Beta-Sigma API¶
BSBase (Base class for BSEqSamp and BSArbSamp)¶
- class PyAstronomy.pyasl.BSBase¶
Functionality to estimate noise from equidistantly and arbitrarily sampled data.
Methods
estimateStdMAD(x, mode)Estimate standard deviation based on median absolute deviation (MAD)
meanUnbStd(x)Mean and (unbiased) standard deviation of the mean.
stdUnbiased(y)Get unbiased estimate of the standard deviation and its standard deviation.
stdc4(n)Calculate c4 factor.
subsetIndexDissection(ndp, N, j)Find array indices of (N+2)-length subsets.
subsetIndices(cd)Compose indices sets defining the subsets to construct the beta sample.
variance(x, mode)Estimate variance from sample
- _checkJP(j)¶
Check validity of specified jump parameter.
- _checkN(N)¶
Check validity of specified order of approximation.
- estimateStdMAD(x, mode)¶
Estimate standard deviation based on median absolute deviation (MAD)
- Parameters
- xarray
Sample from which to determine the standard deviation.
- modestring, {zm, em}
If ‘zm’, the population median is assumed to be zero. If ‘em’, the population median is estimated as the sample median.
- Returns
- stdfloat
Estimate of the standard deviation
- meanUnbStd(x)¶
Mean and (unbiased) standard deviation of the mean.
- Parameters
- xarray
Sampe from which to calculate mean and std
- Returns
- mean, stdfloats
Mean and unbiased standard deviation of the mean
- stdUnbiased(y)¶
Get unbiased estimate of the standard deviation and its standard deviation.
- Parameters
- yarray
Sample from which to estimate standard deviation.
- Returns
- Stdfloat
Unbiased estimate of the standard deviation.
- Std of stdfloat
Standard deviation of the unbiased standard deviation estimator.
- stdc4(n)¶
Calculate c4 factor.
The c4 factor is required to obtain an unbiased estimator for the standard deviation.
It is proportional to the factor B used in Kenney 1940, who started from a slightly different definition of the sample variance.
- Parameters
- nint
Number of points in the sample
- Returns
- c4, ln(c4)float
The c4 factor and its natural logarithm.
- subsetIndexDissection(ndp, N, j)¶
Find array indices of (N+2)-length subsets.
Here, (N+2)-sized sets of indices are constructed, which are required in the construction of the beta sample.
- Parameters
- ndpint
Number of available data points
- Nint
Last order of the Taylor series taken into account. Chunk length will be N+2.
- jint
Jump parameter (>0)
- Returns
- k-indiceslist
A list holding N+2 elements. Each element of the list is an array holding the indices of the data point no. one, two, …, N+2 of the subsets required to construct the beta sample.
- subsetIndices(cd)¶
Compose indices sets defining the subsets to construct the beta sample.
- Parameters
- cdlist
The output of subsetIndexDissection
- Returns
- Subset indices2d array
A 2d-array holding the indices of all subsets, arranged so that result[i,::] holds the N+2 indices pertaining to the i-th subset.
- variance(x, mode)¶
Estimate variance from sample
- Parameters
- xarray
sample
- modestring, {n, nmo}
Estimator to use: ‘n’ for 1/n version with zero mean (not estimated) and ‘nmo’ for 1/(n-1)
BSEqSamp (equidistant sampling)¶
- class PyAstronomy.pyasl.BSEqSamp¶
Methods
betaSigma(y, N, j[, ignoreNaN, returnMAD, ibs])Estimate standard deviation of noise term in data set y.
estimateStdMAD(x, mode)Estimate standard deviation based on median absolute deviation (MAD)
getBetaSample(y, N, j)Construct the beta sample.
getBetaSampleShift(y, N, j)Construct beta sample using shifting procedure.
get_ak(N)Calculate the required coefficients (a_k)
get_rhok(N)Calculate (auto)correlation function for beta sample
meanUnbStd(x)Mean and (unbiased) standard deviation of the mean.
stdUnbiased(y)Get unbiased estimate of the standard deviation and its standard deviation.
stdc4(n)Calculate c4 factor.
subsetIndexDissection(ndp, N, j)Find array indices of (N+2)-length subsets.
subsetIndices(cd)Compose indices sets defining the subsets to construct the beta sample.
variance(x, mode)Estimate variance from sample
- betaSigma(y, N, j, ignoreNaN=True, returnMAD=False, ibs=False)¶
Estimate standard deviation of noise term in data set y.
It is explicitly assumed that the data are equidistantly sampled.
Attribute
Type
Meaning
betaSample
array
The beta sample
estimates
dict
Summary of the estimates obtained from the beta sample (bs).
“s2E”: variance estimate of the bs (expectation value of zero), “s2Evar”: variance of s2E
“sE”: Estimate of std of bs, “sEstd”: Std of sE
“s2”: variance estimate of the bs (mean estimated from bs), “s2var”: variance of s2, “s”: sqrt(s2)
“sME”: Standard deviation based on MAD with zero expectation, “sMEstd”: Estimation of std of sME
“sM”: Standard deviation based on MAD with median estimated from bs, “sMEstd”: Estimation of std of sM
- Parameters
- yarray
Data values from which to estimate standard deviation of noise.
- Nint
Last order of the Taylor series to be taken into account.
- jint
Jump parameter
- ignoreNaNboolean, optional
If True (default), NaN values in the beta sample are ignored in the calculation.
