BOOTSTRAPPING EXAMPLES IN MAPLE

Here we calculate the 95% confidence limit on the median using the bootstrap method. First, we load the required Statistics package: QyQtSSV3aXRoRzYiNiNJK1N0YXRpc3RpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI= This is our dataset: (you can also use Import() or ImportData() to load data from a file) PkklZGF0YUc2IjcsIiInIiIkIiImIiIjRiciIigiIiVGKkYrIiM1

NywiIiciIiQiIiYiIiNGJCIiKCIiJUYnRigiIzU=

This is the median: PkkkbWVkRzYiLUknTWVkaWFuR0YkNiNJJWRhdGFHRiQ=

JCIrKysrK1ghIio=

First we define the number of desired bootstrap resamplings: QyQ+SSJCRzYiIicrKzUhIiI= And this is the standard error on the median, calculated using the Bootstrap method (we use 10000 bootstrap replicates): Pkkoc3RlcnJvckc2Ii1JKkJvb3RzdHJhcEdGJDYmLkknTWVkaWFuR0YkSSVkYXRhR0YkL0ktcmVwbGljYXRpb25zR0YkSSJCR0YkL0knb3V0cHV0R0YkLkkuc3RhbmRhcmRlcnJvckdGJA==

JCIrISo0I2UuIiEiKg==

If we use the output='array' option the output will be an array containing the medians calculated on each bootstrap sample: QyQ+SSlib290c3RhdEc2Ii1JKkJvb3RzdHJhcEdGJTYmLkknTWVkaWFuR0YlSSVkYXRhR0YlL0ktcmVwbGljYXRpb25zR0YlSSJCR0YlL0knb3V0cHV0R0YlLkkmYXJyYXlHJSpwcm90ZWN0ZWRHISIi This is the 95% confidence limit on the median calculated using the Bootstrap percentile method: PkkpY29uZmxpbXNHNiI3JC1JKVF1YW50aWxlR0YkNiRJKWJvb3RzdGF0R0YkJCIjRCEiJC1GJzYkRikkIiR2KkYs

NyQkIiIkIiIhJCIiKEYl

Here is a histogram of the distribution of the medians calculated on the bootstrapped samples: LUkqSGlzdG9ncmFtRzYiNiVJKWJvb3RzdGF0R0YkL0kpYmlud2lkdGhHRiQkIiImISIiL0kvZnJlcXVlbmN5c2NhbGVHRiRJKWFic29sdXRlR0Yk

