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arxiv: 1910.13970 · v2 · pith:7MPJFZG6new · submitted 2019-10-30 · 🌌 astro-ph.IM · astro-ph.CO· physics.data-an

GetDist: a Python package for analysing Monte Carlo samples

Antony Lewis This is my paper

Pith reviewed 2026-05-14 23:54 UTC · model grok-4.3

classification 🌌 astro-ph.IM astro-ph.COphysics.data-an
keywords Monte Carlo samplingkernel density estimationMCMC analysisBayesian inferencePython packagemarginalized posteriorsboundary correctionautomatic bandwidth selection
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The pith

GetDist provides automated kernel density estimation for weighted and correlated Monte Carlo samples with boundary corrections.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

GetDist is a Python package for analyzing samples from Monte Carlo methods such as MCMC in Bayesian inference. It computes one- and two-dimensional marginalized densities via kernel density estimation that accounts for sample weights, correlations, and hard boundaries. The core method applies a linear boundary kernel followed by multiplicative bias correction, with bandwidth chosen automatically from the effective number of samples using heuristics and optimization results. This setup enables production of publication-quality figures, convergence diagnostics, parameter limit tables, and LaTeX output through a simple interface plus an optional graphical user interface. A sympathetic reader would care because reliable density estimation from raw samples is essential for interpreting posterior distributions without manual parameter tuning in scientific applications.

Core claim

The paper's central claim is that GetDist's baseline method of applying a linear boundary kernel then multiplicative bias correction, paired with automatic bandwidth selection following Botev et al. based on effective sample size, yields accurate marginalized densities for typical distributions and boundary conditions in cosmological and physical parameter inference.

What carries the argument

Linear boundary kernel with multiplicative bias correction, followed by an automatically-determined elliptical Gaussian kernel for two-dimensional cases, selected via effective sample size scaling.

If this is right

  • Produces publication-quality plots of one- and two-dimensional marginalized densities using a named-parameter interface.
  • Calculates standard convergence diagnostics for Monte Carlo chains.
  • Generates tables of parameter limits and formatted LaTeX output directly from samples.
  • Supports interactive exploration through a built-in graphical user interface.
  • Handles both weighted and correlated samples without manual intervention.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The automatic handling could reduce systematic errors when visualizing posteriors near parameter boundaries in high-dimensional spaces.
  • Similar boundary-corrected KDE methods might be tested on importance-sampled or nested-sampling outputs in other statistical domains.
  • The effective-sample-size scaling for bandwidth choice offers a template for extending the package to streaming or online sample analysis.
  • Users outside astrophysics could apply the same interface to any set of weighted points for density estimation tasks.

Load-bearing premise

The automatic bandwidth selection and linear boundary kernel produce accurate densities for the typical distributions and boundary conditions encountered in cosmological and physical parameter inference without requiring user tuning.

What would settle it

Direct numerical comparison of GetDist output densities against known analytic posteriors or very high-resolution histograms on test sample sets that include known weights, correlations, and hard boundaries, checking whether the recovered probability mass matches the expected values to within a few percent.

read the original abstract

Monte Carlo techniques, including MCMC and other methods, are widely used in Bayesian inference to generate sets of samples from a parameter space of interest. The Python GetDist package provides tools for analysing these samples and calculating marginalized one- and two-dimensional densities using Kernel Density Estimation (KDE). Many Monte Carlo methods produce correlated and/or weighted samples, for example produced by MCMC, nested, or importance sampling, and there can be hard boundary priors. GetDist's baseline method consists of applying a linear boundary kernel, and then using multiplicative bias correction. The smoothing bandwidth is selected automatically following Botev et al., based on a mixture of heuristics and optimization results using the expected scaling with an effective number of samples (defined here to account for both MCMC correlations and weights). Two-dimensional KDE uses an automatically-determined elliptical Gaussian kernel for correlated distributions. The package includes tools for producing a variety of publication-quality figures using a simple named-parameter interface, as well as a graphical user interface that can be used for interactive exploration. It can also calculate convergence diagnostics, produce tables of limits, and output in LaTeX, and is publicly available.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript describes GetDist, a publicly available Python package for post-processing Monte Carlo samples (MCMC, nested sampling, importance sampling) from Bayesian inference. Its core functionality is kernel density estimation (KDE) of one- and two-dimensional marginalized posteriors, using a linear boundary kernel followed by multiplicative bias correction, automatic bandwidth selection following Botev et al. with effective-sample-size adjustments for correlations and weights, and an elliptical Gaussian kernel for 2D correlated distributions. The package also supplies publication-quality plotting, convergence diagnostics, limit tables, and LaTeX output.

