eigenfoo / littlemcmc

A lightweight and performant implementation of HMC and NUTS in Python, spun out of the PyMC project.

Hello, I'm George! 👋

I’m a data scientist and machine learning researcher based in New York City. I like natural language processing, Bayesian modelling, open source software and coffee. I’m based in New York and I work for Flatiron Health.

In my copious free time, I contribute to and maintain several open-source libraries (particularly the PyMC project). Away from the keyboard, I spend my time drinking coffee, taking photos and obsessing over mechanical keyboards.

Previously, I worked at Point72 Asset Management and Quantopian (acquired by Robinhood), and studied engineering at The Cooper Union with minors in computer science and mathematics.

For more about me (e.g. my blog, projects and résumé), please visit my website.

Contact

I love getting emails from non-bots, and you can also find me on Twitter, Mastodon and LinkedIn.

littlemcmc's Issues

Rework sampling API

Ideally it would be something like

trace, stats = lmc.sample(
    logp_dlogp_func=logp_dlogp_func,
    size=1,
    draws=1000,
    tune=500,
    step="nuts",
    chains=4,
    cores=1,
    progressbar="notebook"
)

instead of

trace, stats = lmc.sample(
    logp_dlogp_func=logp_dlogp_func,
    size=1,
    draws=1000,
    tune=500,
    step=lmc.NUTS(logp_dlogp_func=logp_dlogp_func, size=1),
    chains=4,
    cores=1,
    progressbar="notebook"
)

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
Action
and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

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There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

Return ArviZ output

Instead of returning NumPy arrays and Python dicts as output, we should let there be an option to return the output as an ArviZ object. This would allow much better compatibility.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to pymc3/step_methods/hmc/

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/step_methods/hmc/ since yesterday: please see
the latest run of the even-with-pymc3 GitHub Action
and consider if these commits are worth mirroring in littlemcmc.

Upload as conda package

It would be nice if we could conda install littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

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There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

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There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

Fix regression caused by pymc-devs/pymc3#4285

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

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There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

No copyright or license file in the source files

See notice at the bottom of the LICENSE

   APPENDIX: How to apply the Apache License to your work.

      To apply the Apache License to your work, attach the following
      boilerplate notice, with the fields enclosed by brackets "[]"
      replaced with your own identifying information. (Don't include
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      comment syntax for the file format. We also recommend that a
      file or class name and description of purpose be included on the
      same "printed page" as the copyright notice for easier
      identification within third-party archives.

   Copyright [yyyy] [name of copyright owner]

   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at

Broken progress bar when multiprocessing

Description
When passing cores > 1, the progress bar does not work well: sometimes (when using tqdm_notebook) nothing is shown at all, and sometimes (when using tqdm) the progress bars "fight", occasionally starting on new lines.

Reproducible Example
Simply see the quickstart tutorial.

DOC: write documentation

• Document code itself
• Rerun the notebooks, making sure that multiprocessing works...
• Write a developers guide, explaining how the various modules work together. This will probably be helpful to PyMC3 later on.

s/size/model_ndim/g

Currently we have the size parameter in lmc.sample. However, model_ndim might be a more descriptive variable name (and also mirrors what PyMC3 uses).

Publish in JOSS?

Need to find out if JOSS accepts "derivative" software packages: LittleMCMC is derived mostly from PyMC3 code.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

Why is there weirdness with Jupyter notebooks?

Description

Running littlemcmc in Jupyter notebooks leads to weird behavior.

• All samples are the same
• The PyTorch and JAX models either fail or do not run at all (or at least take a very long time).

See the framework cookbook for an example of both: https://littlemcmc.readthedocs.io/en/stable/tutorials/framework_cookbook.html

Environment

• LittleMCMC version: v0.2.2
• Python version: 3.7
• Operating system: macOS

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
Action
and consider if these commits are worth mirroring in littlemcmc.

