Statistics, the science of data analysis, is the applied mathematics in the 21st century.
People (scientists, goverment, health professionals, companies) collect data in order to answer certain questions. Statisticians's job is to help them extract knowledge and insights from data.
Must-read for (bio)statistics students:
If existing software tools readily solve the problem, all the better.
Often statisticians need to implement their own methods, test new algorithms, or tailor classical methods to new types of data (big, streaming).
This entails at least two essential skills: programming and fundamental knowledge of algorithms.
Not a course on statistical packages. It does not answer questions such as How to fit a linear mixed model in R, Julia, SAS, SPSS, or Stata?
Not a pure programming course, although programming is important and we do homework in Julia.
The new BIOSTAT 203A (Data Management) in fall quarter focuses on programming in R and SAS.
Not a course on data science. The new course BIOSTAT 203B (Introduction to Data Science) in winter quarter focuses on some software tools for data scientists.
This course focuses on algorithms, mostly those in numerical linear algebra and numerical optimization.
To quote James Gentle
The form of a mathematical expression and the way the expression should be evaluated in actual practice may be quite different.
For a common numerical task in statistics, say solving the least squares problem $$ \widehat \beta = ({\bf X}^T {\bf X})^{-1} {\bf X}^T {\bf y}, $$ we need to know which methods/algorithms are out there and what are their advantages and disadvantages. You will fail this course if you use
inv(X'X) * X' * y
Using X \ y in Julia/Matlab (or lm(y ~ X) in R) is correct but not the purpose of this course. We want to understand what computer is doing when calling X \ y.
Course webpage: http://hua-zhou.github.io/teaching/biostatm280-2019spring.
Check the Schedule and Announcements pages frequently.
Jupyter notebooks will be posted before each lecture.