epsie.proposals package

Submodules

epsie.proposals.angular module

class epsie.proposals.angular.ATAdaptiveAngular(parameters, adaptation_duration, componentwise=False, start_step=1, target_rate=None, jump_interval=1)[source]

Bases: epsie.proposals.normal.ATAdaptiveSupport, epsie.proposals.angular.Angular

An angular proposal with adaptive variance, using the algorithm from Andrieu & Thoms.

See ATAdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
start_step (int, optional) – The proposal step index when adaptation phase begins.
target_rate (float, optional) – Target acceptance ratio. By default 0.234 and 0.48 for componentwise scaling.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.

name = 'at_adaptive_angular'

symmetric = True

class epsie.proposals.angular.AdaptiveAngular(parameters, adaptation_duration, jump_interval=1, start_step=1, **kwargs)[source]

Bases: epsie.proposals.normal.AdaptiveSupport, epsie.proposals.angular.Angular

An angular proposoal with adaptive variance, using the algorithm from Veitch et al.

See AdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. The boundaries will be used for the prior widths in the adaptation algorithm.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
start_step (int, optional) – The proposal step to start doing the adaptation (\(k_0+1\) in the equation below). Must be greater than zero. Default is 1.
**kwargs – All other keyword arguments are passed to AdaptiveSupport.setup_adaptation(). See that function for details.

name = 'adaptive_angular'

symmetric = True

class epsie.proposals.angular.Angular(parameters, cov=None, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.normal.Normal

A propsal distribution for parameters that are cyclic over \([0, 2\pi)\).

To generate a jump proposal from a given point, a truncated normal distribution centered on the point and with bounds at \(\pm \pi\) around the point. Cyclic bounds are then applied, resulting in a proposed point that is in \([0, 2\pi)\). For example, if a the given point is at \(1.75\pi\) and the jump is \(+0.5\pi\), then proposed point will be at \(0.25\pi\). Since the same proposal distribution is used regardless of the location, this is a symmetric proposal.

This proposal can handle more than one parameter; however, parameters must all be independent of each other.

Parameters

parameters ((list of) str) – The names of the parameters to create proposals for.
cov ((array of) float, optional) – The covariance to use for the underlying truncated normal distribution, in squared radians. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 sq. radian for all parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

name = 'angular'

symmetric = True

class epsie.proposals.angular.SSAdaptiveAngular(parameters, cov=None, jump_interval=1, jump_interval_duration=None, **kwargs)[source]

Bases: epsie.proposals.normal.SSAdaptiveSupport, epsie.proposals.angular.Angular

An angular proposoal with adaptive variance, using the algorithm from Sivia and Skilling.

See SSAdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. The boundaries will be used for the prior widths in the adaptation algorithm.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.
**kwargs – All other keyword arguments are passed to SSAdaptiveSupport.setup_adaptation(). See that function for details.

name = 'ss_adaptive_angular'

symmetric = True

epsie.proposals.base module

class epsie.proposals.base.BaseAdaptiveSupport[source]

Bases: abc.ABC

Abstract base class for all proposal classes.

property adaptation_duration: The adaptation duration used.

property start_step: The iteration that the adaption begins.

property target_rate: Target acceptance ratio.

class epsie.proposals.base.BaseBirth[source]

Bases: epsie.proposals.base.BaseRandom

Abstract base class for all birth classes.

All birth distributions must inherit from this class, as it lays out all of the functions/attributes that a sampler will try to access.

In addition to the abstract methods/properties, all samplers must set a parameters attribute. This is a list of the names of the parameters the proposal produces jumps for.

symmetric

state

abstract property birth

This should provide random samples from the birth distribution.

Samples should be returned as a dictionary mapping parameters to the proposed birth.

abstract logpdf(xi)[source]

The log pdf of the birth distribution at a point.

Parameters: xi (dict) – Dictionary mapping parameter names to values to evaluate.
Returns: The log pdf of a birth at xi.
Return type: float

name = None

pdf(xi)[source]

The pdf of the birth proposal at the given values.

This just expoentiates logpdf.

Parameters: xi (dict) – Dictionary mapping parameter names to values to evaluate.
Returns: The pdf of a birth at xi.
Return type: float

update(chain)[source]

Update the state of the birth distribution after a jump.

This method may optionally be implemented by a birth. It is called after a birth is evaluated.

class epsie.proposals.base.BaseProposal[source]

Bases: epsie.proposals.base.BaseRandom

Abstract base class for all proposal classes.

All proposals must inherit from this class, as it lays out all of the functions/attributes that a sampler will try to access.

In addition to the abstract methods/properties, all samplers must set a parameters attribute. This is a list of the names of the parameters the proposal produces jumps for.

symmetric

state

nsteps

jump(fromx)[source]: Depending on the current number of chain iterations and the jump_interval either calls the _jump method to provide a random sample or returns fromx.

property jump_interval: Returns the jump interval for a proposal.

property jump_interval_duration: Returns the number of steps after which no more fast jumps are performed.

logpdf(xi, givenx)[source]: Depending on the current number of chain iterations and the jump_interval either calls the _logpdf method or returns 0.0 as the jump from givenx to xi was fully determinate.

name = None

property nsteps

Returns number of update iterations with this proposal.

While for a standard adaptive MCMC this will match the length of the chain for a transdimensional proposal it will differ.

pdf(xi, givenx)[source]

The pdf of the proposal at the given values.

