def _calculate_return_value(
args: typing.Tuple[pd.Series, # ts (time series)
float, # return_period
typing.Union[str, pd.Timedelta], # return_period_size
float, # threshold
typing.Union[str, pd.Timedelta], # r
str, # extremes_type
typing.Union[str,
scipy.stats.rv_continuous], # distribution
str, # distribution_name
typing.Optional[float], # alpha
int, # n_samples
],
) -> typing.Dict[str, typing.Union[str, typing.Optional[float]]]:
(
ts,
return_period,
return_period_size,
threshold,
r,
extremes_type,
distribution,
distribution_name,
alpha,
n_samples,
) = args
model = EVA(data=ts)
model.get_extremes(
method="POT",
extremes_type=extremes_type,
threshold=threshold,
r=r,
)
model.fit_model(
model="MLE",
distribution=distribution,
)
# TODO - this is a hack to avoid spawning nested subprocesses
_n_samples = n_samples % 10
while _n_samples < n_samples:
_n_samples += 10
model.get_return_value(
return_period=return_period,
return_period_size=return_period_size,
alpha=alpha,
n_samples=_n_samples,
)
rv, cil, ciu = model.get_return_value(
return_period=return_period,
return_period_size=return_period_size,
alpha=alpha,
n_samples=n_samples,
)
return {
"distribution_name": distribution_name,
"threshold": threshold,
"rv": rv,
"cil": cil,
"ciu": ciu,
}
def eva_model_pot(battery_wl_preprocessed) -> EVA:
eva_model = EVA(data=battery_wl_preprocessed)
eva_model.get_extremes(
method="POT",
extremes_type="high",
threshold=1.35,
r="24H",
)
return eva_model
def eva_model_bm(battery_wl_preprocessed) -> EVA:
eva_model = EVA(data=battery_wl_preprocessed)
eva_model.get_extremes(
method="BM",
extremes_type="high",
block_size="365.2425D",
errors="raise",
)
return eva_model
def eva_model_bm_emcee(battery_wl_preprocessed) -> EVA:
eva_model = EVA(data=battery_wl_preprocessed)
eva_model.get_extremes(
method="BM",
extremes_type="high",
block_size="365.2425D",
errors="raise",
)
eva_model.fit_model("Emcee", n_walkers=10, n_samples=100)
return eva_model
def eva_model_bm_mle(battery_wl_preprocessed) -> EVA:
eva_model = EVA(data=battery_wl_preprocessed)
eva_model.get_extremes(
method="BM",
extremes_type="high",
block_size="1Y",
errors="raise",
)
eva_model.fit_model("MLE")
return eva_model
def plot_aic_scores(
ts: pd.Series,
thresholds=None,
r: typing.Union[str, pd.Timedelta] = "24H",
extremes_type: str = "high",
distributions: typing.Optional[typing.List[typing.Union[
str, scipy.stats.rv_continuous]]] = None,
ax: typing.Optional[plt.Axes] = None,
figsize: tuple = (8, 5),
) -> plt.Axes:
"""
Plot AIC scores for each distribution and threshold.
Used to investigate which distribution better explains data variance for each
threshold value. Does NOT indicate which threshold value is better because
it will always have the same shape - logarithmic curve.
Parameters
----------
ts : pandas.Series
Time series of the signal.
thresholds : array-like, optional
An array of thresholds for which the AIC plot is plotted.
If None (default), plots AIC for 100 equally-spaced thresholds
between 90th (10th if extremes_type='high') percentile
and 10th largest (smallest if extremes_type='low') value in the series.
r : pandas.Timedelta or value convertible to timedelta, optional
Duration of window used to decluster the exceedances.
By default r='24H' (24 hours).
See pandas.to_timedelta for more information.
extremes_type : str, optional
high (default) - extreme high values
low - extreme low values
distributions : list, optional
List of distributions for which the AIC curves are plotted.
By default these are "genpareto" and "expon".
A distribution must be either a name of distribution from scipy.stats
or a subclass of scipy.stats.rv_continuous.
See https://docs.scipy.org/doc/scipy/reference/stats.html
ax : matplotlib.axes._axes.Axes, optional
If provided, then the plot is drawn on this axes.
If None (default), new figure and axes are created
figsize : tuple, optional
Figure size in inches in format (width, height).
By default it is (8, 5).
Returns
-------
plt.Axes
Axes object.