Significance. If the implementation faithfully realizes the cited KDE methods, GetDist supplies a standardized, low-tuning tool that directly addresses recurring practical difficulties in cosmological and physical parameter estimation (correlated/weighted samples, hard priors). Public code availability supplies the natural verification route and supports reproducibility; the simple named-parameter interface and GUI lower the barrier to producing reliable figures and diagnostics.

major comments (2)
  1. [§3] §3 (KDE implementation): The description states that the 2D kernel is an automatically determined elliptical Gaussian for correlated distributions, but does not specify how the correlation matrix is estimated from the weighted samples or how the effective sample size enters the 2D bandwidth scaling; an explicit equation or pseudocode step would confirm consistency with the 1D case.
  2. [§2.2] §2.2 (boundary correction): The linear boundary kernel plus multiplicative bias correction is presented as the baseline; however, the text does not report quantitative tests (e.g., integrated squared error on truncated Gaussians or Beta distributions) that would demonstrate the correction remains accurate near the hard priors typical in cosmological posteriors.
minor comments (3)
  1. [Abstract, §1] The abstract and §1 refer to “effective number of samples” without a forward reference to the exact definition (Eq. (X) or section) used in the bandwidth formula.
  2. [Figures] Figure captions should state the precise sample size, chain length, and any thinning or weighting applied in the displayed examples.
  3. [References] The reference list should include the full bibliographic entry for Botev et al. (the bandwidth method) and any other external KDE implementations used for comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments on the GetDist manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (KDE implementation): The description states that the 2D kernel is an automatically determined elliptical Gaussian for correlated distributions, but does not specify how the correlation matrix is estimated from the weighted samples or how the effective sample size enters the 2D bandwidth scaling; an explicit equation or pseudocode step would confirm consistency with the 1D case.

    Authors: We agree that additional implementation details would improve clarity. The correlation matrix is obtained from the weighted sample covariance, and the effective sample size (adjusted for both weights and correlations) scales the 2D bandwidth via the same Botev et al. procedure used in 1D. In the revised manuscript we will insert an explicit equation for the 2D bandwidth together with a short pseudocode outline of the steps, confirming consistency with the 1D case. revision: yes

  2. Referee: [§2.2] §2.2 (boundary correction): The linear boundary kernel plus multiplicative bias correction is presented as the baseline; however, the text does not report quantitative tests (e.g., integrated squared error on truncated Gaussians or Beta distributions) that would demonstrate the correction remains accurate near the hard priors typical in cosmological posteriors.

    Authors: The manuscript presents the boundary-correction method as implemented, following the cited literature. Quantitative validation tests were not included in the original text. We will add a concise paragraph (or short appendix) reporting integrated squared error results on truncated Gaussian and Beta distributions to demonstrate performance near hard boundaries. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents GetDist as an implementation of established KDE techniques (linear boundary kernel with multiplicative bias correction, bandwidth selection following Botev et al., and explicit definition of effective sample size to adjust for MCMC correlations and weights). No load-bearing derivation reduces by construction to fitted inputs or self-citations; the central claims concern practical realization of published methods for typical posteriors, with verification supplied by the public code rather than internal equations that equate to their own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central functionality rests on standard KDE assumptions plus the definition of effective sample size to rescale bandwidth; no new entities or ad-hoc fitted constants are introduced beyond the automatic selection procedure.

axioms (2)
  • domain assumption Kernel density estimation with linear boundary kernel and multiplicative bias correction produces unbiased estimates near hard priors
    Invoked as the baseline method without derivation in the abstract
  • domain assumption Botev et al. bandwidth selection scales correctly with effective number of samples after accounting for MCMC correlations and weights
    Used for automatic smoothing choice

pith-pipeline@v0.9.0 · 5490 in / 1266 out tokens · 37399 ms · 2026-05-14T23:54:14.216260+00:00 · methodology

discussion (0)

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Works this paper leans on

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  1. [1]

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    work page

  2. [2]

    • If a prior boundary is well outside the initial sample range, it is ignored for the purpose of this range setting

    Incorporate Prior Boundaries: Specified hard prior boundaries (limmin, limmax, often from sampler metadata) are considered: • If a prior boundary is close to the initial sample range (from step 1), the correspondingrange_min or range_max is adjusted to this prior boundary, and a flag (has_limits_bot or has_limits_top) is set to indicate an active prior at...

    work page

  3. [3]

    This KDE accounts for boundary effects from any active priors and is normalized so its peak value is one