This just expoentiates logpdf.

Parameters

xi (dict) – Dictionary mapping parameter names to values to evaluate.
givenx (dict, optional) – Dictionary mapping parameter names to values of the point from which xi is evaluated.

Returns

The pdf of jumping from givenx to xi.

Return type

float

set_jump_interval(jump_interval, duration=None)[source]: Sets the jump interval and the duration.

abstract property symmetric

Boolean indicating whether the proposal distribution is symmetric.

A jump proposal is symmetric if the proposal probability density has the property that \(p(x'|x) = p(x|x')\), where \(x\) is the current position, \(x'\) is the proposed position. In this, case, the Metropolis-Hastings ratio simplfies to just the ratio of posterior values at the two points.

Note that an adaptive proposal may still be symmetric. Symmetry only means that the current state of the proposal satisfies the above condition; it does not necessarily mean that transitions between states be symmetric.

update(chain)[source]: Depending on the current number of chain iterations and the jump_interval calls the _update method if the proposal distribution was used to sample a new position.

class epsie.proposals.base.BaseRandom[source]

Bases: abc.ABC

Abstract base class for handling random number generation for proposals ans birth distributions.

All proposals must inherit from this class, as it handles random number generation.

Warning

All proposals must use the random number generator provided by this class (see the random_generator attribute) for creating random numbers. Do not attempt to use scipy/numpy’s random number generator. Use of any other generator may result in chains not being independent of each other when run in a parallel environment.

In addition to the abstract methods/properties, all samplers must set a parameters attribute. This is a list of the names of the parameters the proposal produces jumps and births for.

bit_generator

random_generator

random_state

parameters

state

property bit_generator: The random bit generator instance being used.

name = None

property parameters: Sorted tuple of the parameters that proposals are produced for.

property random_generator

The random number generator.

This is an instance of numpy.random.Generator that is derived from the bit generator. It provides methods to create random draws from various distributions.

property random_state: The current state of the random bit generator.

abstract set_state(state)[source]: Set all information needed to produce a deterministic jump.

abstract property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

epsie.proposals.birth module

class epsie.proposals.birth.LogNormalBirth(parameters, mean, std)[source]

Bases: epsie.proposals.base.BaseBirth

Normal birth distribution object used in nested transdimensional proposals to propose birth to parameters which were previously inactive.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
mean (dict) – Dictionary mapping parameters to their means
std (dict) – Dictionary mapping parameters to their stds
Properties –
---------- –
birth (dict) – Returns random variate sample from the uniform distribution for each parameter (dictionary).

logpdf : py:func: Evalues the logpdf of the proposal. Takes dictionary of parameters as input.

property birth

This should provide random samples from the birth distribution.

Samples should be returned as a dictionary mapping parameters to the proposed birth.

logpdf(xi)[source]

The log pdf of the birth distribution at a point.

Parameters: xi (dict) – Dictionary mapping parameter names to values to evaluate.
Returns: The log pdf of a birth at xi.
Return type: float

property mu: Dictionary of parameter -> mu.

name = 'log_normal_birth'

set_state(state)[source]: Set all information needed to produce a deterministic jump.

setup_mu_std(mu, std)[source]: Sets the mean and standard deviation for each parameter in parameters.

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

property std: Dictionary of parameter -> std.

class epsie.proposals.birth.NormalBirth(parameters, mean, std)[source]

Bases: epsie.proposals.base.BaseBirth

Normal birth distribution object used in nested transdimensional proposals to propose birth to parameters which were previously inactive.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
mean (dict) – Dictionary mapping parameters to their means
std (dict) – Dictionary mapping parameters to their stds
Properties –
---------- –
birth (dict) – Returns random variate sample from the uniform distribution for each parameter (dictionary).

logpdf : py:func: Evalues the logpdf of the proposal. Takes dictionary of parameters as input.

property birth

This should provide random samples from the birth distribution.

Samples should be returned as a dictionary mapping parameters to the proposed birth.

logpdf(xi)[source]

The log pdf of the birth distribution at a point.

Parameters: xi (dict) – Dictionary mapping parameter names to values to evaluate.
Returns: The log pdf of a birth at xi.
Return type: float

property mu: Dictionary of parameter -> mu.

name = 'normal_birth'

set_state(state)[source]: Set all information needed to produce a deterministic jump.

setup_mu_std(mu, std)[source]: Sets the mean and standard deviation for each parameter in parameters.

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

property std: Dictionary of parameter -> std.

class epsie.proposals.birth.UniformBirth(parameters, boundaries)[source]

Bases: epsie.proposals.base.BaseBirth

Uniform birth distribution object used in nested transdimensional proposals to propose birth to parameters which were previously inactive.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
boundaries (dict) – Dictionary mapping parameters to boundaries.
Properties –
---------- –
birth (dict) – Returns random variate sample from the uniform distribution for each parameter (dictionary).

logpdf : py:func: Evalues the logpdf of the proposal. Takes dictionary of parameters as input.

property birth

This should provide random samples from the birth distribution.

Samples should be returned as a dictionary mapping parameters to the proposed birth.

property boundaries: Dictionary of parameter -> boundaries.

logpdf(xi)[source]

The log pdf of the birth distribution at a point.

