Background estimation¶
background.py¶
Routines to compute the background from an array of timestamps. This module
is normally imported as bg
when fretbursts is imported.
The important functions are exp_fit()
and exp_cdf_fit()
that
provide two (fast) algorithms to estimate the background without binning.
These functions are not usually called directly but passed to
Data.calc_bg()
to compute the background of a measurement.
See also exp_hist_fit()
for background estimation using an histogram fit.

fretbursts.background.
exp_fit
(ph, tail_min_us=None, clk_p=1.25e08, error_metrics=None)¶ Return a background rate using the MLE of mean waitingtimes.
Compute the background rate, selecting waitingtimes (delays) larger than a minimum threshold.
This function performs a Maximum Likelihood (ML) fit. For exponentiallydistributed waitingtimes this is the empirical mean.
Parameters:  ph (array) – timestamps array from which to extract the background
 tail_min_us (float) – minimum waitingtime in microsecs
 clk_p (float) – clock period for timestamps in
ph
 error_metrics (string or None) – Valid values are ‘KS’ or ‘CM’. ‘KS’ (KolmogorovSmirnov statistics) computes the error as the max of deviation of the empirical CDF from the fitted CDF. ‘CM’ (Cramesvon Mises) uses the L^2 distance. If None, no error metric is computed (returns None).
Returns: 2Tuple – Estimated background rate in cps, and a “quality of fit” index (the lower the better) according to the chosen metric. If error_metrics==None, the returned “quality of fit” is None.
See also

fretbursts.background.
exp_cdf_fit
(ph, tail_min_us=None, clk_p=1.25e08, error_metrics=None)¶ Return a background rate fitting the empirical CDF of waitingtimes.
Compute the background rate, selecting waitingtimes (delays) larger than a minimum threshold.
This function performs a least square fit of an exponential Cumulative Distribution Function (CDF) to the empirical CDF of waitingtimes.
Parameters:  ph (array) – timestamps array from which to extract the background
 tail_min_us (float) – minimum waitingtime in microsecs
 clk_p (float) – clock period for timestamps in
ph
 error_metrics (string or None) – Valid values are ‘KS’ or ‘CM’. ‘KS’ (KolmogorovSmirnov statistics) computes the error as the max of deviation of the empirical CDF from the fitted CDF. ‘CM’ (Cramesvon Mises) uses the L^2 distance. If None, no error metric is computed (returns None).
Returns: 2Tuple – Estimated background rate in cps, and a “quality of fit” index (the lower the better) according to the chosen metric. If error_metrics==None, the returned “quality of fit” is None.
See also

fretbursts.background.
exp_hist_fit
(ph, tail_min_us, binw=5e05, clk_p=1.25e08, weights=’hist_counts’, error_metrics=None)¶ Compute background rate with WLS histogram fit of waitingtimes.
Compute the background rate, selecting waitingtimes (delays) larger than a minimum threshold.
This function performs a Weighed Least Squares (WLS) fit of the histogram of waiting times to an exponential decay.
Parameters:  ph (array) – timestamps array from which to extract the background
 tail_min_us (float) – minimum waitingtime in microsecs
 binw (float) – bin width for waiting times, in seconds.
 clk_p (float) – clock period for timestamps in
ph
 weights (None or string) – if None no weights is applied. if is ‘hist_counts’, each bin has a weight equal to its counts if is ‘inv_hist_counts’, the weight is the inverse of the counts.
 error_metrics (string or None) – Valid values are ‘KS’ or ‘CM’. ‘KS’ (KolmogorovSmirnov statistics) computes the error as the max of deviation of the empirical CDF from the fitted CDF. ‘CM’ (Cramesvon Mises) uses the L^2 distance. If None, no error metric is computed (returns None).
Returns: 2Tuple – Estimated background rate in cps, and a “quality of fit” index (the lower the better) according to the chosen metric. If error_metrics==None, the returned “quality of fit” is None.
See also
Lowlevel background fit functions¶
Generic functions to fit exponential populations.
These functions can be used directly, or, in a typical FRETBursts workflow they are passed to higher level methods.
See also:

fretbursts.fit.exp_fitting.
expon_fit
(s, s_min=0, offset=0.5, calc_residuals=True)¶ Fit sample
s
to an exponential distribution using the ML estimator.This function computes the rate (Lambda) using the maximum likelihood (ML) estimator of the mean waitingtime (Tau), that for an exponentially distributed sample is the samplemean.
Parameters:  s (array) – array of exponetiallydistributed samples
 s_min (float) – all samples <
s_min
are discarded (s_min
must be >= 0).  offset (float) – offset for computing the CDF. See
get_ecdf()
.  calc_residuals (bool) – if True compute the residuals of the fitted exponential versus the empirical CDF.
Returns: A 4tuple of the fitted rate (1/lifetime), residuals array, residuals xaxis array, sample size after threshold.

fretbursts.fit.exp_fitting.
expon_fit_cdf
(s, s_min=0, offset=0.5, calc_residuals=True)¶ Fit of an exponential model to the empirical CDF of
s
.This function computes the rate (Lambda) fitting a line (linear regression) to the log of the empirical CDF.
Parameters:  s (array) – array of exponetiallydistributed samples
 s_min (float) – all samples <
s_min
are discarded (s_min
must be >= 0).  offset (float) – offset for computing the CDF. See
get_ecdf()
.  calc_residuals (bool) – if True compute the residuals of the fitted exponential versus the empirical CDF.
Returns: A 4tuple of the fitted rate (1/lifetime), residuals array, residuals xaxis array, sample size after threshold.

fretbursts.fit.exp_fitting.
expon_fit_hist
(s, bins, s_min=0, weights=None, offset=0.5, calc_residuals=True)¶ Fit of an exponential model to the histogram of
s
using least squares.Parameters:  s (array) – array of exponetiallydistributed samples
 bins (float or array) – if float is the bin width, otherwise is the
array of bin edges (passed to
numpy.histogram
)  s_min (float) – all samples <
s_min
are discarded (s_min
must be >= 0).  weights (None or string) – if None no weights is applied. if is ‘hist_counts’, each bin has a weight equal to its counts if is ‘inv_hist_counts’, the weight is the inverse of the counts.
 offset (float) – offset for computing the CDF. See
get_ecdf()
.  calc_residuals (bool) – if True compute the residuals of the fitted exponential versus the empirical CDF.
Returns: A 4tuple of the fitted rate (1/lifetime), residuals array, residuals xaxis array, sample size after threshold.

fretbursts.fit.exp_fitting.
get_ecdf
(s, offset=0.5)¶ Return arrays (x, y) for the empirical CDF curve of sample
s
.See the code for more info (is a oneliner!).
Parameters:  s (array of floats) – sample
 offset (float, default 0.5) – Offset to add to the y values of the CDF
Returns: (x, y) (tuple of arrays) – the x and y values of the empirical CDF

fretbursts.fit.exp_fitting.
get_residuals
(s, tau_fit, offset=0.5)¶ Returns residuals of sample
s
CDF vs an exponential CDF.Parameters:  s (array of floats) – sample
 tau_fit (float) – mean waitingtime of the exponential distribution to use as reference
 offset (float) – Default 0.5. Offset to add to the empirical CDF.
See
get_ecdf()
for details.
Returns: residuals (array) – residuals of empirical CDF compared with analytical CDF with time constant
tau_fit
.