    1D Kernel Density Estimation (KDE):A 1D kernel density estimate (KDE) of the marginalized posterior for the param- eter is computed over the range_min to range_max established in steps 1 and 2. This KDE accounts for boundary effects from any active priors and is normalized so its peak value is one

    work page

  4. [4]

    Significant Density

    Define “Significant Density” Threshold: For each desired confidence level, calculate a threshold density ratio max_frac_twotail. By default this taken to be the ratio of the probability density at the tails of a Gaussian distribution (at the points defining the specified confidence level, e.g., approximately±1σ for 68%) to its peak density. This threshold...

    work page

  5. [5]

    Flags (marge_limits_bot, marge_limits_top) are set to indicate if the distribution appears significantly trun- cated by a boundary prior; e.g

    Assess Density at Range Edges: The KDE density is evaluated at range_min and range_max. Flags (marge_limits_bot, marge_limits_top) are set to indicate if the distribution appears significantly trun- cated by a boundary prior; e.g. marge_limits_bot is true if there is a hard prior at that end ( has_limits_bot is true) and the KDE density at that end is gre...

    work page

  6. [6]

    Handle Fully Prior-Dominated Cases: If both marge_limits_bot and marge_limits_top are true (i.e., the distribution has high density up against active hard priors at both ends, like a uniform posterior filling its prior range), no interval limits are reported for this confidence level, as the parameter is effectively constrained by these priors rather than...

    work page

  7. [7]

    For unimodal distributions, this ensures all points within the interval have higher probability density than any point outside it

    Compute credible interval from KDE: If step 6 does not apply, the algorithm computes a highest density interval containing the required fraction of the total probability using the following procedure: • The KDE grid points are sorted in descending order of density values • The cumulative sum of these sorted density values (each weighted by the grid spacin...

    work page

  8. [8]

    This limit is derived directly from the sorted weighted samples to ensure robustness

    Report One-Tailed Limits: If, after step 7, one of marge_limits_bot or marge_limits_top is true (indicating the posterior has significant density up against an active prior at one boundary) while the other is false (indicating the posterior falls off towards the other end of the range), a one-tailed limit is reported. This limit is derived directly from t...

    work page

  9. [9]

    Report Two-Tailed Limits: Otherwise, if both marge_limits_bot and marge_limits_top are false (meaning the posterior density is low at both ends of the established range relative to max_frac_twotail), a two-tailed interval is reported • Calculate an equal-tailed two-tail limit (tail_confid_bot, tail_confid_top) directly from the samples. • Calculate the KD...

    work page

  10. [10]

    The current im- plementation assumes stationarity in the sampling process, which may not hold for all sampling methods

    Kernel estimator optimization for non-stationary sampling distributions (e.g., nested sampling results). The current im- plementation assumes stationarity in the sampling process, which may not hold for all sampling methods

    work page

  11. [11]

    Integration of general prior boundary effects into kernel optimization. The current approach to kernel smoothing scale selection does not explicitly account for prior boundaries except for the case where priors are aligned with the parameter axes, potentially leading to suboptimal bandwidth choices in more general cases

    work page

  12. [12]

    While the current methods remain functional in these cases, the use of a global smooth- ing kernel may be far from optimal

    Handling of complex likelihood topologies, particularly for highly multimodal distributions with varying characteristic scales across different modes. While the current methods remain functional in these cases, the use of a global smooth- ing kernel may be far from optimal. Significant improvements could be achieved by implementing more sophisticated appr...

    work page

  13. [13]

    The current implementation optimizes kernel widths solely for density estimation

    Optimization of kernel widths for specific computational tasks. The current implementation optimizes kernel widths solely for density estimation. For other applications, such as calculating tail confidence limits, different optimization criteria may be more appropriate. GetDist can easily be used with any numpy array of samples, but also has built-in supp...

    work page 2007

  14. [14]

    Z. I. Botev, J. F. Grotowski, and D. P. Kroese, Kernel density estimation via diffusion, Ann. Statist.38, 2916 (2010), 1011.2602

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  15. [15]

    Metropolis, A

    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21, 1087 (1953)

    work page 1953

  16. [16]

    Hastings, Monte carlo samping methods using markov chains and their applications, Biometrika 57, 97 (1970)

    W. Hastings, Monte carlo samping methods using markov chains and their applications, Biometrika 57, 97 (1970)

    work page 1970

  17. [17]

    R. M. Neal, Probabilistic inference using Markov Chain Monte Carlo methods (1993), https://cosmologist.info/Neal93

    work page 1993

  18. [18]

