Bioengineering 498a or 599, Spring 2012SyllabusWeek1: (Brief refresher on linear systems analysis)

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Bioengineering 498a or 599, Spring 2012

Syllabus

Week1: (Brief refresher on linear systems analysis)

1.

a. Linear Operators: the black box responses, h, R, H,
and the

fractional
escape rate

2.


Ha
ndouts
: Operators, 32conv, 33linearity, 139ProgCV, Danckwerts53,
Moments.pdf,

Moore’s Gaussian

b. If f
-
> g through the operator: g= f convol h

c. Frequency transforms: Fourier, Laplace, G(
) = F(
)*H(
),


G(s) = F(s)*H(s)

1.

Moments: Around zero; around the mean. Moment generating functions.

2.

Problems.Wk1: Using operator
s to match published system responses.

3.

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)

1.

Testing for linearity and stationarity. These conditions are basic to most
statistical analysis. Changes in distributions or pulse responses?

2.

Time series: discrete samples, xi, i=1,n. Shannon, Nyquist, foldover

in
frequency domain with too low sampling frequencies; Bode plots.

3.

White noise, spectral analysis (Periodogram); smoothing by moving
averages, lag filters, higher order filters, Bode plots and cutoff
frequencies, falloff in dB/octave

4.

Contrasting Filtering

pre and post digitization. Time shifting to correct for
filter delays. Differential Equation state variable form for filters.

1.

Selected Problems for Wk2: in Chapter 2: 2.1,2.4, 2.6, 2.9, 2.10. 2.11, 2.14,
2.23



Week3: (Statistics of more traditional sense
, but seeking the basis of the
observations and tests in terms of the physics and the underlying
phenomena)

2.

Observing and trimming probability density functions.

3.

Mean Variance SD, moments about mean and zero

4.

Using moments and moment generating functions

5.

Q
uantiles and comparisons with standard distributions

6.

Some “Robust” measures that reduce sensitivity to wild points

7.

Using Chapter 2 of Vidakovic text. Quantiles, PDFs and CDFs.

8.

Univariate distributions.

9.

Multivariate distributions. 2.6. Body fat.

10.

Selected p
roblems in Chapter 2: 2.1,2.4, 2.6, 2.9, 2.10. 2.11, 2.14,
2.23


Week4: Introduction to Probability
.(Ch3)

1.

Notation: Intersection (product, AND), Union (OR).

2.

Additivity, inclusion
-
exclusion, Morgan’s rules. Complements.

3.

Venn Diagrams.

4.

Conditional and Total
Probability.

5.

Bayes Rule and Intro to Bayesian Networks.

6.

Selected problems:


Week5:

1.

Sensitivity, Specificity (Ch4): Positive predictive value and Negative
predictive value, Combining tests, ROC curves

2.

Random Variables (Ch5): a selection of discrete and co
ntinuous
distributions

3.


Week6:

Testing Statistical Hypotheses (Ch 9)

1.

Formulating hypotheses and null hypotheses

2.

Interpreting p
-
values correctly, statistical significance ≠ scientific
significance

3.

Testing differences, proportions, in one sample

4.

Central lim
it theorem (Ch6)


Week7:

Two Sample Tests and Power analysis (Ch10)

1.

Comparing normal means

2.

Paired data

3.

Comparing proportions

4.

Relative Risk and Odds Ratios

5.

Power analysis

6.

Multiplicity, False discovery rate


Week8:

ANOVA (Ch11)

1.

More than two populations
(why not use serial paired tests?)

2.

Assumptions for ANOVA


all normally distributed, variances for all
populations equal, independent samples

3.

One
-
way ANOVA

4.

Power analysis in ANOVA


Week9:

Regression (Ch16)

1.

Linear regression. Y on X vs X on Y. Weighting of
error.

2.

Multivariable Regression


Week10:

Goodness of Fit Tests (Ch 13)


1. Fitting data to biological models. Monte Carlo.

1.

Optim
iz
ation of model fits to data

2.

Evaluating Covariance matrices re freedom of parameters

3.

Comparing estimated parameter ranges from covariance versus
MonteCarlo



2. Review