Bioengineering 498a or 599, Spring 2012
Week1: (Brief refresher on linear systems analysis)
a. Linear Operators: the black box responses, h, R, H,
: Operators, 32conv, 33linearity, 139ProgCV, Danckwerts53,
b. If f
> g through the operator: g= f convol h
c. Frequency transforms: Fourier, Laplace, G(
) = F(
G(s) = F(s)*H(s)
Moments: Around zero; around the mean. Moment generating functions.
Problems.Wk1: Using operator
s to match published system responses.
Selected Problems for Wk1.
Week2: (Brief refresher on time series and filtering in data acquisition.
Handouts on time series analysis, variance, covariance, correlation,
comparing calculations for a single population
with time series)
Testing for linearity and stationarity. These conditions are basic to most
statistical analysis. Changes in distributions or pulse responses?
Time series: discrete samples, xi, i=1,n. Shannon, Nyquist, foldover
frequency domain with too low sampling frequencies; Bode plots.
White noise, spectral analysis (Periodogram); smoothing by moving
averages, lag filters, higher order filters, Bode plots and cutoff
frequencies, falloff in dB/octave
pre and post digitization. Time shifting to correct for
filter delays. Differential Equation state variable form for filters.
Selected Problems for Wk2: in Chapter 2: 2.1,2.4, 2.6, 2.9, 2.10. 2.11, 2.14,
Week3: (Statistics of more traditional sense
, but seeking the basis of the
observations and tests in terms of the physics and the underlying
Observing and trimming probability density functions.
Mean Variance SD, moments about mean and zero
Using moments and moment generating functions
uantiles and comparisons with standard distributions
Some “Robust” measures that reduce sensitivity to wild points
Using Chapter 2 of Vidakovic text. Quantiles, PDFs and CDFs.
Multivariate distributions. 2.6. Body fat.
roblems in Chapter 2: 2.1,2.4, 2.6, 2.9, 2.10. 2.11, 2.14,
Week4: Introduction to Probability
Notation: Intersection (product, AND), Union (OR).
exclusion, Morgan’s rules. Complements.
Conditional and Total
Bayes Rule and Intro to Bayesian Networks.
Sensitivity, Specificity (Ch4): Positive predictive value and Negative
predictive value, Combining tests, ROC curves
Random Variables (Ch5): a selection of discrete and co
Testing Statistical Hypotheses (Ch 9)
Formulating hypotheses and null hypotheses
values correctly, statistical significance ≠ scientific
Testing differences, proportions, in one sample
it theorem (Ch6)
Two Sample Tests and Power analysis (Ch10)
Comparing normal means
Relative Risk and Odds Ratios
Multiplicity, False discovery rate
More than two populations
(why not use serial paired tests?)
Assumptions for ANOVA
all normally distributed, variances for all
populations equal, independent samples
Power analysis in ANOVA
Linear regression. Y on X vs X on Y. Weighting of
Goodness of Fit Tests (Ch 13)
1. Fitting data to biological models. Monte Carlo.
ation of model fits to data
Evaluating Covariance matrices re freedom of parameters
Comparing estimated parameter ranges from covariance versus