    R. P. Adams, I. Murray, and D. J. C. MacKay, Nonparametric bayesian density modeling with gaussian processes (2009), arXiv:0912.4896 [stat.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  19. [19]

    R. P. Adams, I. Murray, and D. J. MacKay, The Gaussian process density sampler, inAdvances in Neural Information Processing Systems 21, edited by D. Koller, D. Schuurmans, Y . Bengio, and L. Bottou (2009) pp. 9–16

    work page 2009

  20. [20]

    Efficient Bayesian Inference for a Gaussian Process Density Model

    C. Donner and M. Opper, Efficient bayesian inference for a gaussian process density model (2018), arXiv:1805.11494 [stat.ML]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  21. [21]

    J. D. Hunter, Matplotlib: A 2D graphics environment, Computing in Science & Engineering 9, 90 (2007)

    work page 2007

  22. [22]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanim et al. (Planck), Planck 2018 results. VI. Cosmological parameters, A&A 641, A6 (2020), arXiv:1807.06209 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  23. [23]

    Skilling, Nested Sampling, in American Institute of Physics Conference Series , edited by R

    J. Skilling, Nested Sampling, in American Institute of Physics Conference Series , edited by R. Fischer, R. Preuss, and U. V . Toussaint (2004) pp. 395–405

    work page 2004

  24. [24]

    W. J. Handley, M. P. Hobson, and A. N. Lasenby, POLYCHORD: next-generation nested sampling, MNRAS 453, 4384 (2015), arXiv:1506.00171 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  25. [25]

    Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis

    F. Feroz and M. P. Hobson, Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis, Mon. Not. Roy. Astron. Soc. 384, 449 (2008), arXiv:0704.3704 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  26. [26]

    Cosmological parameters from CMB and other data: a Monte-Carlo approach

    A. Lewis and S. Bridle, Cosmological parameters from CMB and other data: A Monte Carlo approach, Phys. Rev. D 66, 103511 (2002), arXiv:astro-ph/0205436 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  27. [27]

    R. M. Neal, Taking bigger metropolis steps by dragging fast variables (2005), arXiv:math/0502099 [math.ST]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  28. [28]

    Efficient sampling of fast and slow cosmological parameters

    A. Lewis, Efficient sampling of fast and slow cosmological parameters, Phys. Rev. D87, 103529 (2013), arXiv:1304.4473 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    Wand and M

    M. Wand and M. Jones, Kernel Smoothing (Chapman and Hall, 1994) https://cosmologist.info/ISBN/0412552701

    work page arXiv 1994

  30. [30]

    S. J. Sheather, Density estimation, Statist. Sci. 19, 588 (2004). 17

    work page 2004

  31. [31]

    Hansen, Lecture notes on nonparametrics (2009), https://www.ssc.wisc.edu/ ∼bhansen/718/NonParametrics1.pdf

    B. Hansen, Lecture notes on nonparametrics (2009), https://www.ssc.wisc.edu/ ∼bhansen/718/NonParametrics1.pdf

    work page 2009

  32. [32]

    A. Z. Zambom and R. Dias, A Review of Kernel Density Estimation with Applications to Econometrics (2012), arXiv:1212.2812 [stat.ME]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  33. [33]

    Poluektov, Kernel density estimation of a multidimensional efficiency profile, Journal of Instrumentation 10 (02), P02011–P02011

    A. Poluektov, Kernel density estimation of a multidimensional efficiency profile, Journal of Instrumentation 10 (02), P02011–P02011

    work page

  34. [34]

    Jones, Simple boundary correction for kernel density estimation, Stat

    M. Jones, Simple boundary correction for kernel density estimation, Stat. & Comput. 3, 135 (1993), http://link.springer.com/content/pdf/ 10.1007/BF00147776.pdf

    work page doi:10.1007/bf00147776.pdf 1993

  35. [35]

    Jones and D

    M. Jones and D. F. Signorini, A comparison of higher-order bias kernel density estimators, J. Amer. Stat. Assoc. 92, 1063 (1997), http://www.jstor.org/stable/2965571

    work page arXiv 1997

  36. [36]

    Jones and P

    M. Jones and P. J. Foster, A simple nonnegative boundary correction method for kernel density estimation, Stat. Sinica 6, 1005 (1996), http://www3.stat.sinica.edu.tw/statistica/oldpdf/A6n414.pdf

    work page 1996

  37. [37]

    Jones, O

    M. Jones, O. Linton, and J. Nielsen, A simple bias reduction method for density estimation, Biometrika 82, 327 (1995), http://www.jstor. org/stable/2337411

    work page arXiv 1995

  38. [38]

