The DM distribution of unlocalized FRBs yields H0 = 73.8 +14.0/-12.3 km/s/Mpc with 18% uncertainty.
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emcee: The MCMC Hammer
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abstract
We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to $\sim N^2$ for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.
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- abstract We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to $\sim
- method The resultingP 1D mocks are assigned the same covariance matrix as the one em- ployed in the DESI DR1 analysis. These mocks do not include contaminants or systematics; however, we analyze them with the model presented in the previous section, which accounts for both. We extract cosmological constraints using the publicly available affine-invariant Markov chain Monte Carlo (MCMC) ensemble sampleremcee 7 [118]. At each step,emceeproposes 7https://emcee.readthedocs.io/en/stable/ - 23 - 0.9 1.0 1.1
- method For the BAO sector, we utilize the dataset of [89], which incorporates fiducial cosmology corrections through the ratior d/rfid, allowing for a consistent com- parison between theoretical predictions and observations. The exploration of the parameter space is carried out using the Markov Chain Monte Carlo (MCMC) method, implemented through the publicly available Python pack- ageemcee[90]. In this context, the SNIa nuisance pa- rameterMis treated as a free parameter of the Pan- theon dataset (see
- method RPG-2019-350, and Royal Society Grant No. RGS-R2-202004. LIGO was con- structed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates un- der cooperative agreement PHY-0757058. We acknowledge use of iPython [86], Matplotlib [87, 88], NumPy [89], SciPy [90], emcee [91] and SeaBorn [92]. This is LIGO Document P2000231 Glossary and main symbols α(⃗λ ) The fraction of physical sources that are detectable by
- method PLANCK + PP, and (ii) CC + DESBAO + PLANCK + DES, as −2 lnLtot = 𝜒2 tot. (6.8) We estimate the likelihood by implementing the model in Python and use the publicly available affine-invariant Markov Chain Monte Carlo (MCMC) ensemble sampler emcee [145] to obtain the posterior distributions of the model parameters. The resulting samples are then analyzed usingGetDist [146] to obtain marginalized 1D and 2D posterior distributions. Finally, we compare the statistical preference of the current model r
- method consistent solutions across cosmic epochs, and adopt uniform priors as listed in Tab. II. For sampling and likelihood eval- uation, we employ the nested samplerPolyChord, which is well suited for high-dimensional parameter spaces compared to affine-invariant MCMC samplers such asemcee[99-101]. The chains are analyzed usingGetDistto extract the best-fit values [102, 103]. Finally, we compare our models against flat ΛCDM using information criteria such as the Akaike Informa- tion Criterion (AIC) a
- method package that provides a common framework for writing DESI likelihoods. The BAO the- ory and likelihood is implemented in JAX [126] 20. Even though gradient-based sampling methods were implemented, we found that with analytic marginalization over broadband parameters that leaves a few sampled parameters, and using Jax just-in-time compilation and parallelization capabilities, the ensemble sampler emcee [127]21 provided well-sampled posterior estimates in a just a few minutes. In addition to MCMC
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New Way to Date Globular Clusters: Brown Dwarf Cooling Sequences
A new histogram-free likelihood method applied to simulated JWST observations of brown dwarfs shows that globular cluster ages can be determined with formal errors under 0.2 Gyr.
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Cosmologically viable non-polynomial quasi-topological gravity: explicit models, $\Lambda$CDM limit and observational constraints
Non-polynomial quasi-topological gravity models reproduce the standard thermal history, generate dynamical dark energy of geometric origin, and fit supernova, cosmic chronometer, and BAO data competitively with ΛCDM.
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Cosmological analysis of the DESI DR1 Lyman alpha 1D power spectrum
DESI DR1 Lyman-alpha data yields Δ²★=0.379±0.032 and n★=-2.309±0.019 at k★=0.009 km⁻¹s and z=3, sharpening N_eff, α_s, and β_s constraints by factors of 1.18-1.90 when combined with other probes.
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DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars
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Confronting Color Glass Condensate at next-to-leading order with HERA data
A Bayesian global fit at full NLO+NLL accuracy extracts the posterior distribution for the non-perturbative initial condition of the NLO Balitsky-Kovchegov equation from HERA inclusive and charm data.
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$\boldsymbol{B_c}$ Meson Spectroscopy from Bayesian MCMC: Probing Confinement and State Mixing
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Model-independent test of the cosmic distance duality relation with recent observational data
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Interacting $k$-essence field with non-pressureless Dark Matter: Cosmological Dynamics and Observational Constraints
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