PyMC tries to make standard things easy, but keep unusual things possible. Its openness, combined with Python’s flexibility, invite extensions from using new step methods to exotic stochastic processes (see the Gaussian process module). This chapter briefly reviews the ways PyMC is designed to be extended.

The simplest way to create a `Stochastic` object with a nonstandard
distribution is to use the medium or long decorator syntax. See Chapter
*Building models*. If you want to create many stochastics with the same
nonstandard distribution, the decorator syntax can become cumbersome. An actual
subclass of `Stochastic` can be created using the class factory
`stochastic_from_dist`. This function takes the following arguments:

- The name of the new class,
- A
logpfunction,- A
randomfunction,- The NumPy datatype of the new class (for continuous distributions, this should be
float; for discrete distributions,int; for variables valued as non-numerical objects,object),- A flag indicating whether the resulting class represents a vector-valued variable.

The necessary parent labels are read from the `logp` function, and a
docstring for the new class is automatically generated. Instances of the new
class can be created in one line.

Full subclasses of `Stochastic` may be necessary to provide nonstandard
behaviors (see `gp.GP`).

The `StepMethod` class is meant to be subclassed. There are an enormous number of MCMC step methods in the literature, whereas PyMC provides only about half a dozen. Most user-defined step methods will be either Metropolis-Hastings or Gibbs step methods, and these should subclass `Metropolis` or `Gibbs` respectively. More unusual step methods should subclass `StepMethod` directly.

Consider the probability model in `examples/custom_step.py`:

```
mu = pymc.Normal('mu',0,.01, value=0)
tau = pymc.Exponential('tau',.01, value=1)
cutoff = pymc.Exponential('cutoff',1, value=1.3)
D = pymc.Truncnorm('D',mu,tau,-np.inf,cutoff,value=data,observed=True)
```

The stochastic variable `cutoff` cannot be smaller than the largest element
of \(D\), otherwise \(D\)‘s density would be zero. The standard
`Metropolis` step method can handle this case without problems; it will
propose illegal values occasionally, but these will be rejected.

Suppose we want to handle `cutoff` with a smarter step method that doesn’t
propose illegal values. Specifically, we want to use the nonsymmetric proposal
distribution:

\[\begin{eqnarray*}
x_p | x \sim \textup{Truncnorm}(x, \sigma, \max(D), \infty).
\end{eqnarray*}\]

We can implement this Metropolis-Hastings algorithm with the following step method class:

```
class TruncatedMetropolis(pymc.Metropolis):
def __init__(self, stochastic, low_bound, up_bound, *args, **kwargs):
self.low_bound = low_bound
self.up_bound = up_bound
pymc.Metropolis.__init__(self, stochastic, *args, **kwargs)
def propose(self):
tau = 1./(self.adaptive_scale_factor * self.proposal_sd)**2
self.stochastic.value = \
pymc.rtruncnorm(self.stochastic.value, tau, self.low_bound, self.up_bound)
def hastings_factor(self):
tau = 1./(self.adaptive_scale_factor * self.proposal_sd)**2
cur_val = self.stochastic.value
last_val = self.stochastic.last_value
lp_for = pymc.truncnorm_like(cur_val, last_val, tau, self.low_bound, self.up_bound)
lp_bak = pymc.truncnorm_like(last_val, cur_val, tau, self.low_bound, self.up_bound)
if self.verbose > 1:
print self._id + ': Hastings factor %f'%(lp_bak - lp_for)
return lp_bak - lp_for
```

The `propose` method sets the step method’s stochastic’s value to a new
value, drawn from a truncated normal distribution. The precision of this
distribution is computed from two factors: `self.proposal_sd`, which can be
set with an input argument to Metropolis, and `self.adaptive_scale_factor`.
Metropolis step methods’ default tuning behavior is to reduce
`adaptive_scale_factor` if the acceptance rate is too low, and to increase
`adaptive_scale_factor` if it is too high. By incorporating
`adaptive_scale_factor` into the proposal standard deviation, we avoid having
to write our own tuning infrastructure. If we don’t want the proposal to tune,
we don’t have to use `adaptive_scale_factor`.

The `hastings_factor` method adjusts for the asymmetric proposal distribution
[Gelman2004]. It computes the log of the quotient of the ‘backward’ density
and the ‘forward’ density. For symmetric proposal distributions, this quotient
is 1, so its log is zero.

Having created our custom step method, we need to tell MCMC instances to use it
to handle the variable `cutoff`. This is done in `custom_step.py` with
the following line:

```
M.use_step_method(TruncatedMetropolis, cutoff, D.value.max(), np.inf)
```

This call causes \(M\) to pass the arguments `cutoff`, `D.value.max()`,
and `np.inf` to a `TruncatedMetropolis` object’s `__init__` method, and
use the object to handle `cutoff`.