Parameters: xi (dict) – Dictionary mapping parameter names to values to evaluate.
Returns: The log pdf of a birth at xi.
Return type: float

name = 'uniform_birth'

set_state(state)[source]: Set all information needed to produce a deterministic jump.

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

epsie.proposals.bounded_eigenvector module

class epsie.proposals.bounded_eigenvector.AdaptiveBoundedEigenvector(parameters, boundaries, adaptation_duration, cov0=None, target_rate=0.234, shuffle_rate=0.33, start_step=1, jump_interval=1)[source]

Bases: epsie.proposals.eigenvector.AdaptiveEigenvectorSupport, epsie.proposals.bounded_eigenvector.BoundedEigenvector

Uses a bounded eigenvector jump with a adaptive scales

See AdaptiveEigenvectorSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two.
adaptation_duration (int) – The number of steps after which adaptation of the eigenvectors ends. Post-adaptation phase the eigenvectors and eigenvalues are kept constant.
cov0 (array, optional) – The initial covariance matrix of the parameters used to calculate the initial eigenvectors. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If a single float or a 1D array is given, will use a diagonal covariance matrix (i.e., all parameters are independent of each other). Default (None) is to use unit variance for all parameters.
target_rate (float, optional) – Target acceptance ratio. By default 0.234
shuffle_rate (float, optional) – Probability of shuffling the eigenvector jump probabilities. By default 0.33.
start_step (int, optional) – The proposal step index when adaptation phase begins.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.

name = 'adaptive_bounded_eigenvector'

symmetric = False

class epsie.proposals.bounded_eigenvector.BoundedEigenvector(parameters, boundaries, cov=None, shuffle_rate=0.33, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.eigenvector.Eigenvector

Uses a bounded eigenvector jump with a fixed scale.

This proposal calculates the eigenvectors from the covariance matrix and always proposes a jump along a single eigenvector from a univariate normal distribution. Uses a truncated normal distribution whose scale corresponds to the width of the boundaries surface along the specific eigenvector.

This proposal may handle one or more parameters.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If a single float or a 1D array is given, will use a diagonal covariance matrix (i.e., all parameters are independent of each other). Default (None) is to use unit variance for all parameters.
shuffle_rate (float (optional)) – Probability of shuffling the eigenvector jump probabilities. By default 0.33.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

property boundaries: Dictionary of parameter -> boundaries.

property hyperplanes: Returns an array of hyperplanes defining the boundaries

name = 'bounded_eigenvector'

symmetric = False

epsie.proposals.bounded_normal module

class epsie.proposals.bounded_normal.ATAdaptiveBoundedNormal(parameters, boundaries, adaptation_duration, componentwise=False, start_step=1, target_rate=None, jump_interval=1)[source]

Bases: epsie.proposals.normal.ATAdaptiveSupport, epsie.proposals.bounded_normal.BoundedNormal

A bounded adaptive proposal, using the algorithm from Andrieu & Thoms.

See ATAdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. The boundaries will be used for the prior widths in the adaptation algorithm.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
componentwise (bool, optional) – Whether to include a componentwise scaling of the parameters (algorithm 6 in [1]). By default set to False (algorithm 4 in [1]). Componentwise scaling ndim times more expensive than global scaling.
start_step (int, optional) – The proposal step index when adaptation phase begins.
target_rate (float, optional) – Target acceptance ratio. By default 0.234 and 0.48 for componentwise scaling.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.

name = 'at_adaptive_bounded_normal'

symmetric = False

class epsie.proposals.bounded_normal.AdaptiveBoundedNormal(parameters, boundaries, adaptation_duration, start_step=1, jump_interval=1, **kwargs)[source]

Bases: epsie.proposals.normal.AdaptiveSupport, epsie.proposals.bounded_normal.BoundedNormal

A bounded normal proposoal with adaptive variance, using the algorithm from Veitch et al.

See AdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. The boundaries will be used for the prior widths in the adaptation algorithm.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
start_step (int, optional) – The proposal step to start doing the adaptation (\(k_0+1\) in the equation below). Must be greater than zero. Default is 1.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
**kwargs – All other keyword arguments are passed to AdaptiveSupport.setup_adaptation(). See that function for details.

name = 'adaptive_bounded_normal'

symmetric = False

class epsie.proposals.bounded_normal.Boundaries(args)[source]

Bases: tuple

Support class for bounded proposals.

This is basically a length-2 tuple with an abs function. Also has lower and upper attributes to get the first and second item.

Example

>>> b = Boundaries((-1, 1))
>>> b[0], b[1]
(-1, 1)
>>> b.lower, b.upper
(-1, 1)
>>> abs(b)
2

property lower: The lower bound.

property upper: The upper bound.

class epsie.proposals.bounded_normal.BoundedNormal(parameters, boundaries, cov=None, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.normal.Normal

Uses a normal distribution with fixed bounds on a parameter.

This uses a truncated normal distribution for jump proposals, with the truncation dependent on where a given point is with respect to the parameter’s boundaries. As a result, the proposal changes depending on where it is in the parameter space.

This proposal can handle more than one parameter; however, parameters must all be independent of each other.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 for all parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

property boundaries: Dictionary of parameter -> boundaries.

name = 'bounded_normal'

symmetric = False

class epsie.proposals.bounded_normal.SSAdaptiveBoundedNormal(parameters, boundaries, cov=None, jump_interval=1, jump_interval_duration=None, **kwargs)[source]

Bases: epsie.proposals.normal.SSAdaptiveSupport, epsie.proposals.bounded_normal.BoundedNormal

A bounded normal proposoal using the Sivia and Skilling algorithm for adjusting the variance.