    N. W. Hengartnera and E. Matzner-Lober, Asymptotic unbiased density estimators, ESAIM: Prob. & Stat.13, 1 (2009), http://dx.doi.org/ 10.1051/ps:2007055

    work page doi:10.1051/ps:2007055 2009

  39. [39]

    Choi and P

    E. Choi and P. Hall, Miscellanea. data sharpening as a prelude to density estimation, Biometrika 86, 941 (1999)

    work page 1999

  40. [40]

    Hall and M

    P. Hall and M. C. Minnotte, High order data sharpening for density estimation, J. Roy. Stat. Soc. Series B (Stat. Meth.) 64, 141 (2002)

    work page 2002

  41. [41]

    P. Hall, S. N. Lahiri, and Y . K. Truong, . on bandwidth choice for density estimation with dependent data, Ann. Statist. 23, 2241 (1995), http://projecteuclid.org/euclid.aos/1034713655

    work page arXiv 1995

  42. [42]

    Sk ¨old and G

    M. Sk ¨old and G. Roberts, Density estimation for the Metropolis-Hastings algorithm., Scand. J. Stat.30, 699 (2003), http://www.jstor.org/ stable/4616797

    work page arXiv 2003

  43. [43]

    Janssen, J

    P. Janssen, J. S. Marron, N. Veraverbeke, and W. Sarle, Scale measures for bandwidth selection, J. Nonparam. Stat. 5, 359 (1995), http://dx.doi.org/10.1080/10485259508832654

    work page doi:10.1080/10485259508832654 1995

  44. [44]

    Jones, J

    M. Jones, J. Marron, and S. J. Sheather, A brief survey of bandwidth selection for density estimation, J. Amer. Stat. Assoc.91, 401 (1996), http://www.stat.washington.edu/courses/stat527/s14/readings/Jones etal JASA 1996.pdf

    work page 1996

  45. [45]

    O. M. Eidous, M. A. A. S. Marie, and M. H. Ebrahem, A comparative study for bandwidth selection in kernel density estimation, J. Mod. Appl. Stat. Meth. 9, 26 (2010), https://digitalcommons.wayne.edu/jmasm/vol9/iss1/26/

    work page 2010

  46. [46]

    Heidenreich, A

    N.-B. Heidenreich, A. Schindler, and S. Sperlich, Bandwidth selection for kernel density estimation: a review of fully automatic selectors, AStA 97, 403 (2013), http://doi.org/10.1007/s10182-013-0216-y

    work page doi:10.1007/s10182-013-0216-y 2013

  47. [47]

    M. D. Marzio and C. C. Taylor, Using small bias nonparametric density estimators for confidence interval estimation, J. Nonparam. Stat. 21, 229 (2009), http://eprints.whiterose.ac.uk/42950/

    work page 2009

  48. [48]

    M. P. Wand and M. C. Jones, Comparison of smoothing parameterizations in bivariate kernel density estimation, J. Amer. Stat. Assoc. 88, 520 (1993), http://www.jstor.org/stable/2290332

    work page arXiv 1993

  49. [49]

    Wand and M

    M. Wand and M. Jones, Multivariate plug-in bandwidth selection, Comput. Stat. 9, 97 (1994)

    work page 1994

  50. [50]

    Duong and M

    T. Duong and M. Hazelton, Plug-in bandwidth matrices for bivariate kernel density estimation, J. Nonparam. Stat. 15, 17 (2003)

    work page 2003

  51. [51]

    Planck 2013 results. XVI. Cosmological parameters

    P. Ade et al. (Planck Collaboration), Planck 2013 results. XVI. Cosmological parameters, A&A 10.1051/0004-6361/201321591 (2014), arXiv:1303.5076 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201321591 2013

  52. [52]

    M ´esz´aros, J

    A. M ´esz´aros, J. F. Schumann, J. Alonso-Mora, A. Zgonnikov, and J. Kober, Robust multi-modal density estimation (2024), arXiv:2401.10566 [cs.LG]

    work page arXiv 2024

  53. [53]

    Cobaya: Code for Bayesian Analysis of hierarchical physical models

    J. Torrado and A. Lewis, Cobaya: Code for Bayesian Analysis of hierarchical physical models, JCAP 05, 057 (2021), arXiv:2005.05290 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  54. [54]

    Kumar, C

    R. Kumar, C. Carroll, A. Hartikainen, and O. Martin, Arviz a unified library for exploratory analysis of bayesian models in python, Journal of Open Source Software 4, 1143 (2019)

    work page 2019