LSUlUExPVEc2JC0lKVBPTFlHT05TRzYzNyY3JCQiIz8hIiIkIiIhISIiNyQkIiNEISIiJCIiISEiIjckJCIjRCEiIiQiJHEiISIiNyQkIiM/ISIiJCIkcSIhIiI3JjckJCIjRCEiIiQiIiEhIiI3JCQiI0khIiIkIiIhISIiNyQkIiNJISIiJCIlIUgiISIiNyQkIiNEISIiJCIlIUgiISIiNyY3JCQiI0khIiIkIiIhISIiNyQkIiNOISIiJCIiISEiIjckJCIjTiEiIiQiJj9vJSEiIjckJCIjSSEiIiQiJj9vJSEiIjcmNyQkIiNOISIiJCIiISEiIjckJCIjUyEiIiQiIiEhIiI3JCQiI1MhIiIkIiY/VikhIiI3JCQiI04hIiIkIiY/VikhIiI3JjckJCIjUyEiIiQiIiEhIiI3JCQiI1ghIiIkIiIhISIiNyQkIiNYISIiJCInU3dEISIiNyQkIiNTISIiJCInU3dEISIiNyY3JCQiI1ghIiIkIiIhISIiNyQkIiNdISIiJCIiISEiIjckJCIjXSEiIiQiJz9vOiEiIjckJCIjWCEiIiQiJz9vOiEiIjcmNyQkIiNdISIiJCIiISEiIjckJCIjYiEiIiQiIiEhIiI3JCQiI2IhIiIkIichUVsiISIiNyQkIiNdISIiJCInIVFbIiEiIjcmNyQkIiNiISIiJCIiISEiIjckJCIjZyEiIiQiIiEhIiI3JCQiI2chIiIkIidJKTMiISIiNyQkIiNiISIiJCInSSkzIiEiIjcmNyQkIiNnISIiJCIiISEiIjckJCIjbCEiIiQiIiEhIiI3JCQiI2whIiIkIiY/QCohIiI3JCQiI2chIiIkIiY/QCohIiI3JjckJCIjbCEiIiQiIiEhIiI3JCQiI3EhIiIkIiIhISIiNyQkIiNxISIiJCImcWcmISIiNyQkIiNsISIiJCImcWcmISIiNyY3JCQiI3EhIiIkIiIhISIiNyQkIiN2ISIiJCIiISEiIjckJCIjdiEiIiQiJiEpZSUhIiI3JCQiI3EhIiIkIiYhKWUlISIiNyY3JCQiI3YhIiIkIiIhISIiNyQkIiMhKSEiIiQiIiEhIiI3JCQiIyEpISIiJCIkKyMhIiI3JCQiI3YhIiIkIiQrIyEiIjcmNyQkIiMhKSEiIiQiIiEhIiI3JCQiIyYpISIiJCIiISEiIjckJCIjJikhIiIkIiRdIyEiIjckJCIjISkhIiIkIiRdIyEiIjcmNyQkIiMmKSEiIiQiIiEhIiI3JCQiIyEqISIiJCIiISEiIjckJCIjISohIiIkIiVJNSEiIjckJCIjJikhIiIkIiVJNSEiIjcmNyQkIiMhKiEiIiQiIiEhIiI3JCQiIyYqISIiJCIiISEiIjckJCIjJiohIiIkIiIhISIiNyQkIiMhKiEiIiQiIiEhIiI3JjckJCIjJiohIiIkIiIhISIiNyQkIiQrIiEiIiQiIiEhIiI3JCQiJCsiISIiJCIkIT0hIiI3JCQiIyYqISIiJCIkIT0hIiItJSZDT0xPUkc2JiUkSFNWRyQiMXRCPW8xJ1taJiEjOyQiIzUhIiIkIjFyQ3k/ITMnPnEhIzstJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiRTJSEiIi0lKUJPVU5EU19ZRzYjJCIjISkhIiItJS1CT1VORFNfV0lEVEhHNiMkIiVJVCEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUhRyMhIiItJSlDSElMRFJFTkc2Ig==

Helanter\303\244 et al. (2006) estimated the proportion of eggs laid by workers vs. by the queen in colonies of the common wasp as A = nW * p * eW / (nW * p * eW + eQ) where nW are the mean number of workers in a colony, p are the mean proportion of workers that lay eggs in a colony and eW and eQ are the mean number of eggs laid per day by a single reproductive worker and by the queen, respectively. Here we will calculate the 95% confidence limits on this estimate using the parametric bootstrap method. This requires us to specify the mean and the distribution of each of the parameters. By dissecting 1150 workers in a colony p was estimated to be 12/1150; this parameter can be assumed to be binomially distributed eW was estimated from the total number of eggs laid by workers over 5 days (eT=281) in a queenless colony divided by the total number of reproductive workers present (nR=53) divided by 5, whereby eT and nR were each assumed to be Poisson distributed. The mean number of workers nW and the number of eggs laid per day by the queen eQ were each known with very high accuracy (nW=2042, eQ=161) and could, in the calculation of the confidence limits, be assumed to be constant. First, we load the required Statistics package: 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 Next we define the distribution of each of our parameters: 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 We will take 100 000 parametric bootstrap resamplings for p and eW using the Sample() command: 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 This is an array with an estimate for A for each of the parametric bootstrap resamplings: 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 These are the 95% confidence limits calculated using the percentile method, as well as the mean estimate: 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

NyQkIit1JSpvS2IhIzYkIitOd05wPiEjNQ==

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

JCIrZzoieUIiISM1

Here is a histogram of the parametric bootstrap distribution of the A estimates: 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

JSFH