By Derek A. Roff

ISBN-10: 0521846285

ISBN-13: 9780521846288

This advisor to the modern toolbox of tools for information research will serve graduate scholars and researchers around the organic sciences. smooth computational instruments, akin to greatest probability, Monte Carlo and Bayesian tools, suggest that information research not will depend on complex assumptions designed to make analytical techniques tractable. those new 'computer-intensive' equipment are presently no longer always on hand in statistical software program programs and sometimes require extra unique directions. the aim of this e-book consequently is to introduce essentially the most universal of those equipment by way of delivering a comparatively easy description of the options. Examples in their program are supplied all through, utilizing actual facts taken from a variety of organic examine. a chain of software program directions for the statistical software program package deal S-PLUS are supplied in addition to difficulties and strategies for every bankruptcy.

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**Example text**

2) Show that ð1=nÞ ni¼1 ðxi À x" Þ2 is a biased estimator of 2 and that an P unbiased estimator is ð1=n À 1Þ ni¼1 ðxi À x" Þ2 . Hint: There is no loss in generality in assuming that ¼0, which makes the proof simpler. , probability of a sampling unit containing r individuals). Show that the maximum likelihood estimate of is equal to (Total number of individuals counted)/(Total number of sampling units). 4) Generate 20 regression lines using the same probability distribution and estimate the correlation between ^1 and ^2 .

For several samples analysis of variance is appropriate. For example, as described below, one can use the jackknife to estimate a population rate of increase, r (in this case the symbol r is so well entrenched in the literature that I shall use it instead of ). Suppose we had several populations for which we had jackknife estimates: we might wish to ask if there is an overall difference among the populations, which could be done by a oneway ANOVA of the pseudovalues. What is particularly useful about the analysis of the pseudovalues is that one can introduce several independent variables in the analysis.

Y px11 px22 . . pxkk ¼ Qk pxi i x1 x2 . . , age class) and pi is the true proportion in the ith class. Þ À k X i¼1 lnðxi Þ þ k X xi lnðpi Þ ð2:38Þ i¼1 To find the maximum likelihood estimates ð^p1 , p^ 2 , . . , p^ k Þ, we can proceed by differentiating and setting the result to zero, but an easier approach is as follows: the probability of an animal being in age class i is pi and hence the probability that it is not in age class i is 1 À pi. Thus from this perspective we have a simple binomial distribution, all age classes except age class i being collapsed into one.

### Introduction to Computer-Intensive Methods of Data Analysis in Biology by Derek A. Roff

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