Add more details to divergence warnings

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

New commits to `pymc3/sampling.py` or `pymc3/step_methods/hmc/`

This is an auto-generated issue, triggered by the even-with-pymc3 workflow.

There have been new commits to pymc3/sampling.py or pymc3/step_methods/hmc/ since
yesterday: please see the latest run of the even-with-pymc3 GitHub
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and consider if these commits are worth mirroring in littlemcmc.

Multiprocess sampling fails on macOS

Description

Please provide a minimal, self-contained, and reproducible example.

import numpy as np
import scipy.stats
import littlemcmc as lmc


def logp_func(x, loc=0, scale=1):
    return np.log(scipy.stats.norm.pdf(x, loc=loc, scale=scale))


def dlogp_func(x, loc=0, scale=1):
    return -(x - loc) / scale


def logp_dlogp_func(x, loc=0, scale=1):
    return logp_func(x, loc=loc, scale=scale), dlogp_func(x, loc=loc, scale=scale)


trace, stats = lmc.sample(logp_dlogp_func=logp_dlogp_func, model_ndim=1)

Please provide the full traceback.

Click to expand...

Traceback (most recent call last):-----------------------------------------------------------------| 0.00% [0/8000 00:00<00:00 Sampling 4 chains, 0 divergences]
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 261, in main
    old_handlers)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 297, in _serve_one
    code = spawn._main(child_r)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 114, in _main
    prepare(preparation_data)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 225, in prepare
    _fixup_main_from_path(data['init_main_from_path'])
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 277, in _fixup_main_from_path
Traceback (most recent call last):
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 261, in main
    run_name="__mp_main__")
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 263, in run_path
    old_handlers)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 297, in _serve_one
    code = spawn._main(child_r)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 114, in _main
    pkg_name=pkg_name, script_name=fname)
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 96, in _run_module_code
Traceback (most recent call last):
    prepare(preparation_data)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 261, in main
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 225, in prepare
    mod_name, mod_spec, pkg_name, script_name)
    _fixup_main_from_path(data['init_main_from_path'])
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 277, in _fixup_main_from_path
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 85, in _run_code
    old_handlers)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 297, in _serve_one
    run_name="__mp_main__")
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 263, in run_path
    exec(code, run_globals)
  File "/Users/george/littlemcmc/tests/foo.py", line 18, in <module>
    code = spawn._main(child_r)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 114, in _main
    trace, stats = lmc.sample(logp_dlogp_func=logp_dlogp_func, model_ndim=1)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 188, in sample
    prepare(preparation_data)
    pkg_name=pkg_name, script_name=fname)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 225, in prepare
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 96, in _run_module_code
    mod_name, mod_spec, pkg_name, script_name)
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 85, in _run_code
    _fixup_main_from_path(data['init_main_from_path'])
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 277, in _fixup_main_from_path
    exec(code, run_globals)
  File "/Users/george/littlemcmc/tests/foo.py", line 18, in <module>
    run_name="__mp_main__")
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 263, in run_path
    trace, stats = lmc.sample(logp_dlogp_func=logp_dlogp_func, model_ndim=1)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 188, in sample
    traces, stats = _mp_sample(**sample_args, **parallel_args)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 300, in _mp_sample
    traces, stats = _mp_sample(**sample_args, **parallel_args)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 300, in _mp_sample
    pkg_name=pkg_name, script_name=fname)
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 96, in _run_module_code
    pickle_backend=pickle_backend,
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in __init__
    mod_name, mod_spec, pkg_name, script_name)
    pickle_backend=pickle_backend,
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in __init__
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 85, in _run_code
    exec(code, run_globals)
  File "/Users/george/littlemcmc/tests/foo.py", line 18, in <module>
    trace, stats = lmc.sample(logp_dlogp_func=logp_dlogp_func, model_ndim=1)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 188, in sample
    traces, stats = _mp_sample(**sample_args, **parallel_args)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 300, in _mp_sample
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in <listcomp>
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in <listcomp>
    pickle_backend=pickle_backend,
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in __init__
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 278, in __init__
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 278, in __init__
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in <listcomp>
    self._process.start()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/process.py", line 112, in start
    self._process.start()
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/process.py", line 112, in start
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 278, in __init__
    self._popen = self._Popen(self)
    self._process.start()
    self._popen = self._Popen(self)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/process.py", line 112, in start
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/context.py", line 291, in _Popen
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/context.py", line 291, in _Popen
    self._popen = self._Popen(self)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/context.py", line 291, in _Popen
    return Popen(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 35, in __init__
    return Popen(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 35, in __init__
    return Popen(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 35, in __init__
    super().__init__(process_obj)
    super().__init__(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_fork.py", line 20, in __init__
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_fork.py", line 20, in __init__
    super().__init__(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_fork.py", line 20, in __init__
    self._launch(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 42, in _launch
    self._launch(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 42, in _launch
    self._launch(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 42, in _launch
    prep_data = spawn.get_preparation_data(process_obj._name)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 143, in get_preparation_data
    prep_data = spawn.get_preparation_data(process_obj._name)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 143, in get_preparation_data
    _check_not_importing_main()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 136, in _check_not_importing_main
    prep_data = spawn.get_preparation_data(process_obj._name)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 143, in get_preparation_data
    _check_not_importing_main()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 136, in _check_not_importing_main
    is not going to be frozen to produce an executable.''')
RuntimeError:
        An attempt has been made to start a new process before the
        current process has finished its bootstrapping phase.

