Recently I came across the problem with suspiciously large difference in the averages of two groups while analysing some Omics data. An article dealing with similar issues can be seen here. The data distribution is shown below in Figure 1 (FYI: the fold change was around 6 - which is very large for this kind... Continue Reading →

# Plausible Reasoning for Scientific Problems: Belief Driven by Priors and Data.

Plausible reasoning requires constructing rational arguments by use of syllogisms, and their analysis by deductive and inductive logic. Using this method of reasoning and expressing our beliefs, in a scientific hypothesis, in a numerical manner using probability theory is one of my interest. I try to condense the material from the first 4 chapters of... Continue Reading →

# Regression & Finite Mixture Models

I wrote a post a while back about Mixture Distributions and Model Comparisons. This post continues on that theme and tries to model multiple data generating processes into a single model. The code for this post is available at the github repository. There were many useful resources that helped me understand this model, and some... Continue Reading →

# Model Checking: Posterior Predictive Checks

Once a model is fit and parameters estimated, we would look at how well the model explains the data and what aspects of the data generation process in nature are not captured by the model. Most of the material covered in this post follows the examples from: [1] Gelman, A., Carlin, J. B., Stern, H. S.,... Continue Reading →

# Mixture Distributions and Model Comparison

The following text and code snippets show examples from two books on Bayesian Data Analysis: [1] Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan, second edition. Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition. http://doi.org/10.1016/B978-0-12-405888-0.09999-2 [2] Albert, J., Gentleman, R., Parmigiani, G., & Hornik, K.... Continue Reading →