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BME 322 Probability &
Statistics for BME
Course Description:
BME 322 is a combined lecture
and laboratory course that provides an introductory treatment of
probability theory, including distribution functions, moments,
and random variables. Practical applications include; estimation
of means and variances, hypothesis testing, sampling theory and
linear regression. The application of normal and exponential
distributions in the statistical analysis of biological variables
is covered extensively. Introduction to random processes,
correlation functions and spectral density functions are also
covered.
Prerequisites:
Math 261, Math 262, Biology
K101, Physics 251, BME 211, BME 331 & proficiency in MATLAB
and LabVIEW.
Corequisites:
BME 334
Instructional Goals:
This course provides
the foundational skills for advanced statistical analysis of
biological signals. The basic analytical concepts of probability
theory, statistical design of experiments and data analysis and
representation of biological variables as random processes are
demonstrated and practiced through computer based analysis of
biologically relevant data sets provided throughout the course.
All computational homework assignments are carried out using
MATLAB. All laboratory exercises are carried out using LabVIEW.
General Lecture Topics:
BME 322 is
comprised of three interrelated subject areas, all involving the
use of mathematical and computational tools to distill biological
data into meaningful statistical representations. The first
subject area broadly introduces the topic of probability theory
(e.g. relative-frequency, set theory, and axioms of probability,
conditional probability, independence, and Bernoulli trials) as
related to sampled data. This leads to the introduction of random
variables and distribution functions (e.g. probability density
functions, mean values and moments, Gaussian random variables,
density functions conditional density functions, joint
distributions, covariance, sums of random variables) along with
sampling and estimation theory (e.g. point and interval
estimation, sampling distributions, estimation of means and
variances, hypothesis testing, regression analysis and
goodness-of-fit tests). The second subject area focuses upon
random process definitions and measurement of random processes
from biological signal sources (e.g. correlation,
cross-correlation and applications to analysis of random
processes from multiple biological sources). The third subject
area utilizes recent articles from the scientific literature
demonstrating the application of these and other mathematical
processing techniques ( e.g. spectral density, properties of
spectral density, and mean-square values from spectral density)
in the study of biological signals and physiological systems.
Refer to the lecture schedule for specific topics and dates.
Required Textbooks:
Intuitive
Probability and Random Processes using MATLAB by Steven Kay
(2006), Springer. ISBN: 0-387-24157-4. Both electronic and
printed handouts will also be distributed throughout the
semester.
Additional reference materials:
Probabilistic Methods of
signal and System analysis by Cooper & McGillem (1999),
Oxford University Press. ISBN: 0-190512354-9.
Probability and Random
Processes by Childers (1997), McGraw-Hill. ISBN: 0-256-13361-1.
Probability and Statistics for
the Engineering, Computing and Physical Sciences by Dougherty
(1990), Prentice Hall. ISBN: 013711995X
Principles of Neuroscience by
Kandel & Schwartz (2002), Elsevier. ISBN: 0838577016
Physiology by Berne (Editor),
Levy, Koeppen & Stanton (2002), Mosby. ISBN: 0815109520
Biomedical Engineering Handbook 2 nd edition by Bronzino
(Editor), CRC Press, ISBN 0849383463
Outcomes:
Upon completion of the course,
students should be able to
Solve simple probability problems with electrical and
computer engineering applications using the basic axioms of
probability. [a, e]
Describe the fundamental properties of probability
density functions with applications to single and multivariate
random variables. [a, b2, e]
Describe the functional characteristics of probability
density functions frequently encountered in life science research
such as the Binomial, Uniform, Gaussian and Poisson. [a, b2]
Determine the first through fourth moments of any
probability density function using the moment generating
function. [a, e]
Calculate confidence intervals and levels of
statistical significance using fundamental measures of
expectation and variance for a given numerical data set. [b2]
Discern between random variables and random processes
for given mathematical functions and numerical data sets. [a, b2]
Determine the power spectral density of a random
process for given mathematical functions and biological data
sets. [a, b2]
Determine whether a random process is ergodic or
nonergodic and demonstrate an ability to quantify the level of
correlation between sets of random processes for given
mathematical functions and biological data sets. [a, b2]
Model complex families of signals by means of random
processes. [a]
Determine the random process model for the output of a
linear system when the system and input random process models are
known. [a, c, e]
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