Monte Carlo Tools Frank Krauss Institute for Particle Physics - PowerPoint PPT Presentation

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University GGI, 24.&26.9.2007 F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Topics of the lectures Lecture 1: Tour through Event Generators 1 Hard physics simulation: Parton Level event generation Dressing the partons: Parton Showers Soft physics simulation: Hadronization Beyond factorization: Underlying Event Lecture 2: Higher Orders in Monte Carlos 2 Some nomenclature: Anatomy of HO calculations Merging vs. Matching Thanks to the other Sherpas: T.Gleisberg, S.H¨ oche, S.Schumann, F.Siegert, M.Sch¨ onherr, J.Winter; other MC authors: S.Gieseke, K.Hamilton, L.Lonnblad, F.Maltoni, M.Mangano, P.Richardson, M.Seymour, T.Sjostrand, B.Webber, . . . . F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Simulation’s paradigm Basic strategy Sketch of an event Divide event into stages, separated by different scales. �� Signal/background: �� Exact matrix elements. �� QCD-Bremsstrahlung: �� Parton showers (also in initial state). �� Multiple interactions: �� Beyond factorization: Modeling. �� Hadronization: �� Non-perturbative QCD: Modeling. F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Today’s lecture: Event Generation in a Nutshell Monte Carlo integration Parton level event generation Parton showers Multiple interactions Hadronization F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo integration Convergence of numerical integration 1 � d x D f ( � Consider I = x ). 0 Convergence behavior crucial for numerical evaluations. For integration ( N = number of evaluations of f ): Trapezium rule ≃ 1 / N 2 / D Simpson’s rule ≃ 1 / N 4 / D √ Central limit theorem ≃ 1 / N . Therefore: Use central limit theorem. F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo integration Monte Carlo integration Use random vectors � x i − → : Evaluate estimate of the integral � I � rather than I . N � I ( f ) � = 1 � f ( � x i ). N i =1 (This is the original meaning of Monte Carlo: Use random numbers for integration.) Quality of estimate given by error estimator (variance) � E ( f ) � 2 = 1 N − 1 [ � I 2 ( f ) � − � I ( f ) � 2 ]. Name of the game: Minimize � E ( f ) � . Problem: Large fluctuations in integrand f Solution: Smart sampling methods F. Krauss IPPP Monte Carlo Tools

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo integration Importance sampling Basic idea: Put more samples in regions, where f largest = ⇒ improves convergence behavior (corresponds to a Jacobian transformation). Assume a function g ( � x ) similar to f ( � x ); obviously then, f ( � x ) / g ( � x ) is comparably smooth, hence � E ( f / g ) � is small. F. Krauss IPPP Monte Carlo Tools

Monte Carlo Tools Frank Krauss Institute for Particle Physics - PowerPoint PPT Presentation

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University GGI, 24.&26.9.2007 F. Krauss IPPP Monte

Monte Carlo Approximation of Monte Carlo Filters Adam M. Johansen et al. Collaborators Include:

Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University

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Monte Carlo Tools Frank Krauss Institute for Particle Physics - PowerPoint PPT Presentation

Orientation MC integration Matrix elements Parton showers Hadronization Underlying Event Upshot Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University GGI, 24.&26.9.2007 F. Krauss IPPP Monte

Monte Carlo Approximation of Monte Carlo Filters Adam M. Johansen et al. Collaborators Include:

Monte Carlo Tools Frank Krauss Institute for Particle Physics Phenomenology Durham University

Monte Carlo Methods An introduction to Monte Carlo (MC) methods How to use MC methods

Monte Carlo Estimation 7 January 2019 OSU CSE 1 Monte Carlo Methods Class of computational

QUASI-EQUILIBRIUM MONTE-CARLO: OFF-LATTICE KINETIC MONTE CARLO SIMULATION OF HETEROEPITAXY

Draft 1 Density estimation by Monte Carlo and randomized quasi-Monte Carlo (RQMC) Pierre

Chapter 5: Monte Carlo Methods Monte Carlo methods are learning methods Experience

Monte Carlo Methods Guojin Chen Christopher Cprek Chris Rambicure Monte Carlo Methods 1.

4. THE MONTE CARLO METHOD 4.1 I ntroduction This chapter is aimed at describing the Monte Carlo

Monte Carlo Integration Monte Carlo methods use random numbers for sampling Although

Monte Carlo Methods Why Monte Carlo? Computation of number ( 1) n +1 = 1 1 2 + 1

Monte Carlo Control CMPUT 366: Intelligent Systems S&amp;B 5.3-5.5, 5.7 Lecture Outline 1.

Monte Carlo Generators Monte Carlo Generators Monte Carlo Generators QCD Lecture III P .

Linear Regression: Prior Linear Regression: Posterior 4 4 2 2 0 0 2 2 Prior P ( )

Draft 1 Density estimation by Monte Carlo and randomized quasi-Monte Carlo Pierre LEcuyer

Monte Carlo Simulation technique S. B. Santra Department of Physics Indian Institute of

Semiparametric models with functional responses in a model assisted survey sampling setting e

t s s

Data Mining II Data Preprocessing Heiko Paulheim Introduction Give me six hours to

An Evaluation of Effect of Packet Sampling on Anomaly Detection Method Takuya Motodate

Convergence Analysis for Anisotropic Monte Carlo Sampling Spectra Gurprit Singh

The Effect of Colouring on Student Stress Levels TRO Conference, 2017 April Powell, Kaitlin

Why programmers? Applied Rationality for Programmers a 1-day event in

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Monte Carlo Control CMPUT 366: Intelligent Systems S&B 5.3-5.5, 5.7 Lecture Outline 1.

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