        This probably means that you are not using fork to start your
        child processes and you have forgotten to use the proper idiom
        in the main module:

            if __name__ == '__main__':
                freeze_support()
                ...

        The "freeze_support()" line can be omitted if the program
        is not going to be frozen to produce an executable.
    is not going to be frozen to produce an executable.''')
RuntimeError:
        An attempt has been made to start a new process before the
        current process has finished its bootstrapping phase.

        This probably means that you are not using fork to start your
        child processes and you have forgotten to use the proper idiom
        in the main module:

            if __name__ == '__main__':
                freeze_support()
                ...

        The "freeze_support()" line can be omitted if the program
        is not going to be frozen to produce an executable.
    _check_not_importing_main()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 136, in _check_not_importing_main
    is not going to be frozen to produce an executable.''')
RuntimeError:
        An attempt has been made to start a new process before the
        current process has finished its bootstrapping phase.

        This probably means that you are not using fork to start your
        child processes and you have forgotten to use the proper idiom
        in the main module:

            if __name__ == '__main__':
                freeze_support()
                ...

        The "freeze_support()" line can be omitted if the program
        is not going to be frozen to produce an executable.
Traceback (most recent call last):
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 261, in main
    old_handlers)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/forkserver.py", line 297, in _serve_one
    code = spawn._main(child_r)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 114, in _main
    prepare(preparation_data)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 225, in prepare
    _fixup_main_from_path(data['init_main_from_path'])
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 277, in _fixup_main_from_path
    run_name="__mp_main__")
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 263, in run_path
    pkg_name=pkg_name, script_name=fname)
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 96, in _run_module_code
    mod_name, mod_spec, pkg_name, script_name)
  File "/Users/george/miniconda3/lib/python3.7/runpy.py", line 85, in _run_code
    exec(code, run_globals)
  File "/Users/george/littlemcmc/tests/foo.py", line 18, in <module>
    trace, stats = lmc.sample(logp_dlogp_func=logp_dlogp_func, model_ndim=1)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 188, in sample
    traces, stats = _mp_sample(**sample_args, **parallel_args)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 300, in _mp_sample
    pickle_backend=pickle_backend,
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in __init__
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 433, in <listcomp>
    for chain, seed, start in zip(range(chains), seeds, start_points)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 278, in __init__
    self._process.start()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/process.py", line 112, in start
    self._popen = self._Popen(self)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/context.py", line 291, in _Popen
    return Popen(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 35, in __init__
    super().__init__(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_fork.py", line 20, in __init__
    self._launch(process_obj)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/popen_forkserver.py", line 42, in _launch
    prep_data = spawn.get_preparation_data(process_obj._name)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 143, in get_preparation_data
    _check_not_importing_main()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/spawn.py", line 136, in _check_not_importing_main
    is not going to be frozen to produce an executable.''')
RuntimeError:
        An attempt has been made to start a new process before the
        current process has finished its bootstrapping phase.