By default, the maximum possible standard deviation is set to be 1.49 times largest boundary width (via the max_cov argument). At this value, there is a 50% chance that a jump will be larger than the boundary width. For more details on the adaptation algorithm, see SSAdaptiveSupport.

Parameters

parameters ((list of) str) – The names of the parameters.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. The boundaries will be used for the prior widths in the adaptation algorithm.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 for all parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.
**kwargs – All other keyword arguments are passed to SSAdaptiveSupport.setup_adaptation(). See that function for details.

name = 'ss_adaptive_bounded_normal'

symmetric = False

epsie.proposals.discrete module

class epsie.proposals.discrete.AdaptiveBoundedDiscrete(parameters, boundaries, adaptation_duration, successive=None, jump_interval=1, **kwargs)[source]

Bases: epsie.proposals.normal.AdaptiveSupport, epsie.proposals.discrete.BoundedDiscrete

A bounded discrete proposoal with adaptive variance.

See AdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. If floats are provided, the floor (ceil) of the lower (upper) bound will be used.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
**kwargs – All other keyword arguments are passed to AdaptiveSupport.setup_adaptation(). See that function for details.

name = 'adaptive_bounded_discrete'

symmetric = False

class epsie.proposals.discrete.AdaptiveNormalDiscrete(parameters, prior_widths, adaptation_duration, successive=None, jump_interval=1, **kwargs)[source]

Bases: epsie.proposals.normal.AdaptiveSupport, epsie.proposals.discrete.NormalDiscrete

A discrete proposoal with adaptive variance, using the algorithm from Veitch et al.

See AdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
prior_widths (dict) – Dictionary mapping parameter names to values giving the width of each parameter’s prior. The values may be floats, or any object that has an __abs__ method that will return a float.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
**kwargs – All other keyword arguments are passed to AdaptiveSupport.setup_adaptation(). See that function for details.

name = 'adaptive_discrete'

symmetric = True

class epsie.proposals.discrete.BoundedDiscrete(parameters, boundaries, cov=None, successive=None, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.bounded_normal.BoundedNormal

A proposal for discrete parameters with bounds.

This is a discretized form of BoundedNormal. Jump proposals are produced in the same manner as NormalDiscrete, except that the distribution used to draw \(\Delta x\) (before applying the floor/ceil or round) is a truncated normal. As such, this is not a symmetric distribution.

The variance used for drawing \(\Delta x\) need not be an integer, and can be set. Multiple parameters are supported, however, they all must be independent of each other.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. If floats are provided, the floor (ceil) of the lower (upper) bound will be used.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 for all parameters.
successive (dict, optional) – Dictionary of bools, keys must be parameters and items bools. If False then the proposal never produces the same integer on successive jumps. Default is False for all parameters
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

name = 'bounded_discrete'

property successive: Dictionary of successive toggles for each parameter. If True allows two equal integers on successive jumps.

symmetric = False

class epsie.proposals.discrete.NormalDiscrete(parameters, cov=None, successive=None, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.normal.Normal

A proposal for discrete parameters.

The jump proposals produced by this are always integer values. For a given point \(x \in \mathbb{Z}\), a new point \(x' = x + \bar{\Delta x}\) is generated by using

\[\begin{split}\bar{\Delta x} = \begin{cases} \lfloor \Delta x \rfloor \textrm{ if } \Delta x < 0, \\ \lceil \Delta x \rceil \textrm{ if } \Delta x > 0, \end{cases}\end{split}\]

where \(\Delta x \sim \mathcal{N}(0, \sigma)\) if successive is False. This results in a stepped probability density that is zero \(\in [0, 1)\). In other words, the proposal will never produce the same integer on successive jumps, and it will most often draw integers closest to the current point.

If successive is True, then for a given point \(x \in \mathbb{Z}\), a new point \(x' = x + \bar{\Delta x}\) is generated by using

\[\bar{\Delta x} = Round\left(\mathcal{N}(0, \sigma)\right),\]

meaning that the proposal can now propose the same integer on successive jumps.

The variance used for drawing \(\Delta x\) need not be an integer, and can be set. Multiple parameters are supported, however, they all must be independent of each other.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 for all parameters.
successive (dict, optional) – Dictionary of bools, keys must be parameters and items bools. If False then the proposal never produces the same integer on successive jumps. Default is False for all parameters
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

name = 'discrete'

property successive: Dictionary of successive toggles for each parameter. If True allows two equal integers on successive jumps.

symmetric = True

class epsie.proposals.discrete.SSAdaptiveBoundedDiscrete(parameters, boundaries, cov=None, successive=None, jump_interval=1, jump_interval_duration=None, **kwargs)[source]

Bases: epsie.proposals.normal.SSAdaptiveSupport, epsie.proposals.discrete.BoundedDiscrete

A bounded discrete proposoal with adaptive variance, using the algorithm from Sivia and Skilling.

See AdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
boundaries (dict) – Dictionary mapping parameters to boundaries. Boundaries must be a tuple or iterable of length two. If floats are provided, the floor (ceil) of the lower (upper) bound will be used.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 for all parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.
**kwargs – All other keyword arguments are passed to SSAdaptiveSupport.setup_adaptation(). See that function for details.

name = 'ss_adaptive_bounded_discrete'

symmetric = False

class epsie.proposals.discrete.SSAdaptiveNormalDiscrete(parameters, cov=None, successive=None, jump_interval=1, jump_interval_duration=None, **kwargs)[source]

Bases: epsie.proposals.normal.SSAdaptiveSupport, epsie.proposals.discrete.NormalDiscrete

A discrete proposoal with adaptive variance, using the algorithm from Sivia and Skilling.

See SSAdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If 2D array is given, the off-diagonal terms must be zero. Default is 1 for all parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.
**kwargs – All other keyword arguments are passed to SSAdaptiveSupport.setup_adaptation(). See that function for details.

name = 'ss_adaptive_discrete'

symmetric = True

epsie.proposals.eigenvector module

class epsie.proposals.eigenvector.AdaptiveEigenvector(parameters, adaptation_duration, cov0=None, target_rate=0.234, shuffle_rate=0.33, start_step=1, jump_interval=1)[source]

Bases: epsie.proposals.eigenvector.AdaptiveEigenvectorSupport, epsie.proposals.eigenvector.Eigenvector

Uses jumps along eigenvectors with adaptive scales.

See AdaptiveEigenvectorSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
adaptation_duration (int) – The number of steps after which adaptation of the eigenvectors ends. Post-adaptation phase the eigenvectors and eigenvalues are kept constant.
cov0 (array, optional) – The initial covariance matrix of the parameters used to calculate the initial eigenvectors. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If a single float or a 1D array is given, will use a diagonal covariance matrix (i.e., all parameters are independent of each other). Default (None) is to use unit variance for all parameters.
target_rate (float (optional)) – Target acceptance ratio. By default 0.234
shuffle_rate (float, optional) – Probability of shuffling the eigenvector jump probabilities. By default 0.33.
start_step (int, optional) – The proposal step index when adaptation phase begins.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.

name = 'adaptive_eigenvector'

symmetric = True

class epsie.proposals.eigenvector.AdaptiveEigenvectorSupport[source]

Bases: epsie.proposals.base.BaseAdaptiveSupport

Utility class for adding AdaptiveEigenvector proposal support.

The adaptation algorithm is based on Algorithm 8 in [1].

See [1] for details.

Notes

For the vanishing decay we use

\[\gamma_{g+1} = \left(g - g_{0}\right)^{-0.6} - C,\]

where \(g_{0}\) is the iteration at which adaptation starts, by default \(g_{0}=1\) and \(C\) is a positive constant ensuring that when the adaptation phase ends the vanishing decay tends to zero. By default assumes that the adaptation phase never ends (only decays with time)

References

[1] Andrieu, Christophe & Thoms, Johannes. (2008). A tutorial on adaptive MCMC. Statistics and Computing. 18. 10.1007/s11222-008-9110-y.

recursive_covariance(chain)[source]: Recursively updates the covariance given the latest observation. Weights all sampled points uniformly.

set_state(state)[source]

setup_adaptation(adaptation_duration, start_step=1, target_rate=0.234)[source]

Sets up the adaptation parameters.

Parameters

adaptation_duration (int) – The number of adaptation steps.
start_step (int, optional) – The proposal step when the adaptation phase begins.
target_rate (float, optional) – Target acceptance rate. By default 0.234

property state

class epsie.proposals.eigenvector.Eigenvector(parameters, cov=None, shuffle_rate=0.33, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.base.BaseProposal

Uses a eigenvector jump with a fixed scale that is determined by the given covariance matrix.

This proposal may handle one or more parameters.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If a single float or a 1D array is given, will use a diagonal covariance matrix (i.e., all parameters are independent of each other). Default (None) is to use unit variance for all parameters.
shuffle_rate (float, optional) – Probability of shuffling the eigenvector jump probabilities. By default 0.33.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

property bit_generator: The random bit generator instance being used.

property cov: The covariance matrix used.

property eigvals: Returns the eigenvalues

property eigvects: Returns the eigenvectors

name = 'eigenvector'

set_state(state)[source]: Set all information needed to produce a deterministic jump.

property shuffle_rate

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

symmetric = True

epsie.proposals.joint module

class epsie.proposals.joint.JointProposal(*proposals, bit_generator=None)[source]

Bases: epsie.proposals.base.BaseProposal

A collection of jump proposals for multiple parameters.

Parameters

*proposals – The arguments should provide the constituent proposals to use.
bit_generator (epsie.BIT_GENERATOR instance or int, optional) – The random bit generator to use, or an integer/None. If the latter, a bit generator will be created using epsie.create_bit_generator().

proposals

The constituent proposals.

Type: list

name = 'joint'

set_state(state)[source]: Set all information needed to produce a deterministic jump.

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

property symmetric

Boolean indicating whether the proposal distribution is symmetric.

A jump proposal is symmetric if the proposal probability density has the property that \(p(x'|x) = p(x|x')\), where \(x\) is the current position, \(x'\) is the proposed position. In this, case, the Metropolis-Hastings ratio simplfies to just the ratio of posterior values at the two points.

