def byConfidenceInterval(self) -> ConfidenceIntervalResults:
"""
Classifies individual observations as data, lower outliers, and
upper outliers. Leverages a definition of confidence interval
that extends one standard deviation of the upper data above,
and one standard deviation of the lower data below. All other
data are outliers.
"""
global_mean: Rational = Moment.mean(self.data)
upper, lower = ops.splitList(self.data.data,
lambda obs: obs <= global_mean)
upper_std_dev: Rational = Moment.std_dev(Vector(upper))
lower_std_dev: Rational = Moment.std_dev(Vector(lower))
np_upper = np.std(upper)
np_lower = np.std(lower)
upper_outliers, upper_data = ops.splitList(
upper, lambda obs: obs <= global_mean + upper_std_dev)
lower_outliers, lower_data = ops.splitList(
lower, lambda obs: obs >= global_mean - lower_std_dev)
return ConfidenceIntervalResults(global_mean, upper_std_dev,
lower_std_dev,
upper_data + lower_data,
Vector(lower_outliers).sort().data,
Vector(upper_outliers).sort().data)
def test_gaussian() -> None:
truth: np.array = np.random.normal(0, 1, size=100)
wide: np.array = np.random.normal(0, 3, size=100)
biased: np.array = np.random.normal(6, 1, size=100)
to_ll: Callable[[List[Rational]], Callable[
[Rational], Rational]] = lambda data: Likelihood.gaussian(
Moment.mean(Vector(data)), Moment.std_dev(Vector(data)))
truth_ll: Callable[[Rational], Rational] = to_ll(truth)
wide_ll: Callable[[Rational], Rational] = to_ll(wide)
biased_ll: Callable[[Rational], Rational] = to_ll(biased)
draw_truth_from_truth: Rational = Likelihood.log_likelihood(
truth, truth_ll)
draw_wide_from_truth: Rational = Likelihood.log_likelihood(wide, truth_ll)
draw_biased_from_truth: Rational = Likelihood.log_likelihood(
biased, truth_ll)
draw_truth_from_wide: Rational = Likelihood.log_likelihood(truth, wide_ll)
draw_wide_from_wide: Rational = Likelihood.log_likelihood(wide, wide_ll)
draw_biased_from_wide: Rational = Likelihood.log_likelihood(
biased, wide_ll)
draw_truth_from_biased: Rational = Likelihood.log_likelihood(
truth, biased_ll)
draw_wide_from_biased: Rational = Likelihood.log_likelihood(
wide, biased_ll)
draw_biased_from_biased: Rational = Likelihood.log_likelihood(
biased, biased_ll)
assert draw_truth_from_truth > draw_wide_from_truth
assert draw_truth_from_truth > draw_biased_from_truth
assert draw_wide_from_wide < draw_truth_from_wide # Note that draws from the middle of wide will have higher likelihood
assert draw_wide_from_wide > draw_biased_from_wide
assert draw_biased_from_biased > draw_truth_from_biased
assert draw_biased_from_biased > draw_wide_from_biased
def test_std_dev() -> None:
assert withinTol(Moment.std_dev(vn01), np.std(n01)) == True
def test_variance() -> None:
test: float = Moment.variance(vn01)
truth: float = np.var(n01)
assert withinTol(Moment.variance(vn01), np.var(n01)) == True
def test_trimmed_mean() -> None:
p: int = 10
assert Moment.trimmed_mean(vsimple, 1) == 2
assert withinTol(Moment.trimmed_mean(vn01, p), np.mean(n01[p:-p]))
def test_mean() -> None:
assert Moment.mean(vsimple) == 2.25
test: float = Moment.mean(vn01)
truth: float = np.mean(n01)
assert withinTol(Moment.mean(vn01), np.mean(n01)) == True
def to_gaussian(data: List[Rational]) -> Callable[[Rational], Rational]:
return Likelihood.gaussian(Moment.mean(Vector(data)),
Moment.std_dev(Vector(data)))