Its often convenient to get a handle to a custom step method instance directly
for debugging purposes. `M.step_method_dict[cutoff]` returns a list of all
the step methods \(M\) will use to handle `cutoff`:

```
>>> M.step_method_dict[cutoff]
[<custom_step.TruncatedMetropolis object at 0x3c91130>]
```

There may be more than one, and conversely step methods may handle more than one stochastic variable. To see which variables step method \(S\) is handling, try:

```
>>> S.stochastics
set([<pymc.distributions.Exponential 'cutoff' at 0x3cd6b90>])
```

All step methods must implement the following methods:

`step()`:- Updates the values of
`self.stochastics`. `tune()`:Tunes the jumping strategy based on performance so far. A default method is available that increases

`self.adaptive_scale_factor`(see below) when acceptance rate is high, and decreases it when acceptance rate is low. This method should return`True`if additional tuning will be required later,and`False`otherwise.`competence(s):`- A class method that examines stochastic variable \(s\) and returns a
- value from 0 to 3 expressing the step method’s ability to handle the
variable. This method is used by
`MCMC`instances when automatically assigning step methods. Conventions are: - 0
- I cannot safely handle this variable.
- 1
- I can handle the variable about as well as the standard
`Metropolis`step method. - 2
- I can do better than
`Metropolis`. - 3
- I am the best step method you are likely to find for this variable in most cases.

For example, if you write a step method that can handle

`MyStochasticSubclass`well, the competence method might look like this:class MyStepMethod(pymc.StepMethod): def __init__(self, stochastic, *args, **kwargs): ... @classmethod def competence(self, stochastic): if isinstance(stochastic, MyStochasticSubclass): return 3 else: return 0

Note that PyMC will not even attempt to assign a step method automatically if its

`__init__`method cannot be called with a single stochastic instance, that is`MyStepMethod(x)`is a legal call. The list of step methods that PyMC will consider assigning automatically is called`pymc.StepMethodRegistry`.`current_state()`:This method is easiest to explain by showing the code:

state = {} for s in self._state: state[s] = getattr(self, s) return state

`self._state`should be a list containing the names of the attributes needed to reproduce the current jumping strategy. If an`MCMC`object writes its state out to a database, these attributes will be preserved. If an`MCMC`object restores its state from the database later, the corresponding step method will have these attributes set to their saved values.

Step methods should also maintain the following attributes:

`_id`:- A string that can identify each step method uniquely (usually something
- like
`<class_name>_<stochastic_name>`).

`adaptive_scale_factor`:- An ‘adaptive scale factor’. This attribute is only needed if the default
`tune()`method is used. `_tuning_info`:- A list of strings giving the names of any tuning parameters. For
`Metropolis`instances, this would be`adaptive_scale_factor`. This list is used to keep traces of tuning parameters in order to verify ‘diminishing tuning’ [Roberts2007].

All step methods have a property called `loglike`, which returns the sum of
the log-probabilities of the union of the extended children of
`self.stochastics`. This quantity is one term in the log of the Metropolis-
Hastings acceptance ratio. The `logp_plus_loglike` property gives the sum of
that and the log-probabilities of `self.stochastics`.

A Metropolis-Hastings step method only needs to implement the following
methods, which are called by `Metropolis.step()`:

`reject()`:Usually just

def reject(self): self.rejected += 1 [s.value = s.last_value for s in self.stochastics]

`propose():`- Sets the values of all
`self.stochastics`to new, proposed values. This method may use the`adaptive_scale_factor`attribute to take advantage of the standard tuning scheme.

Metropolis-Hastings step methods may also override the `tune` and `competence` methods.

Metropolis-Hastings step methods with asymmetric jumping distributions may
implement a method called `hastings_factor()`, which returns the log of the
ratio of the ‘reverse’ and ‘forward’ proposal probabilities. Note that no
`accept()` method is needed or used.

By convention, Metropolis-Hastings step methods use attributes called
`accepted` and `rejected` to log their performance.

Gibbs step methods handle conjugate submodels. These models usually have two components: the ‘parent’ and the ‘children’. For example, a gamma-distributed variable serving as the precision of several normally-distributed variables is a conjugate submodel; the gamma variable is the parent and the normal variables are the children.

This section describes PyMC’s current scheme for Gibbs step methods, several of
which are in a semi-working state in the *sandbox* directory. It is meant to be
as generic as possible to minimize code duplication, but it is admittedly
complicated. Feel free to subclass `StepMethod` directly when writing Gibbs
step methods if you prefer.

