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Importance Sampling - Astrostatistics

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ReferencesImportance SamplingJessi CisewskiCarnegie Mellon UniversityJune 2014JessiCisewski (CMU) Importance SamplingReferencesOutline1Recall:Monte Carlo integration2Importance Sampling3Examplesof Importance Sampling (a)MonteCarlo, Monaco(b)MonteCarlo Casino?Some content and examples from Wasserman (2004)JessiCisewski (CMU) Importance SamplingReferencesSimpleillustration: what is ?Area Area = r2(2r)(2r)= 4JessiCisewski (CMU) Importance SamplingReferencesMonteCarlo Integration: motivationI= bah(y)dyGoal:evaluate this integralSometimeswe can findI( ifh( ) is a function from Calc I)Butsometimes we can t and need a way to approximateI. MonteCarlo methods are one (of many) approaches to do (CMU) Importance SamplingReferencesTheLaw of Large NumbersWhilenothing is more uncertain than theduration of a single life, nothing is more certainthan the average duration of a thousand lives.

Idea of importance sampling: draw the sample from a proposal distribution and re-weight the integral using importance weights so that the correct distribution is targeted

  Importance, Sampling, Importance sampling

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