"""
# Get default `thresholds`
if thresholds is None:
thresholds = get_default_thresholds(
ts=ts,
extremes_type=extremes_type,
num=100,
)
# Get default `distributions`
if distributions is None:
distributions = [
"genpareto",
"expon",
]
distribution_names: typing.List[str] = []
for distribution in distributions:
if isinstance(distribution, str):
distribution_names.append(distribution)
else:
distribution_names.append(distribution.name)
# Calculate AIC values
model = EVA(data=ts)
results = []
for distribution, distribution_name in zip(distributions,
distribution_names):
for threshold in thresholds:
model.get_extremes(
method="POT",
extremes_type=extremes_type,
threshold=threshold,
r=r,
)
model.fit_model(model="MLE", distribution=distribution)
results.append({
"distribution_name": distribution_name,
"threshold": threshold,
"aic": model.AIC,
})
results = pd.DataFrame(data=results).sort_values("threshold",
ascending=True)
with plt.rc_context(rc=pyextremes_rc):
if ax is None:
_, ax = plt.subplots(figsize=figsize, dpi=96)
ax.grid(False)
for i, (distribution_name,
df) in enumerate(results.groupby("distribution_name")):
ax.plot(
df.loc[:, "threshold"],
df.loc[:, "aic"],
color=pyextremes_rc["axes.prop_cycle"].by_key()["color"][i],
lw=2,
ls="-",
label=distribution_name,
zorder=(i + 3) * 5,
)
# Plot legend
ax.legend(frameon=True, framealpha=0.9)
# Label axes
ax.set_xlabel("Threshold")
ax.set_ylabel("AIC Score")
return ax
def plot_return_value_stability(
ts: pd.Series,
return_period,
return_period_size: typing.Union[str, pd.Timedelta] = "365.2425D",
thresholds=None,
r: typing.Union[str, pd.Timedelta] = "24H",
extremes_type: str = "high",
distributions: typing.Optional[typing.List[typing.Union[
str, scipy.stats.rv_continuous]]] = None,
alpha: typing.Optional[float] = None,
n_samples: int = 100,
figsize: tuple = (8, 5),
) -> tuple: # pragma: no cover
"""
Plot return value stability plot for given threshold values.
The return value stability plot shows return values for given return period
for given thresholds.
The purpose of this plot is to investigate statibility and sensitivity of the
Generalized Pareto Distribution model to threshold value.
Threshold value selection should still be guided by the mean residual life plot
and the parameter stability plot. This plot should be used as additional check.
Parameters
----------
ts : pandas.Series
Time series of the signal.
return_period : number
Return period.
Given as a multiple of `return_period_size`.
return_period_size : str or pandas.Timedelta, optional
Size of return period (default='365.2425D').
If set to '30D', then a return period of 12
would be roughly equivalent to a 1 year return period (360 days).
thresholds : array-like, optional
An array of thresholds for which the mean residual life plot is plotted.
If None (default), plots mean residual life for 100 equally-spaced thresholds
between 90th (10th if extremes_type='low') percentile
and 10th largest (smallest if extremes_type='low') value in the series.
r : str or pandas.Timedelta, optional
Duration of window used to decluster the exceedances.
By default r='24H' (24 hours).
extremes_type : str, optional
high (default) - extreme high values
low - extreme low values
distributions : list, optional
List of distributions for which the return value curves are plotted.
By default these are "genpareto" and "expon".
A distribution must be either a name of distribution from with scipy.stats
or a subclass of scipy.stats.rv_continuous.
See https://docs.scipy.org/doc/scipy/reference/stats.html
alpha : float, optional
Confidence interval width in the range (0, 1).
If None (default), then confidence interval is not shown.
n_samples : int, optional
Number of bootstrap samples used to estimate
confidence interval bounds (default=100).
Ignored if `alpha` is None.
figsize : tuple, optional
Figure size in inches in format (width, height).
By default it is (8, 5).
Returns
-------
figure : matplotlib.figure.Figure
Figure object.
axes : matplotlib.axes._axes.Axes
Axes object.
"""
# Get default `thresholds`
if thresholds is None:
thresholds = get_default_thresholds(
ts=ts,
extremes_type=extremes_type,
num=100,
)
# Get default `distributions`
if distributions is None:
distributions = [
"genpareto",
"expon",
]
# Instantiate model
model = EVA(data=ts)
# Calculate return values for each threshold and distribution
return_values: typing.Dict[str, typing.List[float]] = {}
ci_lower: typing.Dict[str, typing.List[float]] = {}
ci_upper: typing.Dict[str, typing.List[float]] = {}
for distribution in distributions:
for threshold in thresholds:
model.get_extremes(
method="POT",
extremes_type=extremes_type,
threshold=threshold,
r=r,
)
model.fit_model(
model="MLE",
distribution=distribution,
)
rv, cil, ciu = model.get_return_value(
return_period=return_period,
return_period_size=return_period_size,
alpha=alpha,
n_samples=n_samples,
)
try:
return_values[distribution].append(rv)
ci_lower[distribution].append(cil)
ci_upper[distribution].append(ciu)
except KeyError:
return_values[distribution] = [rv]
ci_lower[distribution] = [cil]
ci_upper[distribution] = [ciu]
with plt.rc_context(rc=pyextremes_rc):
# Create figure and axes
fig, ax = plt.subplots(figsize=figsize, dpi=96)
ax.grid(False)
# Plot central estimate of return values
for i, distribution in enumerate(distributions):
color = pyextremes_rc["axes.prop_cycle"].by_key()["color"][i]
ax.plot(
thresholds,
return_values[distribution],
color=color,
lw=2,
ls="-",
label=distribution,
zorder=(i + 3) * 5,
)
# Plot confidence bounds
if alpha is not None:
for ci in [ci_lower[distribution], ci_upper[distribution]]:
ax.plot(
thresholds,
ci,
color=color,
lw=1,
ls="--",
zorder=(i + 2) * 5,
)
ax.fill_between(
thresholds,
ci_lower[distribution],
ci_upper[distribution],
facecolor=color,
edgecolor="None",
alpha=0.25,
zorder=(i + 1) * 5,
)
# Plot legend
ax.legend(
frameon=True,
framealpha=0.9,
)
# Label axes
ax.set_xlabel("Threshold")
ax.set_ylabel("Return value")
return fig, ax
