pecos.metrics module

The metrics module contains metrics that describe the quality control analysis or compute quantities that might be of use in the analysis

qci(mask, tfilter=None)

Compute the quality control index (QCI) for each column, defined as:

$QCI={\displaystyle \frac{\sum _{t\in T}{X}_{dt}}{|T|}}$

where $T$ is the set of timestamps in the analysis. $X_{dt}$ is a data point for column $d$ time t` that passed all quality control test. $|T|$ is the number of data points in the analysis.

Parameters:

• mask (pandas DataFrame) – Test results mask, returned from pm.mask

• tfilter (pandas Series, optional) – Time filter containing boolean values for each time index

Returns:

Quality control index

Return type:

pandas Series

rmse(data1, data2, tfilter=None)

Compute the root mean squared error (RMSE) for each column, defined as:

$RMSE=\sqrt{{\displaystyle \frac{\sum (dat{a}_1-dat{a}_2{)}^2}{n}}}$

where $dat{a}_1$ is a time series, $dat{a}_2$ is a time series, and $n$ is a number of data points.

Parameters:

• data1 (pandas DataFrame) – Data

• data2 (pandas DataFrame) – Data. Note, the column names in data1 must equal the column names in data2

• tfilter (pandas Series, optional) – Time filter containing boolean values for each time index

Returns:

Root mean squared error

Return type:

pandas Series

time_integral(data, tfilter=None)

Compute the time integral (F) for each column, defined as:

$F=\int fdt$

where $f$ is a column of data $dt$ is the time step between observations. The integral is computed using the trapezoidal rule from numpy.trapezoid. Results are given in [original data units]*seconds. NaN values are set to 0 for integration.

Parameters:

• data (pandas DataFrame) – Data

• tfilter (pandas Series, optional) – Time filter containing boolean values for each time index

Returns:

Integral

Return type:

pandas Series

time_derivative(data, tfilter=None)

Compute the derivative (f’) of each column, defined as:

$f^{\prime }={\displaystyle \frac{df}{dt}}$

where $f$ is a column of data $dt$ is the time step between observations. The derivative is computed using central differences from numpy.gradient. Results are given in [original data units]/seconds.

Parameters:

• data (pandas DataFrame) – Data

• tfilter (pandas Series, optional) – Filter containing boolean values for each time index

Returns:

Derivative of the data

Return type:

pandas DataFrame

probability_of_detection(observed, actual, tfilter=None)

Compute probability of detection (PD) for each column, defined as:

$PD={\displaystyle \frac{TP}{TP+FN}}$

where $TP$ is number of true positives and $FN$ is the number of false negatives.

Parameters:

• observed (pandas DataFrame) – Estimated conditions (True = background, False = anomalous), returned from pm.mask

• actual (pandas DataFrame) – Actual conditions, (True = background, False = anomalous). Note, the column names in observed must equal the column names in actual

• tfilter (pandas Series, optional) – Filter containing boolean values for each time index

Returns:

Probability of detection

Return type:

pandas Series

false_alarm_rate(observed, actual, tfilter=None)

Compute false alarm rate (FAR) for each column, defined as:

$FAR={\displaystyle \frac{TN}{TN+FP}}$

where $TN$ is number of true negatives and $FP$ is the number of false positives.

Parameters:

• estimated (pandas DataFrame) – Estimated conditions (True = background, False = anomalous), returned from pm.mask

• actual (pandas DataFrame) – Actual conditions, (True = background, False = anomalous). Note, the column names in observed must equal the column names in actual.

• tfilter (pandas Series, optional) – Filter containing boolean values for each time index

Returns:

False alarm rate

Return type:

pandas Series