fonnesbeck / bios8366

Advanced Statistical Computing at Vanderbilt University Medical Center's Department of Biostatistics

Bios8366

Advanced Statistical Computing at Vanderbilt University's Department of Biostatistics

Course covers numerical optimization, statistical machine learning, Markov Chain Monte Carlo (MCMC), variational inference (VI) algorithms, data augmentation algorithms with applications for model fitting and techniques for dealing with missing data.

Prerequisites: Bios 6341 (Fundamentals of Probability), Bios 6342 (Contemporary Statistical Inference), or permission of instructor. Students must be familiar with basic probability, have some formal programming experience, and be comfortable using the Git version control system.

To run the course materials, the first step is to install Python. Though your computer likely already has Python installed, we recommend installing the Miniforge distribution of Python, as it includes useful utilities for manipulating your Python environment. Alternatively, you can install the commercial Anaconda Python distribution.

Having set up Python, to then install the Python packages for the course, clone the repository and run:

conda env create -f environment.yml

All content is licensed under CC-BY-SA 3.0 unless otherwise stated.

FAQ

Can I audit this course?

While we strongly prefer that students attend BIOS 8366 for credit, there are circumstances under which we will allow auditing. Auditors will be expected to attend lectures regularly and complete all homeworks, but will be exempted from completing the final course project.

bios8366's Issues

Use URL rather than file system location to import data

Moving to URLs will allow notebooks to be standalone.

wrong implementation of function "conditional".

The conditional function takes as input (x_new, x, y, params), there is no need to pass y in the function. By definition of conditional probability above conditional distribution, "x_new" represent "x" and "x" represent "y".

Correct implementation would be:

def conditional(x_new, x, params):
B = exponential_cov(x_new, x, params)
C = exponential_cov(x, x, params)
A = exponential_cov(x_new, x_new, params)
mu = np.linalg.inv(C).dot(B.T).T.dot(x) // y is replace by x.
sigma = A - B.dot(np.linalg.inv(C).dot(B.T))
return(mu.squeeze(), sigma.squeeze())

E-step for ZIP data

In the Expectation and Maximization notebook,

I am not sure, but can you check the following E-step

     a = psi * (x == 0)
     b = (1-psi)*poisson.pmf(x, mu)

is correct? The following can be correct.

    a = (1-psi) * (x == 0)
    b = psi*poisson.pmf(x, mu)

typo in e_step

Excellent work.
And I found a typo in Section3_1-Expectation-Maximization.ipynb-General formulation

from scipy.stats.distributions import norm

def e_step(x, mu, sigma, psi):
    a = psi * norm.pdf(x, mu[0], sigma[0])
    b = (1. - psi) * norm.pdf(x, mu[1], sigma[1])
    return b / (a + b)

should be

def e_step(x, mu, sigma, psi):
    a = (1. - psi) * norm.pdf(x, mu[0], sigma[0])
    b =  psi * norm.pdf(x, mu[1], sigma[1])
    return b / (a + b)

Becasue m_step output psi of second distribution and to be consistent with formula.