# Statistics for Bioengineering Sciences: With MATLAB and WinBUGS Support (Springer Texts in Statistics)

## Brani Vidakovic

Language: English

Pages: 753

ISBN: 1461403936

Format: PDF / Kindle (mobi) / ePub

Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing engineering fields, bioengineering and biomedical engineering, while implementing software that engineers are familiar with.

The author integrates introductory statistics for engineers and introductory biostatistics as a single textbook heavily oriented to computation and hands on approaches. For example, topics ranging from the aspects of disease and device testing, Sensitivity, Specificity and ROC curves, Epidemiological Risk Theory, Survival Analysis, or Logistic and Poisson Regressions are covered.

In addition to the synergy of engineering and biostatistical approaches, the novelty of this book is in the substantial coverage of Bayesian approaches to statistical inference. Many examples in this text are solved using both the traditional and Bayesian methods, and the results are compared and commented.

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var(x,0) Flag 0 in the argument list indicates that the ratio 1/(n − 1) is used to calculate the sample variance. If the flag is 1, then var(x,1) stands for s2∗ = 1 n (X i − X )2 , n i=1 which is sometimes used instead of s2 . We will see later that both estimators have good properties: s2 is an unbiased estimator of the population variance while s2∗ is the maximum likelihood estimator. The square root of the sample variance is the sample standard deviation: s= 1 n (X i − X )2 . n − 1 i=1

these are usually standard numerical values for which ratios make sense and the origin is absolute. Length, weight, and age are all examples of ratio data. Interval and ratio data are examples of numerical data. MATLAB provides a way to keep such heterogeneous data in a single structure array with a syntax resembling C language. Structures are arrays comprised of structure elements and are accessed by named fields. The fields (data containers) can contain any type of data. Storage in the

guesses red with a probability of 0.7 and green with a probability of 0.3. (a) What is the probability that the subject will guess correctly? (b) Given that a subject guesses correctly, what is the probability that the light flashed red? 3.10 Exercises 99 3.15. Propagation of Genes. The following example shows how the ideas of independence and conditional probability can be employed in studying genetic evolution. Consider a single gene that has two forms, recessive (R) and dominant (D). Each

matching this group is 1/120 for the general population. For both methods, also find the PPV, that is, the probability that a person who tested positive and was randomly selected from the same age group in the general population has the disease if no other clinical information is available. (c) Mr. Smith is one of the 52 subjects in the study and he tested positive under a Raman spectroscopy test. What is the probability that Mr. Smith has the disease? 126 4 Sensitivity, Specificity, and

X 2 = n is binomial B in n, λ1λ+1λ2 (Exercise 5.5). Furthermore, the Poisson distribution is a limiting form for a binomial model, i.e., lim n,np→∞,λ n x 1 p (1 − p)n− x = λ x e−λ . x! x (5.6) The MATLAB commands for Poisson CDF, PDF, quantile, and random number are poisscdf, poisspdf, poissinv, and poissrnd. In WinBUGS the Poisson distribution is denoted as dpois(lambda). Example 5.11. Poisson Model for EBs. After 7 days of aggregation, the microscopy images of 2000 embryonic bodies (EBs)