Note that an adaptive proposal may still be symmetric. Symmetry only means that the current state of the proposal satisfies the above condition; it does not necessarily mean that transitions between states be symmetric.

epsie.proposals.nested_transdimensional module

class epsie.proposals.nested_transdimensional.NestedTransdimensional(parameters, model_proposal, proposals, birth_distributions, bit_generator=None)[source]

Bases: epsie.proposals.base.BaseProposal

Nested transdimensional proposal.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
model_proposal (proposal) – The model hopping proposals. This must be a discrete, bounded proposal.
proposals (list of proposals) – The transdimensional proposals that are being turned on/off.
birth_distributions (list of objects) – Objects that match transdimensional proposals and are used to birth new samples and evaluate their proposal probability. Must use structure as given in the example.
bit_generator (BIT_GENERATOR or int, optional) – The random bit generator to use, or an integer/None. If the latter, a bit generator will be created using epsie.create_bit_generator().

proposals

The constituent in-model proposals.

Type: list of proposals

model_proposal

The model hopping proposal

Type: epsie.proposals.discrete.BoundedDiscrete

property model_proposal

name = 'nested_transdimensional'

property proposals

set_state(state)[source]: Set all information needed to produce a deterministic jump.

setup_births(birth_distributions)[source]: Matches birth distributions to proposals. Note that order of parameters matters

setup_proposals(model_proposal, proposals)[source]

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

property symmetric

Boolean indicating whether the proposal distribution is symmetric.

A jump proposal is symmetric if the proposal probability density has the property that \(p(x'|x) = p(x|x')\), where \(x\) is the current position, \(x'\) is the proposed position. In this, case, the Metropolis-Hastings ratio simplfies to just the ratio of posterior values at the two points.

Note that an adaptive proposal may still be symmetric. Symmetry only means that the current state of the proposal satisfies the above condition; it does not necessarily mean that transitions between states be symmetric.

transdimensional = True

epsie.proposals.normal module

class epsie.proposals.normal.ATAdaptiveNormal(parameters, adaptation_duration, diagonal=False, componentwise=False, start_step=1, target_rate=None, jump_interval=1)[source]

Bases: epsie.proposals.normal.ATAdaptiveSupport, epsie.proposals.normal.Normal

Uses a normal distribution with adaptive covariance for proposals.

See ATAdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
diagonal (bool, optional) – Whether to train off-diagonal elements of the proposal covariance. By default set to False; off-diagonal elements are being trained.
componentwise (bool, optional) – Whether to include a componentwise scaling of the parameters (algorithm 6 in [1]). By default set to False (algorithm 4 in [1]). Componentwise scaling ndim times more expensive than global scaling.
start_step (int, optional) – The proposal step index when adaptation phase begins.
target_rate (float, optional) – Target acceptance ratio. By default 0.234 and 0.48 for componentwise scaling.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
**kwargs – All other keyword arguments are passed to AdaptiveSupport.setup_adaptation(). See that function for details.

name = 'at_adaptive_normal'

symmetric = True

class epsie.proposals.normal.ATAdaptiveSupport[source]

Bases: epsie.proposals.base.BaseAdaptiveSupport

Utility class for adding ATAdaptiveNormal proposal support.

The adaptation algorithm is based on Algorithm 4 and 6 in [1].

See [1] for details.

Notes

For the vanishing decay we use

\[\gamma_{g+1} = \left(g - g_{0}\right)^{-0.6} - C,\]

where :math: g_{0} is the iteration at which adaptation starts, by default :math: g_{0}=1 and :math: C is a positive constant ensuring that when the adaptation phase ends the vanishing decay tends to zero.

References

[1] Andrieu, Christophe & Thoms, Johannes. (2008). A tutorial on adaptive MCMC. Statistics and Computing. 18. 10.1007/s11222-008-9110-y.

set_state(state)[source]

setup_adaptation(adaptation_duration, diagonal=False, componentwise=False, start_step=1, target_rate=None)[source]

Sets up the adaptation parameters.

Parameters

adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
diagonal (bool, optional) – Whether to train off-diagonal elements of the proposal covariance. By default set to False; off-diagonal elements are being trained.
componentwise (bool, optional) – Whether to include a componentwise scaling of the parameters (algorithm 6 in [1]). By default set to False (algorithm 4 in [1]). Componentwise scaling ndim times more expensive than global scaling.
start_step (int, optional) – The proposal step when the adaptation phase begins.
target_rate (float, optional) – Target acceptance ratio. By default 0.234 and 0.48 for componentwise scaling.

property state

class epsie.proposals.normal.AdaptiveNormal(parameters, prior_widths, adaptation_duration, start_step=1, jump_interval=1, **kwargs)[source]

Bases: epsie.proposals.normal.AdaptiveSupport, epsie.proposals.normal.Normal

Uses a normal distribution with adaptive variance for proposals.

See AdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
prior_widths (dict) – Dictionary mapping parameter names to values giving the width of each parameter’s prior. The values may be floats, or any object that has an __abs__ method that will return a float.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
start_step (int, optional) – The proposal step index when adaptation phase begins.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After adaptation_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
**kwargs – All other keyword arguments are passed to AdaptiveSupport.setup_adaptation(). See that function for details.

name = 'adaptive_normal'

symmetric = True

class epsie.proposals.normal.AdaptiveSupport[source]

Bases: epsie.proposals.base.BaseAdaptiveSupport

Utility class for adding adaptive variance support to a proposal.

The adaptation algorithm is based on Eqs. 35 and 36 of Veitch et al. 1. The with of the proposal at each step is based on the width of the prior and whether or not the previous proposal was accepted or not. See Notes for more details.

