6. Saving and managing sampling results

6.1. Accessing Sampled Data

The recommended way to access data from an MCMC run, irrespective of the database backend, is to use the trace method:

>>> from pymc.examples import disaster_model
>>> from pymc import MCMC
>>> M = MCMC(disaster_model)
>>> M.sample(10)
Sampling: 100% [00000000000000000000000000000000000000000000000000] Iterations: 10
>>> M.trace('early_mean')[:]
array([ 2.28320992,  2.28320992,  2.28320992,  2.28320992,  2.28320992,
        2.36982455,  2.36982455,  3.1669422 ,  3.1669422 ,  3.14499489])

M.trace('early_mean') returns a copy of the Trace instance associated with the tallyable object early_mean:

>>> M.trace('early_mean')
<pymc.database.ram.Trace object at 0x7fa4877a8b50>

Particular subsamples from the trace are obtained using the slice notation [], similar to NumPy arrays. By default, trace returns the samples from the last chain. To return the samples from all the chains, use chain=None:

>>> M.sample(5)
Sampling: 100% [000000000000000000000000000000000000000000000000000] Iterations: 5
>>> M.trace('early_mean', chain=None)[:]
array([ 2.28320992,  2.28320992,  2.28320992,  2.28320992,  2.28320992,
      2.36982455,  2.36982455,  3.1669422 ,  3.1669422 ,  3.14499489,
      3.14499489,  3.14499489,  3.14499489,  2.94672454,  3.10767686])

6.1.1. Output Summaries

PyMC samplers include a couple of methods that are useful for obtaining summaries of the model, or particular member nodes, rather than the entire trace. The summary method can be used to generate a pretty-printed summary of posterior quantities. For example, if we want a statistical snapshot of the early_mean node:

>>> M.early_mean.summary()

early_mean:

    Mean             SD               MC Error        95% HPD interval
    ------------------------------------------------------------------
    3.075            0.287            0.01             [ 2.594  3.722]


    Posterior quantiles:

    2.5             25              50              75             97.5
     |---------------|===============|===============|---------------|
    2.531            2.876           3.069          3.255         3.671

A method of the same name exists for the sampler, which yields summaries for every node in the model.

Alternatively, we may wish to write posterior statistics to a file, where they may be imported into a spreadsheet or plotting package. In that case, write_csv may be called to generate a comma-separated values (csv) file containing all available statistics for each node:

M.write_csv("disasters.csv", variables=["early_mean", "late_mean", "switchpoint"])

Summary statistics of stochastics from the disaster_model example, shown in a spreadsheet.

write_csv is called with a single mandatory argument, the name of the output file for the summary statistics, and several optional arguments, including a list of parameters for which summaries are desired (if not given, all model nodes are summarized) and an alpha level for calculating credible intervalse (defaults to 0.05).

6.2. Saving Data to Disk

By default, the database backend selected by the MCMC sampler is the ram backend, which simply holds the data in memory. Now, we will create a sampler that instead will write data to a pickle file:

>>> M = MCMC(disaster_model, db='pickle', dbname='Disaster.pickle')
>>> M.db
<pymc.database.pickle.Database object at 0x7fa486623d90>
>>> M.sample(10)
>>> M.db.close()

Note that in this particular case, no data is written to disk before the call to db.close. The close method will flush data to disk and prepare the database for a potential session exit. Closing a Python session without calling close beforehand is likely to corrupt the database, making the data irretrievable. To simply flush data to disk without closing the database, use the commit method.

Some backends not only have the ability to store the traces, but also the state of the step methods at the end of sampling. This is particularly useful when long warm-up periods are needed to tune the jump parameters. When the database is loaded in a new session, the step methods query the database to fetch the state they were in at the end of the last trace.

Check that you close() the database before closing the Python session.

6.3. Reloading a Database

To load a file created in a previous session, use the load function from the backend:

>>> db = pymc.database.pickle.load('Disaster.pickle')
>>> len(db.trace('early_mean')[:])
10

The db object also has a trace method identical to that of Sampler. You can hence inspect the results of a model, even when you don’t have the model around.

