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A compression algorithm for the combination of PDF sets.

Carrazza S, Latorre JI, Rojo J, Watt G - Eur Phys J C Part Fields (2015)

Bottom Line: We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets.The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions.We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy.

ABSTRACT

The current PDF4LHC recommendation to estimate uncertainties due to parton distribution functions (PDFs) in theoretical predictions for LHC processes involves the combination of separate predictions computed using PDF sets from different groups, each of which comprises a relatively large number of either Hessian eigenvectors or Monte Carlo (MC) replicas. While many fixed-order and parton shower programs allow the evaluation of PDF uncertainties for a single PDF set at no additional CPU cost, this feature is not universal, and, moreover, the a posteriori combination of the predictions using at least three different PDF sets is still required. In this work, we present a strategy for the statistical combination of individual PDF sets, based on the MC representation of Hessian sets, followed by a compression algorithm for the reduction of the number of MC replicas. We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets. The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions. We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

No MeSH data available.


The value of the total error function, Eq. (5), for the compression of the 1000 replica set of NNPDF3.0 NLO, as a function of the number of GA generations, for different values of the number of replicas in the compressed set . After 15k iterations, the error function saturates and no further improvement of the error function would be achieved for longer training
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Fig6: The value of the total error function, Eq. (5), for the compression of the 1000 replica set of NNPDF3.0 NLO, as a function of the number of GA generations, for different values of the number of replicas in the compressed set . After 15k iterations, the error function saturates and no further improvement of the error function would be achieved for longer training

Mentions: In Fig. 6 we show the dependence of the total ERF as a function of the number of iterations of the GA for , and 90. We observe that the first 1k iterations are extremely important during the minimization, while after 15k iterations the total error function is essentially flat for any required number of compressed replicas. For each compression, the final value of the error function is different, with deeper minima being achieved as we increase the number of compressed replicas, as expected. The flatness of the ERF as a function of the number of iterations confirms that the current parameters provide a suitably efficient minimization strategy.Fig. 7


A compression algorithm for the combination of PDF sets.

Carrazza S, Latorre JI, Rojo J, Watt G - Eur Phys J C Part Fields (2015)

The value of the total error function, Eq. (5), for the compression of the 1000 replica set of NNPDF3.0 NLO, as a function of the number of GA generations, for different values of the number of replicas in the compressed set . After 15k iterations, the error function saturates and no further improvement of the error function would be achieved for longer training
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4594162&req=5

Fig6: The value of the total error function, Eq. (5), for the compression of the 1000 replica set of NNPDF3.0 NLO, as a function of the number of GA generations, for different values of the number of replicas in the compressed set . After 15k iterations, the error function saturates and no further improvement of the error function would be achieved for longer training
Mentions: In Fig. 6 we show the dependence of the total ERF as a function of the number of iterations of the GA for , and 90. We observe that the first 1k iterations are extremely important during the minimization, while after 15k iterations the total error function is essentially flat for any required number of compressed replicas. For each compression, the final value of the error function is different, with deeper minima being achieved as we increase the number of compressed replicas, as expected. The flatness of the ERF as a function of the number of iterations confirms that the current parameters provide a suitably efficient minimization strategy.Fig. 7

Bottom Line: We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets.The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions.We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133 Milan, Italy.

ABSTRACT

The current PDF4LHC recommendation to estimate uncertainties due to parton distribution functions (PDFs) in theoretical predictions for LHC processes involves the combination of separate predictions computed using PDF sets from different groups, each of which comprises a relatively large number of either Hessian eigenvectors or Monte Carlo (MC) replicas. While many fixed-order and parton shower programs allow the evaluation of PDF uncertainties for a single PDF set at no additional CPU cost, this feature is not universal, and, moreover, the a posteriori combination of the predictions using at least three different PDF sets is still required. In this work, we present a strategy for the statistical combination of individual PDF sets, based on the MC representation of Hessian sets, followed by a compression algorithm for the reduction of the number of MC replicas. We illustrate our strategy with the combination and compression of the recent NNPDF3.0, CT14 and MMHT14 NNLO PDF sets. The resulting compressed Monte Carlo PDF sets are validated at the level of parton luminosities and LHC inclusive cross sections and differential distributions. We determine that around 100 replicas provide an adequate representation of the probability distribution for the original combined PDF set, suitable for general applications to LHC phenomenology.

No MeSH data available.