This is only meant to be used in conjuction with proposals that have independent parameters, each with their own standard deviation. Specifically, the propsal must have an isdiagonal attribute and an _std attribute.

Notes

For a given parameter, the standard deviation of the \(k^{\rm th}\) iteration is given by 1:

\[\sigma_k = \sigma_{k-1} + \alpha_{k-1} \left[\left(k - k_0\right)^{-\beta} - 0.1\right]\frac{\Delta}{10},\]

where \(\alpha_{k-1} = 1 - \xi\) if the previous iteration was accpeted and \(\alpha_{k-1} = -\xi\) if the previous iteration was rejected. Here, \(\xi\) is the target acceptance rate, \(\Delta\) is the prior width, \(\beta\) is the adaptation decay, and \(k_0\) gives the iteration after which the adaptation begins. The initial standard deviation \(\sigma_0\) to use is a free parameter. The default in this function is to use \(\sigma_0 = (1-\xi)0.09\Delta\).

References

1(1,2): J. Veitch et al., “Parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library, ” Phys. Rev. D91 042003 (2015), arXiv:1409.7215 [gr-qc].

property deltas: The prior widths, as a numpy array.

property prior_widths: The width of the prior used for each parameter.

set_state(state)[source]

setup_adaptation(prior_widths, adaptation_duration, adaptation_decay=None, start_step=1, target_rate=0.234, initial_std=None)[source]

Sets up the adaptation parameters.

Parameters

prior_widths (dict) – Dictionary mapping parameter names to values giving the width of each parameter’s prior. The values may be floats, or any object that has an __abs__ method that will return a float.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a chain exceeds this value.
adaptation_decay (int, optional) – The decay rate to use for the adaptation size (\(beta\) in the equation in the notes). If not provided, will use \(1/\log_10(T)\), where \(T\) is the adaptation duration.
start_step (int, optional) – The proposal step to start doing the adaptation (\(k_0+1\) in the equation below). Must be greater than zero. Default is 1.
target_rate (float, optional) – The target acceptance rate. Default is 0.234.
initial_std (array, optional) – The initial standard deviation to use. Default is to use (1 - target_rate)*0.09*prior_widths.

property state

class epsie.proposals.normal.Normal(parameters, cov=None, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.base.BaseProposal

Uses a normal distribution with a fixed variance for proposals.

This proposal may handle one or more parameters.

Parameters

parameters ((list of) str) – The names of the parameters to produce proposals for.
cov (array, optional) – The covariance matrix of the parameters. May provide either a single float, a 1D array with length ndim, or an ndim x ndim array, where ndim = the number of parameters given. If a single float or a 1D array is given, will use a diagonal covariance matrix (i.e., all parameters are independent of each other). Default (None) is to use unit variance for all parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

cov

The covariance matrix being used.

Type: numpy.ndarray

property cov: The covariance matrix used.

property isdiagonal

Whether or not the parameters are independent of each other.

If True (the parameters are independent), then a normal distribution will be used for proposals. Otherwise, a multivariate normal is used.

name = 'normal'

set_state(state)[source]: Set all information needed to produce a deterministic jump.

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

property std

The standard deviation.

Raises a ValueError if the covariance matrix is not diagonal.

symmetric = True

class epsie.proposals.normal.SSAdaptiveNormal(parameters, cov=None, jump_interval=1, jump_interval_duration=None, **kwargs)[source]

Bases: epsie.proposals.normal.SSAdaptiveSupport, epsie.proposals.normal.Normal

Uses a normal distribution with adaptive variance for proposals.

See SSAdaptiveSupport for details on the adaptation algorithm.

Parameters

parameters ((list of) str) – The names of the parameters.
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.
**kwargs – All other keyword arguments are passed to SSAdaptiveSupport.setup_adaptation(). See that function for details.

name = 'ss_adaptive_normal'

symmetric = True

class epsie.proposals.normal.SSAdaptiveSupport[source]

Bases: epsie.proposals.base.BaseAdaptiveSupport

Utility class for adding adaptive variance support to a proposal.

The adaptation algorithm is based on a method in Sivia and Skilling 2.

Notes

At each iteration \(k\), the variance is scaled by a factor \(\gamma(k)\)

\[\gamma(k) = \alpha(k) \gamma(k-1),\]

where

\[\begin{split}\alpha(k) = \begin{cases} e^{1/N_a(k)} &\textrm{ if } \frac{N_a(k)}{k} > \xi,\\ e^{-1/(k-N_a(k))} &\textrm{ if } \frac{N_a(k)}{k} < \xi,\\ 1 &\textrm{ if } \frac{N_a(k)}{k} = \xi. \end{cases}\end{split}\]

Here, \(N_a(k)\) is the number of iterations that have been accepted to this point (so that \(k-N_a(k)\) is the number of rejections), and \(\xi\) is the target acceptance rate. The initial \(gamma\) is set to 1.

References

2: Sivia D., Skilling J., “Data Analysis: A Bayesian Tutorial,” Oxford Univ. Press, Oxford (2006)

max_std = None

n_accepted = None

set_state(state)[source]

setup_adaptation(target_rate=0.234, max_cov=None)[source]

Sets up the adaptation parameters.