- returnMADboolean, optional
If True, the estimate obtained using the MAD is returned instead of that of the MVU estimator (default is False). The standard error is estimated by scaling the standard deviation of the MVU estimator by a factor of 1.64.
- ibsboolean, optional
If True, an independent beta sample is constructed. Default is False.
- Returns
- Estimate of STD in beta sample and the STD of the estimate: float, float
The standard deviation determined in the beta sample. Non-robust estimates sE and sEstd if returnMAD is False (default) or robust estimates sME and sMEstd if returnMAD is True. The estimates attribute holds a more comprehensive summary of the estimates.
- getBetaSample(y, N, j)¶
Construct the beta sample.
- Parameters
- yarray
Values from which to estimate noise
- Nint
Last order of the Taylor series taken into account
- jint
Jump parameter (>0)
- Returns
- Beta samplearray
An array holding all available beta values.
- getBetaSampleShift(y, N, j)¶
Construct beta sample using shifting procedure.
- Parameters
- yarray
Values from which to estimate noise
- Nint
Last order of the Taylor series taken into account
- jint
Jump parameter (>0)
- Returns
- Beta samplearray
An array holding all available beta values.
- get_ak(N)¶
Calculate the required coefficients (a_k)
- Parameters
- Nint
Order of approximation
- Returns
- akarray
The coefficients
- get_rhok(N)¶
Calculate (auto)correlation function for beta sample
- Parameters
- Nint
Order of approximation
- Returns
- correlation functionarray
Correlation function
BSArbSamp (arbitrary sampling)¶
- class PyAstronomy.pyasl.BSArbSamp¶
Estimate noise in equidistantly sampled data.
Methods
betaSigma(x, y, N, j[, ignoreNaN, ...])Estimate standard deviation of noise term in data set y.
estimateStdMAD(x, mode)Estimate standard deviation based on median absolute deviation (MAD)
getBetaSample(x, y, N, j)Combine data points to calculate beta values.
getBetaSampleShift(x, y, N, j)Construct beta sample using shifting procedure.
getCoeffsArbSamp(t[, gamma])Calculate coefficients (ak) for arbitrary sampling.
meanUnbStd(x)Mean and (unbiased) standard deviation of the mean.
stdUnbiased(y)Get unbiased estimate of the standard deviation and its standard deviation.
stdc4(n)Calculate c4 factor.
subsetIndexDissection(ndp, N, j)Find array indices of (N+2)-length subsets.
subsetIndices(cd)Compose indices sets defining the subsets to construct the beta sample.
variance(x, mode)Estimate variance from sample
- betaSigma(x, y, N, j, ignoreNaN=True, returnMAD=False, ibs=False)¶
Estimate standard deviation of noise term in data set y.
In this implementation, arbitrary sampling is taken into account.
The method assigns the following attributes, which may be accessed after execution to work with the result:
Attribute
Type
Meaning
betaSample
array
The beta sample
estimates
dict
Summary of the estimates obtained from the beta sample (bs).
“s2E”: variance estimate of the bs (expectation value of zero), “s2Evar”: variance of s2E
“sE”: Estimate of std of bs, “sEstd”: Std of sE
“s2”: variance estimate of the bs (mean estimated from bs), “s2var”: variance of s2, “s”: sqrt(s2)
“sME”: Standard deviation based on MAD with zero expectation, “sMEstd”: Estimation of std of sME
“sM”: Standard deviation based on MAD with median estimated from bs, “sMEstd”: Estimation of std of sM
- Parameters
- xarray
Sampling of the data.
- yarray
Data values from which to estimate standard deviation of noise.
- Nint
Last order of the Taylor series to be taken into account.
- jint, optional
Jump parameter (default is one, i.e., consecutive data points are combined to estimate the noise).
- ignoreNaNboolean, optional
If True (default), NaN values in the beta sample are ignored in the calculation.
- returnMADboolean, optional
If True, the estimate obtained using the MAD is returned instead of that of the MVU estimator (default is False). The standard error is estimated by scaling the standard deviation of the MVU estimator by a factor of 1.64.
- ibsboolean, optional
If True, an independent beta sample is constructed. Default is False.
- Returns
- Estimate of STD in beta sample and the STD of the estimate: float, float
The standard deviation determined in the beta sample. Non-robust estimates sE and sEstd if returnMAD is False (default) or robust estimates sME and sMEstd if returnMAD is True. The estimates attribute holds a more comprehensive summary of the estimates.
- getBetaSample(x, y, N, j)¶
Combine data points to calculate beta values.
- Parameters
- xarray
Sampling of data
- yarray
Values from which to estimate noise
- Nint
Last order of the Taylor series taken into account
- jint
Jump parameter (>0)
- Returns
- Betasarray
An array holding all available beta values.
- getBetaSampleShift(x, y, N, j)¶
Construct beta sample using shifting procedure.
- Parameters
- x, yarray
Values from which to estimate noise
- Nint
Last order of the Taylor series taken into account
- jint
Jump parameter (>0)
- Returns
- Beta samplearray
An array holding all available beta values.
- getCoeffsArbSamp(t, gamma=1.0)¶
Calculate coefficients (ak) for arbitrary sampling.
- Parameters
- tarray
Sampling instants of the subset.
- gammafloat, optional
Scaling of the coefficients (default is one).
- Returns
- akarray
Set of coefficients.
