bayesian_blocks¶
- astropy.stats.bayesian_blocks(t, x=None, sigma=None, fitness='events', **kwargs)[source]¶
Compute optimal segmentation of data with Scargle’s Bayesian Blocks
This is a flexible implementation of the Bayesian Blocks algorithm described in Scargle 2013 [1].
- Parameters:
- tnumpy:array_like
data times (one dimensional, length N)
- xnumpy:array_like, optional
data values
- sigmanumpy:array_like or
python:float
, optional data errors
- fitness
python:str
orobject
the fitness function to use for the model. If a string, the following options are supported:
‘events’ : binned or unbinned event data. Arguments are
gamma
, which gives the slope of the prior on the number of bins, orncp_prior
, which is \(-\ln({\tt gamma})\).‘regular_events’ : non-overlapping events measured at multiples of a fundamental tick rate,
dt
, which must be specified as an additional argument. Extra arguments arep0
, which gives the false alarm probability to compute the prior, orgamma
, which gives the slope of the prior on the number of bins, orncp_prior
, which is \(-\ln({\tt gamma})\).‘measures’ : fitness for a measured sequence with Gaussian errors. Extra arguments are
p0
, which gives the false alarm probability to compute the prior, orgamma
, which gives the slope of the prior on the number of bins, orncp_prior
, which is \(-\ln({\tt gamma})\).
In all three cases, if more than one of
p0
,gamma
, andncp_prior
is chosen,ncp_prior
takes precedence overgamma
which takes precedence overp0
.Alternatively, the fitness parameter can be an instance of
FitnessFunc
or a subclass thereof.- **kwargs
any additional keyword arguments will be passed to the specified
FitnessFunc
derived class.
- Returns:
- edges
ndarray
array containing the (N+1) edges defining the N bins
- edges
See also
astropy.stats.histogram
compute a histogram using bayesian blocks
References
[1]Scargle, J et al. (2013) https://ui.adsabs.harvard.edu/abs/2013ApJ…764..167S
[2]Bellman, R.E., Dreyfus, S.E., 1962. Applied Dynamic Programming. Princeton University Press, Princeton. https://press.princeton.edu/books/hardcover/9780691651873/applied-dynamic-programming
[3]Bellman, R., Roth, R., 1969. Curve fitting by segmented straight lines. J. Amer. Statist. Assoc. 64, 1079–1084. https://www.tandfonline.com/doi/abs/10.1080/01621459.1969.10501038
Examples
Event data:
>>> t = np.random.normal(size=100) >>> edges = bayesian_blocks(t, fitness='events', p0=0.01)
Event data with repeats:
>>> t = np.random.normal(size=100) >>> t[80:] = t[:20] >>> edges = bayesian_blocks(t, fitness='events', p0=0.01)
Regular event data:
>>> dt = 0.05 >>> t = dt * np.arange(1000) >>> x = np.zeros(len(t)) >>> x[np.random.randint(0, len(t), len(t) // 10)] = 1 >>> edges = bayesian_blocks(t, x, fitness='regular_events', dt=dt)
Measured point data with errors:
>>> t = 100 * np.random.random(100) >>> x = np.exp(-0.5 * (t - 50) ** 2) >>> sigma = 0.1 >>> x_obs = np.random.normal(x, sigma) >>> edges = bayesian_blocks(t, x_obs, sigma, fitness='measures')