Bayesian Data Analysis

I am continually learning about and implementing Bayesian techniques for data analysis. Below is a record of the resources I have used followed by examples of my work that have employed these methods.

Books and courses

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Below are the books I have worked through for learning how to conduct Bayesian data analyses. I plan to revisit both Kruschke so that I can practice the coding alongside the theory.

Tutorials

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I have GitHub repository of Jupyter notebooks where I follow, annotate, and experiment with tutorials on using the probabilistic programming language PyMC3.

I have also contributed my tutorial on fitting splines with PyMC3 to the official pymc3-examples repository.

Examples

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Computational biology

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Below are some instances where I have used Bayesian methods in my research.

KRAS A59 comutation with the MAPK pathway

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Source

I worked with a post-doc in the Haigis lab on analyzing the comutation of the rare KRAS A59 mutations with the MAPK pathway in human colorectal cancer sequencing data. We found that a hypermutation phenotype (likely due to MSI) was associated with an increase in odds of a MAPK pathway, regardless of the mutational status of KRAS. However, KRAS A59E/T mutant tumor samples had similar probabilities of having a concomitant MAPK mutation as KRAS WT tumors, far higher than other KRAS mutant tumors.

This work will likely be published within the next year or so as part of a broader study of the dynamics of the Kras A59 mutants.

Comutation of SIRT4 in colorectal cancer

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Source

For a collaboration with Prof. Marcia Haigis, I conducted a comutation analysis with SIRT4 with various genes in PI3K pathway, KRAS, and BRAF. We found novel comutation interactions that she used as preliminary data in a grant proposal.

Differential gene expression of DUSP genes

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I did a small analysis to see if there was evidence for differential expression of DUSP genes associated with the KRAS alleles or with the loss APC in human samples of colorectal cancer tumors.

Miscellaneous analyses

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Analyzing the results of “Inhibiting and Facilitating Conditions of the Human Smile: A Nonobtrusive Test of the Facial Feedback Hypothesis”

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Source | Website

After reading about it in Daniel Kahneman’s Thinking, Fast and Slow, I conducted my own analysis of the results from a replication report on the famous social psychology paper “Inhibiting and Facilitating Conditions of the Human Smile: A Nonobtrusive Test of the Facial Feedback Hypothesis”. I began with several different visualizations of the data and then fit several different models, analyzing each and comparing them all together. The full analysis can be found here: https://jhrcook.github.io/wagenmaker-data-analysis/.

TidyTuesdays

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TidyTuesday is a tradition in the R programming community where a new dataset is provided each Tuesday for everyone to play with. While some days I try to create visually appealing data visualizations, I generally take the opportunity to experiment with modeling. Below are the instances where I have explored Bayesian data analysis.

August 11, 2020 Avatar: The Last Airbender: I experimented with prior predictive checks.
August 4, 2020 European energy: Using multi-level models to explain energy source usage per country.
July 14, 2020 Astronaut database: Compared the results of a Poisson regression model using Frequentist and Bayesian methods.
July 7, 2020 Coffee ratings: Using various regression models to explain coffee rating using qualitative metrics.
June 23, 2020 Caribou location tracking: Hierarchical modeling of caribou speeds.
June 9, 2020 Passwords: Experimented with modeling the security of passwords based off of their characteristics.
May 5, 2020 Animal Crossing - New Horizons: I used sentiment analysis of game reviews to model a players rating of the game.

Blog Posts

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Uncanny X-Men - Bayesian version

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I wrote a post as a follow-up on an article to Julia Silge’s Uncanny X-Men analysis. She used a bootstrapping method to build confidence intervals for an estimate of some feature of the comic books (more details are in my original post). My analysis was focussed on how this was similar to using a Bayesian technique, while also highlighting how a fit Bayesian model is more easily interpreted than 95% confidence intervals from a permutation test.

Splines

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I have two blog posts about modeling splines. The first is a more detailed introduction to these forms of transformations and how the model interprets the spline basis. The second is a more exploratory comparison of different structures for multi-level and hierarchical spline regressions. These models are more problematic to fit, so I experimented with different forms of spline bases and hierarchical prior distributions.

Understanding the “funnel of doom”

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Another post I made was just a PyMC3 version of Betancourt’s post on funnel degeneracies that commonly plague hierarchical models. The main point was to increase my own understanding of the theory Betancourt explained and the diagnostics he demonstrated. Also, this served as an opportunity to create a model in PyMC3 with a mixture of centered and non-centered parameterizations, a technique I may need in my own work.

Non-linear modeling of serial dilutions

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This was a post following the model for serial dilutions in the Bayesian Data Analysis book by Gelman et al. I built the model with Stan and sampling from the posterior with MCMC then conducted some standard analyses of the posterior distributions and predictions.

Comparing MCMC runtimes

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I did a brief analysis of the runtimes of MCMC sampling from a very large (several thousand parameters) hierarchical negative binomial model under several conditions. Unexpectedly, this drove me to update my graduate project to version 4 of PyMC for the gain in sampling speed.