To add a new trace to this file, we need to create an MCMC instance. This time, instead of setting db='pickle', we will pass the existing Database instance and sample as usual. A new trace will be appended to the first:

>>> M = MCMC(disaster_model, db=db)
>>> M.sample(5)
Sampling: 100% [000000000000000000000000000000000000000000000000000] Iterations: 5
>>> len(M.trace('early_model', chain=None)[:])
15
>>> M.db.close()

6.3.1. The ram backend

Used by default, this backend simply holds a copy in memory, with no output written to disk. This is useful for short runs or testing. For long runs generating large amount of data, using this backend may fill the available memory, forcing the OS to store data in the cache, slowing down all other applications.

6.3.2. The no_trace backend

This backend simply does not store the trace. This may be useful for testing purposes.

6.3.3. The txt backend

With the txt backend, the data is written to disk in ASCII files. More precisely, the dbname argument is used to create a top directory into which chain directories, called Chain_<#>, are going to be created each time sample is called:

dbname/
  Chain_0/
    <object0 name>.txt
    <object1 name>.txt
    ...
  Chain_1/
    <object0 name>.txt
    <object1 name>.txt
    ...
  ...

In each one of these chain directories, files named <variable name>.txt are created, storing the values of the variable as rows of text:

# Variable: e
# Sample shape: (5,)
# Date: 2008-11-18 17:19:13.554188
3.033672373807017486e+00
3.033672373807017486e+00
...

While the txt backend makes it easy to load data using other applications and programming languages, it is not optimized for speed nor memory efficiency. If you plan on generating and handling large datasets, read on for better options.

6.3.4. The pickle backend

The pickle database relies on the cPickle module to save the traces. Use of this backend is appropriate for small-scale, short-lived projects. For longer term or larger projects, the pickle backend should be avoided since generated files might be unreadable across different Python versions. The pickled file is a simple dump of a dictionary containing the NumPy arrays storing the traces, as well as the state of the Sampler‘s step methods.

6.3.5. The sqlite backend

The sqlite backend is based on the python module sqlite3 (built-in to Python versions greater than 2.4) . It opens an SQL database named dbname, and creates one table per tallyable objects. The rows of this table store a key, the chain index and the values of the objects:

key (INTT), trace (INT),  v1 (FLOAT), v2 (FLOAT), v3 (FLOAT) ...

The key is autoincremented each time a new row is added to the table, that is, each time tally is called by the sampler. Note that the savestate feature is not implemented, that is, the state of the step methods is not stored internally in the database.

6.3.6. The hdf5 backend

The hdf5 backend uses pyTables to save data in binary HDF5 format. The hdf5 database is fast and can store huge traces, far larger than the available RAM. Data can be compressed and decompressed on the fly to reduce the disk footprint. Another feature of this backends is that it can store arbitrary objects. Whereas the other backends are limited to numerical values, hdf5 can tally any object that can be pickled, opening the door for powerful and exotic applications (see pymc.gp).

The internal structure of an HDF5 file storing both numerical values and arbitrary objects is as follows:

/ (root)
  /chain0/ (Group) 'Chain #0'
    /chain0/PyMCSamples (Table(N,)) 'PyMC Samples'
    /chain0/group0 (Group) 'Group storing objects.'
      /chain0/group0/<object0 name> (VLArray(N,)) '<object0 name> samples.'
      /chain0/group0/<object1 name> (VLArray(N,)) '<object1 name> samples.'
      ...
  /chain1/ (Group) 'Chain #1'
    ...

All standard numerical values are stored in a Table, while objects are stored in individual VLArrays.

The hdf5 Database takes the following parameters:

• dbname (string) Name of the hdf5 file.
• dbmode (string) File mode: a: append, w: overwrite, r: read-only.
• dbcomplevel (int (0-9)) Compression level, 0: no compression.
• dbcomplib (string) Compression library (zlib, bzip2, lzo)

According the the pyTables manual, zlib ([Roelofs2010]) has a fast decompression, relatively slow compression, and a good compression ratio. LZO ([Oberhumer2008]) has a fast compression, but a low compression ratio. bzip2 ([Seward2007]) has an excellent compression ratio but requires more CPU. Note that some of these compression algorithms require additional software to work (see the pyTables manual).

6.4. Writing a New Backend

It is relatively easy to write a new backend for PyMC. The first step is to look at the database.base module, which defines barebone Database and Trace classes. This module contains documentation on the methods that should be defined to get a working backend.

Testing your new backend should be trivial, since the test_database module contains a generic test class that can easily be subclassed to check that the basic features required of all backends are implemented and working properly.