

    This model runs a Bayesian hypothesis comparing if y1 and y2 come
    from the same distribution. Returns are assumed to be T-distributed.

    In addition, computes annual volatility and Sharpe of in and
    out-of-sample periods.

    This model replicates the example used in:
    Kruschke, John. (2012) Bayesian estimation supersedes the t
    test. Journal of Experimental Psychology: General.

    Parameters
    ----------
    y1 : array-like
        Array of returns (e.g. in-sample)
    y2 : array-like
        Array of returns (e.g. out-of-sample)
    samples : int, optional
        Number of posterior samples to draw.

    Returns
    -------
    model : pymc.Model object
        PyMC3 model containing all random variables.
    trace : pymc3.sampling.BaseTrace object
        A PyMC3 trace object that contains samples for each parameter
        of the posterior.

    See Also
    --------
    plot_stoch_vol : plotting of tochastic volatility model
    """

    y = np.concatenate((y1, y2))

    mu_m = np.mean(y)
    mu_p = 0.000001 * 1 / np.std(y)**2

    sigma_low = np.std(y) / 1000
    sigma_high = np.std(y) * 1000
    with pm.Model() as model:
        group1_mean = pm.Normal('group1_mean',
                                mu=mu_m,
                                tau=mu_p,
                                testval=y1.mean())
        group2_mean = pm.Normal('group2_mean',
                                mu=mu_m,
                                tau=mu_p,
                                testval=y2.mean())
        group1_std = pm.Uniform('group1_std',
                                lower=sigma_low,
                                upper=sigma_high,
                                testval=y1.std())
        group2_std = pm.Uniform('group2_std',
                                lower=sigma_low,
                                upper=sigma_high,
                                testval=y2.std())
        nu = pm.Exponential('nu_minus_two', 1 / 29., testval=4.) + 2.

        returns_group1 = pm.T('group1',
                              nu=nu,
                              mu=group1_mean,
                              lam=group1_std**-2,
                              observed=y1)
        returns_group2 = pm.T('group2',
                              nu=nu,
                              mu=group2_mean,
                              lam=group2_std**-2,
                              observed=y2)

        diff_of_means = pm.Deterministic('difference of means',
                                         group2_mean - group1_mean)
        pm.Deterministic('difference of stds', group2_std - group1_std)
        pm.Deterministic(
            'effect size', diff_of_means / pm.sqrt(
                (group1_std**2 + group2_std**2) / 2))

        pm.Deterministic(
            'group1_annual_volatility',
            returns_group1.distribution.variance**.5 * np.sqrt(252))
        pm.Deterministic(
            'group2_annual_volatility',
            returns_group2.distribution.variance**.5 * np.sqrt(252))

        pm.Deterministic(
            'group1_sharpe', returns_group1.distribution.mean /
            returns_group1.distribution.variance**.5 * np.sqrt(252))
        pm.Deterministic(
            'group2_sharpe', returns_group2.distribution.mean /
            returns_group2.distribution.variance**.5 * np.sqrt(252))

        step = pm.NUTS()

        trace = pm.sample(samples, step)
    return model, trace
예제 #3
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    lam1 = group1_std**-2
    lam2 = group2_std**-2

    group1 = pm.StudentT('drug', nu=nu, mu=group1_mean, lam=lam1, observed=y1)
    group2 = pm.StudentT('placebo',
                         nu=nu,
                         mu=group2_mean,
                         lam=lam2,
                         observed=y2)

    diff_of_means = pm.Deterministic('difference of means',
                                     group1_mean - group2_mean)
    diff_of_stds = pm.Deterministic('difference of stds',
                                    group1_std - group2_std)
    effect_size = pm.Deterministic(
        'effect size', diff_of_means / pm.sqrt(
            (group1_std**2 + group2_std**2) / 2))

    step = pm.NUTS()


def run(n=3000):
    if n == "short":
        n = 500
    with model:
        trace = pm.sample(n, step)

    burn = n / 10

    pm.traceplot(trace[burn:])
    pm.plots.summary(trace[burn:])
예제 #4
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with pm.Model() as model:
    group1_mean = pm.Normal('group1_mean', mu=mu_m, tau=mu_p, testval=y1.mean())
    group2_mean = pm.Normal('group2_mean', mu=mu_m, tau=mu_p, testval=y2.mean())
    group1_std = pm.Uniform('group1_std', lower=sigma_low, upper=sigma_high, testval=y1.std())
    group2_std = pm.Uniform('group2_std', lower=sigma_low, upper=sigma_high, testval=y2.std())
    nu = pm.Exponential('nu_minus_one', 1/29.) + 1
    
    lam1 = group1_std**-2
    lam2 = group2_std**-2

    group1 = pm.T('drug', nu=nu, mu=group1_mean, lam=lam1, observed=y1)
    group2 = pm.T('placebo', nu=nu, mu=group2_mean, lam=lam2, observed=y2)

    diff_of_means = pm.Deterministic('difference of means', group1_mean - group2_mean)
    diff_of_stds = pm.Deterministic('difference of stds', group1_std - group2_std)
    effect_size = pm.Deterministic('effect size', diff_of_means / pm.sqrt((group1_std**2 + group2_std**2) / 2))

    step = pm.NUTS()

def run(n=3000):
    if n == "short":
        n = 500
    with model:
        trace = pm.sample(n, step)

    burn = n/10

    pm.traceplot(trace[burn:]);
    pm.plots.summary(trace[burn:])
        
if __name__ == '__main__':