        This probably means that you are not using fork to start your
        child processes and you have forgotten to use the proper idiom
        in the main module:

            if __name__ == '__main__':
                freeze_support()
                ...

        The "freeze_support()" line can be omitted if the program
        is not going to be frozen to produce an executable.
Traceback (most recent call last):
  File "tests/foo.py", line 18, in <module>
    trace, stats = lmc.sample(logp_dlogp_func=logp_dlogp_func, model_ndim=1)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 188, in sample
    traces, stats = _mp_sample(**sample_args, **parallel_args)
  File "/Users/george/littlemcmc/littlemcmc/sampling.py", line 305, in _mp_sample
    for draw in sampler:
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 469, in __iter__
    draw = ProcessAdapter.recv_draw(self._active)
  File "/Users/george/littlemcmc/littlemcmc/parallel_sampling.py", line 337, in recv_draw
    msg = ready[0].recv()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/connection.py", line 250, in recv
    buf = self._recv_bytes()
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/connection.py", line 407, in _recv_bytes
    buf = self._recv(4)
  File "/Users/george/miniconda3/lib/python3.7/multiprocessing/connection.py", line 383, in _recv
    raise EOFError
EOFError

Please provide any additional information below.

• I assume the error is caused by the recv but the other end is already closed.
• If I wrap the code in an if __name__ == "__main__", it runs fine.
• This code also runs fine on Linux.

Environment

• LittleMCMC version: from source
• Python version: 3.7
• Operating system: macOS

Remove `report.py`

report.py is mainly used for diagnostic warnings, which is less of a concern here: we simply return all the sampler statistics to the user. We can probably safely remove it.

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Support for discrete variables in Hamiltonian Monte Carlo sampler

Ive read in the documentation that this library only supports continuous variables. Any thoughts on adding support for loglikelihood functions that have a mixture of continuous and discrete parameters? The following papers seem to be addressing how to build a sampler in such a case:
Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods

Continuous Relaxations for DiscreteHamiltonian Monte Carlo

Auxiliary-variable Exact Hamiltonian MonteCarlo Samplers for Binary Distributions

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MAINT: new commits to pymc3/step_methods/hmc/

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Improve documentation

• Progress bar does not render well in rst; remove it.
• Add sample function docstring.
• Include some preamble on why LittleMCMC is necessary at all? Perhaps in a developer guide?
• Add more meat to docs/index.rst

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Remove unreachable lines in sampling code; test model logp before sampling

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Use a better shape for trace object

Currently we flatten the trace object to have shape [num_variables, num_chains * num_samples]. Really, it ought to be [num_chains, num_samples, num_variables] (or whatever reasonable choice ArviZ makes: we should target compatibility with them.

https://github.com/eigenfoo/littlemcmc/blob/master/littlemcmc/sampling.py#L213-L214

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Consider supporting deterministic variables?

a.k.a. generated quantities in Stan. It would be nice to support them natively somehow (i.e. along with the multiprocessing), and return them inside the trace object. We should look at how PyMC3 handles deterministics.

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Improve documentation

• Describe the necessary properties of the logp_dlogp_func
  • Shape of outputs must be same as shapes of inputs
  • Pickleable
  • Variables must be on R (i.e. unconstrained)
• Update demo notebook with cores > 1, to demonstrate multiprocessing.

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