PopulationandSamples

PopulationandSamples - Likelihood v Bayesian Point...

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9/19/11 11 School of Chemical Samples Population
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9/19/11 22 School of Chemical Examples Population - Clearly defined ‘aggregate’ of creatures, objects, etc. . People living in IN Oranges produced in Argentina Daily production rate of ethylene over the past one year
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9/19/11 33 School of Chemical Examples (II) Sample - Collection of objects from the population - Randomly chosen
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9/19/11 44 School of Chemical Illustration Population: 320 Students, Spring 2011 Interested in: mean height Sample: randomly chosen 10 5'4"+5'9"+6'2"+6'1"+5'11"+5'9"+5'7"+5'6"+6'6"+5'8" 10 = 5'10" Sample mean height x Population mean height μ Estimati on , weigh t , weight , weight variance variance variance x i - x ( ) 2 i =1 10 å 10 - 1 s 2 σ 2 max x i ( ) maximum maximum maximum
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9/19/11 55 School of Chemical Point Estimation Estimation ( a.k.a Parameter Estimation) Estimators: v v Variance & Mean Squared Error v Comparison of different estimators Methods of Estimation: v Moments v Maximum
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Unformatted text preview: Likelihood v Bayesian Point Estimates e . g ., x = 5.2 5. 2 5. 4 5. 6 5. 5.1 x 5.3 How to come up with an interval like this? How to quantify Surety of the result? 9/19/11 How to come up with an interval like this? How to quantify Surety of the result? 66 School of Chemical Confidence Intervals Probabilit y Confidence Interval P a X b ( ) P X 1 c X 2 ( ) Baske t Bal l Rin g Pole 9/19/11 77 School of Chemical Central Limit Theorem S 1 : X 11 + X 12 +...+ X 1 n n = X 1 S 2 : X 21 + X 22 +...+ X 2 n n = X 2 S 50 : X 501 + X 502 +...+ X 50 n n = X 50 freque ncy X 2 4 6 8 1 5 1 1 5 2 CLT: states follows a normal distribution X N m , s / n ( ) Transformed variable follows standard normal distribution Z = X -m s / n N 0,1 ( )...
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PopulationandSamples - Likelihood v Bayesian Point...

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