emcee v3: A Python ensemble sampling toolkit for affine-invariant MCMC

Foreman-Mackey, Daniel; Farr, W. M.; Sinha, Manodeep; Archibald, Anne M.; Hogg, David W.; Sanders, J. S.; Zuntz, Joe; Williams, Peter K. G.; Nelson, Andrew; Val-Borro, Miguel de; Erhardt, Tobias; Pashchenko, I. N.; Abril, Oriol

doi:10.21105/joss.01864

Cited by 231 publications

(95 citation statements)

References 6 publications

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“…As recommended by Hogg & Foreman-Mackey (2018), we use the integrated autocorrelation time to test for convergence of our MCMC chains. We calculate the autocorrelation times using EMCEE's built in functionality (Foreman-Mackey et al 2019). The chains mix quickly in terms of M 200 , but the main quantity of interest, σ /m, typically has a longer autocorrelation time because of the more complex shape of the posterior as a function of σ /m (in particular, the σ /m-c degeneracy).…”

Section: A P P E N D I X C : M C M C S a M P L I N Gmentioning

confidence: 99%

The surprising accuracy of isothermal Jeans modelling of self-interacting dark matter density profiles

Robertson

Massey

Eke

et al. 2020

Monthly Notices of the Royal Astronomical Society

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Recent claims of observational evidence for self-interacting dark matter (SIDM) have relied on a semi-analytic method for predicting the density profiles of galaxies and galaxy clusters containing SIDM. We present a thorough description of this method, known as isothermal Jeans modelling, and then test it with a large ensemble of haloes taken from cosmological simulations. Our simulations were run with cold and collisionless dark matter (CDM) as well as two different SIDM models, all with dark matter only variants as well as versions including baryons and relevant galaxy formation physics. Using a mix of different box sizes and resolutions, we study haloes with masses ranging from 3 × 1010 to $3 \times 10^{15} \mathrm{\, M_\odot }$. Overall, we find that the isothermal Jeans model provides as accurate a description of simulated SIDM density profiles as the Navarro–Frenk–White profile does of CDM haloes. We can use the model predictions, compared with the simulated density profiles, to determine the input DM–DM scattering cross-sections used to run the simulations. This works especially well for large cross-sections, while with CDM our results tend to favour non-zero (albeit fairly small) cross-sections, driven by a bias against small cross-sections inherent to our adopted method of sampling the model parameter space. The model works across the whole halo mass range we study, although including baryons leads to DM profiles of intermediate-mass ($10^{12} - 10^{13} \mathrm{\, M_\odot }$) haloes that do not depend strongly on the SIDM cross-section. The tightest constraints will therefore come from lower and higher mass haloes: dwarf galaxies and galaxy clusters.

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Section: A P P E N D I X C : M C M C S a M P L I N Gmentioning

confidence: 99%

The surprising accuracy of isothermal Jeans modelling of self-interacting dark matter density profiles

Robertson

Massey

Eke

et al. 2020

Monthly Notices of the Royal Astronomical Society

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“…Finally, we implement MCMC sampling using the Python package emcee [33]. To improve sampling efficiency, we use ensemble move proposals based on the differential evolution [34], differential evolution snooker [35], and kernel density [36] proposal updates.…”

Section: Parameter Inferencementioning

confidence: 99%

“…The source code for pydemic is freely available online at https://github.com/uiuc-covid19-modeling/pydemic. This work made use of NumPy [66], SciPy [67], pandas [68], emcee [33], corner.py [69], and Matplotlib [70].…”

Section: Code Availabilitymentioning

confidence: 99%

Modeling COVID-19 dynamics in Illinois under non-pharmaceutical interventions

Wong

Weiner

Tkachenko

et al. 2020

Preprint

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We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its sub-regions in order to account for the wide disparities in population size and density. Without prior information on non-pharmaceutical interventions (NPIs), the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing Stay-at-Home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.

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“…The source code for pydemic is freely available online at https://github.com/uiuc-covid19-modeling/pydemic. This work made use of NumPy [18], SciPy [19], pandas [20], emcee [21], corner.py [22], and Matplotlib [23].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Projections and early-warning signals of a second wave of the COVID-19 epidemic in Illinois

Weiner

Wong

Elbanna

et al. 2020

Preprint

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We present two different scenarios for a second wave of the COVID-19 epidemic in Illinois and simulate them using our previously described age-of-infection model, calibrated to real-time hospital and deaths data. In the first scenario we assume that the parameters of the second wave in Illinois would be similar to those currently observed in other states such as Arizona, Florida, and Texas. We estimate doubling times of hospitalizations and test positivity in all states with relevant publicly available data and calculate the corresponding effective reproduction numbers for Illinois. These parameters are remarkably consistent in states with rapidly growing epidemics. We conjecture that the emergence of the second wave of the epidemic in these states can be attributed to superspreading events at large parties, crowded bars, and indoor dining. In our second, more optimistic scenario we assume changes in Illinois state policy would result in successful mitigation of superspreading events and thus would lower the effective reproduction number to the value observed in late June 2020. In this case our calculations show effective suppression of the second wave in Illinois. Our analysis also suggests that the logarithmic time derivatives of COVID-19 hospitalizations and case positivity can serve as a simple but strong early-warning signal of the onset of a second wave.

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emcee v3: A Python ensemble sampling toolkit for affine-invariant MCMC

Cited by 231 publications

References 6 publications

The surprising accuracy of isothermal Jeans modelling of self-interacting dark matter density profiles

The surprising accuracy of isothermal Jeans modelling of self-interacting dark matter density profiles

Modeling COVID-19 dynamics in Illinois under non-pharmaceutical interventions

Projections and early-warning signals of a second wave of the COVID-19 epidemic in Illinois

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