hyperspy.external.astroML.bayesian_blocks module

Bayesian Block implementation

Dynamic programming algorithm for finding the optimal adaptive-width histogram.

Based on Scargle et al 2012 [1]_

References

1

http://adsabs.harvard.edu/abs/2012arXiv1207.5578S

class hyperspy.external.astroML.bayesian_blocks.Events(p0=0.05, gamma=None)

Bases: hyperspy.external.astroML.bayesian_blocks.FitnessFunc

Fitness for binned or unbinned events

Parameters

  • p0 (float) – False alarm probability, used to compute the prior on N (see eq. 21 of Scargle 2012). Default prior is for p0 = 0.

  • gamma (float or None) – If specified, then use this gamma to compute the general prior form, p ~ gamma^N. If gamma is specified, p0 is ignored.

fitness(N_k, T_k)
prior(N, Ntot)
class hyperspy.external.astroML.bayesian_blocks.FitnessFunc(p0=0.05, gamma=None)

Bases: object

Base class for fitness functions

Each fitness function class has the following: - fitness(…) : compute fitness function.

Arguments accepted by fitness must be among [T_k, N_k, a_k, b_k, c_k]

  • prior(N, Ntot) : compute prior on N given a total number of points Ntot

property args
fitness()
gamma_prior(N, Ntot)

Basic prior, parametrized by gamma (eq. 3 in Scargle 2012)

p0_prior(N, Ntot)
prior(N, Ntot)
validate_input(t, x, sigma)

Check that input is valid

class hyperspy.external.astroML.bayesian_blocks.PointMeasures(p0=None, gamma=None)

Bases: hyperspy.external.astroML.bayesian_blocks.FitnessFunc

Fitness for point measures

Parameters

gamma (float) – specifies the prior on the number of bins: p ~ gamma^N if gamma is not specified, then a prior based on simulations will be used (see sec 3.3 of Scargle 2012)

fitness(a_k, b_k)
prior(N, Ntot)
class hyperspy.external.astroML.bayesian_blocks.RegularEvents(dt, p0=0.05, gamma=None)

Bases: hyperspy.external.astroML.bayesian_blocks.FitnessFunc

Fitness for regular events

This is for data which has a fundamental “tick” length, so that all measured values are multiples of this tick length. In each tick, there are either zero or one counts.

Parameters

  • dt (float) – tick rate for data

  • gamma (float) – specifies the prior on the number of bins: p ~ gamma^N

fitness(T_k, N_k)
validate_input(t, x, sigma)

Check that input is valid

hyperspy.external.astroML.bayesian_blocks.bayesian_blocks(t, x=None, sigma=None, fitness='events', **kwargs)

Bayesian Blocks Implementation

This is a flexible implementation of the Bayesian Blocks algorithm described in Scargle 2012 [1]_

Parameters

  • t (array_like) – data times (one dimensional, length N)

  • x (array_like (optional)) – data values

  • sigma (array_like or float (optional)) – data errors

  • fitness (str or object) –

    the fitness function to use. If a string, the following options are supported:

    • ’events’binned or unbinned event data

      extra arguments are p0, which gives the false alarm probability to compute the prior, or gamma which gives the slope of the prior on the number of bins.

    • ’regular_events’non-overlapping events measured at multiples

      of a fundamental tick rate, dt, which must be specified as an additional argument. The prior can be specified through gamma, which gives the slope of the prior on the number of bins.

    • ’measures’fitness for a measured sequence with Gaussian errors

      The prior can be specified using gamma, which gives the slope of the prior on the number of bins. If gamma is not specified, then a simulation-derived prior will be used.

    Alternatively, the fitness can be a user-specified object of type derived from the FitnessFunc class.

Returns

edges – array containing the (N+1) bin edges

Return type

ndarray

Examples

Event data:

>>> t = np.random.normal(size=100)
>>> bins = bayesian_blocks(t, fitness='events', p0=0.01)

Event data with repeats:

>>> t = np.random.normal(size=100)
>>> t[80:] = t[:20]
>>> bins = bayesian_blocks(t, fitness='events', p0=0.01)

Regular event data:

>>> dt = 0.01
>>> t = dt * np.arange(1000)
>>> x = np.zeros(len(t))
>>> x[np.random.randint(0, len(t), len(t) / 10)] = 1
>>> bins = bayesian_blocks(t, fitness='regular_events', dt=dt, gamma=0.9)

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)
>>> bins = bayesian_blocks(t, fitness='measures')

References

1

Scargle, J et al. (2012) http://adsabs.harvard.edu/abs/2012arXiv1207.5578S

See also

astroML.plotting.hist()

histogram plotting function which can make use of bayesian blocks.