Hierarchical Linear Regression – 2 Level Random Effects Model

Regression is a popular approach to modelling where a response variable is modelled as a function of certain predictors - to understand the relations between variables. I used a linear model in a previous post, using the bread and peace model - and various ways to solve the equation. In this post, I want to fit … Continue reading Hierarchical Linear Regression – 2 Level Random Effects Model

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Compare Transformations & Batch Effects in Omics Data

While analysing high dimensional data, e.g. from Omics (Genomics, Transcriptomics, Proteomics etc.) - we are essentially measuring multiple response variables (i.e. genes, proteins, metabolites etc.) in multiple samples, resulting in a $latex rXn$ matrix X with r variables and n samples. The data capture can lead to multiple batches or groups in the data - … Continue reading Compare Transformations & Batch Effects in Omics Data

Parameter Estimation

In statistical or mathematical models our aim is to look at the data and estimate the parameters and uncertainty of those estimations. Generally speaking, looking at a data set, we wish to choose a likelihood/noise/sampling distribution, that fits the data. A distribution requires some parameters, Θ, e.g. a normal distribution (which is a very common error/noise … Continue reading Parameter Estimation

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 Mixture Distributions and Model Comparison