Gibbs step methods that subclass PyMC’s `Gibbs` should define the following
class attributes:

`child_class`:- The class of the children in the submodels the step method can handle.
`parent_class`:- The class of the parent.
`parent_label`:- The label the children would apply to the parent in a conjugate submodel.
- In the gamma-normal example, this would be
`tau`.

`linear_OK`:- A flag indicating whether the children can use linear combinations
- involving the parent as their actual parent without destroying the conjugacy.

A subclass of `Gibbs` that defines these attributes only needs to implement a
`propose()` method, which will be called by `Gibbs.step()`. The resulting
step method will be able to handle both conjugate and ‘non-conjugate’ cases.
The conjugate case corresponds to an actual conjugate submodel. In the
non-conjugate case all the children are of the required class, but the parent
is not. In this case the parent’s value is proposed from the likelihood and
accepted based on its prior. The acceptance rate in the non-conjugate case will
be less than one.

The inherited class method `Gibbs.competence` will determine the new step
method’s ability to handle a variable \(x\) by checking whether:

- all \(x\)‘s children are of class
child_class, and either applyparent_labelto \(x\) directly or (iflinear_OK=True) to aLinearCombinationobject (chapterBuilding models), one of whose parents contains \(x\).- \(x\) is of class
parent_class

If both conditions are met, `pymc.conjugate_Gibbs_competence` will be
returned. If only the first is met, `pymc.nonconjugate_Gibbs_competence` will
be returned.

PyMC provides a convenient platform for non-MCMC fitting algorithms in addition
to MCMC. All fitting algorithms should be implemented by subclasses of
`Model`. There are virtually no restrictions on fitting algorithms, but many
of `Model`‘s behaviors may be useful. See Chapter *Fitting Models*.

Unless there is a good reason to do otherwise, Monte Carlo fitting algorithms
should be implemented by subclasses of `Sampler` to take advantage of the
interactive sampling feature and database backends. Subclasses using the
standard `sample()` and `isample()` methods must define one of two methods:

`draw()`:- If it is possible to generate an independent sample from the posterior at
- every iteration, the
`draw`method should do so. The default`_loop`method can be used in this case.

`_loop()`:- If it is not possible to implement a
`draw()`method, but you want to - take advantage of the interactive sampling option, you should override
`_loop()`. This method is responsible for generating the posterior samples and calling`tally()`when it is appropriate to save the model’s state. In addition,`_loop`should monitor the sampler’s`status`attribute at every iteration and respond appropriately. The possible values of`status`are: `'ready'`:- Ready to sample.
`'running'`:- Sampling should continue as normal.
`'halt'`:- Sampling should halt as soon as possible.
`_loop`should call the`halt()`method and return control.`_loop`can set the status to`'halt'`itself if appropriate (eg the database is full or a`KeyboardInterrupt`has been caught). `'paused'`:- Sampling should pause as soon as possible.
`_loop`should return, but should be able to pick up where it left off next time it’s called.

- If it is not possible to implement a

Samplers may alternatively want to override the default `sample()` method. In
that case, they should call the `tally()` method whenever it is appropriate
to save the current model state. Like custom `_loop()` methods, custom
`sample()` methods should handle `KeyboardInterrupts` and call the
`halt()` method when sampling terminates to finalize the traces.

If you’re going to implement a new step method, fitting algorithm or unusual (non-numeric-valued) `Stochastic` subclass, you should understand the issues related to in-place updates of `Stochastic` objects’ values. Fitting methods should never update variables’ values in-place for two reasons:

- In algorithms that involve accepting and rejecting proposals, the ‘pre-proposal’ value needs to be preserved uncorrupted. It would be possible to make a copy of the pre-proposal value and then allow in-place updates, but in PyMC we have chosen to store the pre-proposal value as
`Stochastic.last_value`and require proposed values to be new objects. In-place updates would corrupt`Stochastic.last_value`, and this would cause problems. `LazyFunction`‘s caching scheme checks variables’ current values against its internal cache by reference. That means if you update a variable’s value in-place, it or its child may miss the update and incorrectly skip recomputing its value or log-probability.

However, a `Stochastic` object’s value can make in-place updates to itself if the updates don’t change its identity. For example, the `Stochastic` subclass `gp.GP` is valued as a `gp.Realization` object. GP realizations represent random functions, which are infinite-dimensional stochastic processes, as literally as possible. The strategy they employ is to ‘self-discover’ on demand: when they are evaluated, they generate the required value conditional on previous evaluations and then make an internal note of it. This is an in-place update, but it is done to provide the same behavior as a single random function whose value everywhere has been determined since it was created.