Lecture 2

Lecture 2 - Sampling distributions and Monte Carlo...

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1 Sampling distributions and Monte Carlo experiments Generate artificial data samples from known probability distribution Each experiment (‘replication’) is a sample of N primitive experiments We can establish sampling distribution of statistics experimentally – this is useful if the sampling distribution cannot be derived theoretically Hence it is particularly useful for non-normal parent distributions or statistics which are non-linear functions of data The technique can be used for other statistics - eg rejection probabilities Estimating the mean Theoretical value Experimental value Sample size 100 Mean 0 .0000586 Standard deviation 0.1 .0997881 Sample size 1000 Mean 0 .0004816 Standard deviation 0.03162 .0320018 Sampling distribution of the Mean: 100 observations 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 Experiment Theory
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2 Sampling distribution of the Mean: 1000 observations 0 0.05 0.1 0.15 0.2 0.25 0.3 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 Experiment Theory Central Limit Theorem - 25 observations Fra ctio n mean25 -.642268 .764554 0 .0586 Central Limit Theorem - 1000 observations Fraction mean1k -.13113 .113951 0 .0606
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3 The Wage data Data on 3296 working age individuals in US Data covers hourly wage sex years of schooling years of work experience We are interested in mean wage
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Lecture 2 - Sampling distributions and Monte Carlo...

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