Parameters

target_rate (float, optional) – The target acceptance rate. Default is 0.234.
max_cov (float, optional) – The maximum value any element in the covariance matrix is allowed to obtain. If an adapatation step would cause any element to exceed this value, the covariance matrix will not be changed. Default (None) means that no cap will be applied.

property state

epsie.proposals.solid_angle module

Proposals for sampling on the surface of a 2-sphere.

class epsie.proposals.solid_angle.AdaptiveIsotropicSolidAngle(azimuthal_parameter, polar_parameter, adaptation_duration, start_step=1, target_rate=0.234, radec=False, degs=False, jump_interval=1)[source]

Bases: epsie.proposals.solid_angle.AdaptiveIsotropicSolidAngleSupport, epsie.proposals.solid_angle.IsotropicSolidAngle

An adaptive isotropic solid angle proposal based on the von Mises-Fisher distribution.

See AdaptiveIsotropicSolidAngleSupport and IsotropicSolidAngle for more details on the adaptation algorithm and the proposal distribution.

Parameters

azimuthal_parameter (str) – The name of the azimuthal parameter.
polar_parameter (str) – The name of the polar parameter.
adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
start_step (int, optional) – The proposal step index when adaptation phase begins.
target_rate (float, optional) – Target acceptance ratio. By default 0.234 and 0.48 for componentwise scaling.
radec (bool, optional) – Defines the polar angle convention. By default False, i.e. the polar angle range is [0, np.pi]. If radec = True, then the polar angle range is [-np.pi/2, np.pi/2].
degs (bool, optional) – Whether the input parameters are in degrees. By default False (radians).
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.

name = 'adaptive_isotropic_solid_angle'

symmetric = True

class epsie.proposals.solid_angle.AdaptiveIsotropicSolidAngleSupport[source]

Bases: epsie.proposals.base.BaseAdaptiveSupport

A utility class for adding adaptation support for the IsotropicSolidAngle proposal.

The adaptation adapts the concentration parameter to achieve a specific acceptance ration.

Notes

For the vanishing decay we use

\[\gamma_{g+1} = \left(g - g_{0}\right)^{-0.6} - C,\]

where :math: g_{0} is the iteration at which adaptation starts, by default :math: g_{0}=1 and :math: C is a positive constant ensuring that when the adaptation phase ends the vanishing decay tends to zero.

set_state(state)[source]

setup_adaptation(adaptation_duration, start_step, target_rate)[source]

Sets up the adaptation parameters.

Parameters

adaptation_duration (int) – The number of proposal steps over which to apply the adaptation. No more adaptation will be done once a proposal exceeds this value.
start_step (int, optional) – The proposal step when the adaptation phase begins.
target_rate (float, optional) – Target acceptance ratio. By default 0.234 and 0.48 for componentwise scaling.

property state

class epsie.proposals.solid_angle.IsotropicSolidAngle(azimuthal_parameter, polar_parameter, kappa=10, radec=False, degs=False, jump_interval=1, jump_interval_duration=None)[source]

Bases: epsie.proposals.base.BaseProposal

Uses the von Mises-Fisher distribution with a fixed concentration parameter.

The von Mises-Fisher distribution is an isotropic distribution on the surface of a 2-sphere and is analogoues to the isotropic normal distribution on a plane (where the covariance matrix is proportional to unity).

Parameters

azimuthal_parameter (str) – The name of the azimuthal parameter.
polar_parameter (str) – The name of the polar parameter.
kappa (float, optional) –
The distribution concentration parameter. The mean angular distance of a jump in degrees for several values of kappa is:

kappa = 1 : 69 degrees kappa = 10 : 23 degrees kappa = 100 : 7 degrees
radec (bool, optional) – Defines the polar angle convention. By default False, i.e. the polar angle range is [0, np.pi]. If radec = True, then the polar angle range is [-np.pi/2, np.pi/2].
degs (bool, optional) – Whether the input parameters are in degrees. By default False (radians).
jump_interval (int, optional) – The jump interval of the proposal, the proposal only gets called every jump interval-th time. After jump_interval_duration number of proposal steps elapses the proposal will again be called on every chain iteration. By default jump_interval = 1.
jump_interval_duration (int, optional) – The number of proposals steps during which values of jump_interval other than 1 are used. After this elapses the proposal is called on each iteration.

property isdegs: Whether input and ouput values are in degrees.

property isradec: Whether the polar angle assumes the right-ascension declination convention and runs in range [-np.pi/2, np.pi/2].

property kappa: Returns the concentration parameter of the von Mises-Fisher distribution.

name = 'isotropic_solid_angle'

property norm: Returns the normalisation constant for the von Mises-Fisher distribution.

set_state(state)[source]: Set all information needed to produce a deterministic jump.

property state: Returns all information needed to produce a deterministic jump. The information returned by this property should be everything needed such that if you pass it to set_state, you will get the same proposal on the next call of jump. The information should be returned as a dictionary. At the very least, this should include the current state of the proposal’s random_state. For adaptive proposals, this may also include the buffer used to adjust the proposal distribution.

symmetric = True

epsie.proposals package

Submodules

epsie.proposals.angular module

epsie.proposals.base module

epsie.proposals.birth module

epsie.proposals.bounded_eigenvector module

epsie.proposals.bounded_normal module

epsie.proposals.discrete module

epsie.proposals.eigenvector module

epsie.proposals.joint module

epsie.proposals.nested_transdimensional module

epsie.proposals.normal module

epsie.proposals.solid_angle module

Module contents