MCMCSE

Provides tools for computing Monte Carlo standard errors (MCSE) in Markov chain Monte Carlo (MCMC). A python/numpy implementation of mcmcse.r, extended to support numpy broadcasting.

It implements the following methods:

• mcse:
  • Computes the MCMC estimate of expectation of g, with standard error.
• mcse_mat:
  • Only for mimicking mcmcse.R API, as the function mcse already supports numpy arrays. See mcse.
• mcse_p:
  • Computes the MCMC estimate of percentile p, with standard error.
• mcse_p_mat:
  • Only for mimicking mcmcse.r API, as the function mcse_p already supports numpy arrays. See mcse_p.
• mcse_q:
  • Computes the MCMC estimate of quantile q, with standard error.
• mcse_q_mat:
  • Only for mimicking mcmcse.r API, as the function mcse_q already supports numpy arrays. See mcse_q.
• ess:
  • Estimate effective sample size (ESS) as described in Gong and Felgal (2015).

See bellow for documentation, or follow the respected links.

Methods

mcse

Computes the MCMC estimate of expectation of g, with standard error. NOTE: function broadcasts over numpy arrays

Arguments:

• x: data
  • if one sample is of shape (n1,n2, ..., nk) than x.shape == (n_samples, n1,n2,...nk)
• size: batch size
  • size in ["sqroot", "cuberoot"] or size is numeric default is sqroot
• g: function which expectation is to be computed and estimated
  • if a sample is of shape (n1,...,nk), g has to handle such inputs
• method: which method to use
  • method in ["bm", "obm", "tukey", "bartlett"] default is bm

Returns:

• est: estimated expectation of g
  • est.shape == (n1,n2,...nk)
• ess: estimated standard error, of the expectation of g
  • ess.shape ==(n1,n2,...,nk) Note when they have dimension zero, numerics are returned

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mcse_mat

Only for mimicking mcmcse.R, as the function mcse supports numpy arrays of any shape. It thus only forwards its arguments to mcse. See mcse.

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mcse_p

Computes the MCMC estimate of percentile p, with standard error. NOTE: function broadcasts over numpy arrays

Arguments:

• x: data
  • if one sample is of shape (n1,n2, ..., nk) than x.shape == (n_samples, n1,n2,...nk)
• p: percentile to compute
  • 0<=p<=100
• size: batch size
  • size in ["sqroot", "cuberoot"] or size is numeric default is sqroot
• g: function which percentiles are to be computed and estimated
  • if a sample is of shape (n1,...,nk), g has to handle such inputs
• method: which method to use
  • method in ["bm", "obm", "sub"] default is bm

Returns:

• est: estimated percentile
  • est.shape == (n1,n2,...nk)
• ess: estimated standard error of the percentile
  • ess.shape ==(n1,n2,...,nk) Note when they have dimension zero, numerics are returned

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mcse_p_mat

Only for mimicking mcmcse.r, as the function mcse_p supports numpy arrays of all shapes. It thus only forwards its arguments to mcse_p. See mcse_p

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mcse_q

Computes the MCMC estimate of quantile q, with standard error. NOTE: function broadcasts over numpy arrays

Arguments:

• x: data
  • if one sample is of shape (n1,n2, ..., nk) than x.shape == (n_samples, n1,n2,...nk)
• q: quantile to compute
  • 0<=q<=100
• size: batch size
  • size in ["sqroot", "cuberoot"] or size is numeric default is sqroot
• g: function which quantiles are to be computed and estimated
  • if a sample is of shape (n1,...,nk), g has to handle such inputs
• method: which method to use
  • method in ["bm", "obm", "sub"] default is bm

Returns:

• est: estimated quantile
  • est.shape == (n1,n2,...nk)
• ess: estimated standard error of the quantile
  • ess.shape ==(n1,n2,...,nk) Note when they have dimension zero, numerics are returned

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mcse_q_mat

Only for mimicking mcmcse.r, as the function mcse_q supports numpy arrays of all shapes. It thus only forwards its arguments to mcse_q. See mcse_q.

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ess

Estimate effective sample size (ESS) as described in Gong and Felgal (2015).

Arguments:

• x: data
  • if one sample is of shape (n1,n2, ..., nk) than x.shape == (n_samples, n1,n2,...nk)
• g: function which expectation is to be computed and estimated
  • if a sample is of shape (n1,...,nk), g has to handle such inputs
• kwargs: arguments to be passed to mcse

Returns:

• ess: estimated sample size

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mcmcse.py by Žiga Sajovic, XLAB is licensed under a Creative Commons Attribution 4.0 International License.