Some Statistical Techniques Behind Bioinformatics Methods & Genomics Discoveries

I have a confession. I don’t like “statistics”. It gets really vague and complicated really fast, especially with all the symbols, and as it turns out, I can’t do without some parts of it. Biology today has been described numerous times as an “information science”, which is a fancy way of saying it has an overwhelming amount of information that we need to analyse, classify, etc., and therefore, math has to be an integral part of it.

This phenomenon is very obvious in genomics. Modern sequencing technologies have allowed us to generate millions of data points per experiment. Behind every variant calling tool, expression heatmap, or cancer mutation database is a statistical model or algorithm doing the heavy lifting, testing hypotheses and finding signals in noisy data.

Therefore, this piece walks through some of the foundational statistical concepts and techniques that power common analyses in bioinformatics, especially in genomics and cancer variant studies. As usual, this is for me as much as it’s for you, so I’ll keep it digestible.

1. Bayesian Inference

This is a statistical technique that handles complex and noisy data efficiently, and these are two words often used to describe biological data. It is probabilistic, meaning it seeks to estimate the probability of an uncertain parameter based on observed data. Ideally, you start off with a “prior” probability or prior belief and then update your belief as new data comes to light. An example of how it is typically written is P(genotype | s.data), which uses Bayes’ theorem to update the belief about which genotype a person has based on how well the sequencing data supports it.

This is especially useful for distinguishing real mutations from sequencing errors. For example, if a variant is present in 30% of the sequence reads, the tool calculates the probability of a true heterozygous mutation versus random noise, taking into account base quality scores, alignment confidence, and allele balance. Tools like the Genome Analysis Toolkit (GATK) and FreeBayes use Bayesian statistics to estimate the probability of a genotype given the observed sequencing reads.

Bayesian models let these tools remain robust even when read depth is low or sequencing is noisy, which is common in cancer samples with degraded or impure DNA. It is very much loved because it allows users to propagate uncertainty throughout their analyses; that is, to continuously account for any errors inherent in the data such that final predictions, inferences, and decisions are reliable and not riddled with inaccuracies.

If you’re into more technical stuff, this research paper might be a fun read for you. P.S. The mentioned limitation about computational challenge might not be true today.

2. Hidden Markov Models (HMMs)

A Hidden Markov Model is a statistical model that we use when we observe an outcome, but the underlying process that generated it is hidden. The observed data are called symbols, and the hidden process is made up of states. For example, in genomics, the sequence we see might come from either a protein-coding or non-coding region, but we don’t directly observe that source. An HMM can learn the patterns that distinguish coding from non-coding sequences, and once trained, it can predict which parts of a foreign/new sequence are likely to come from a coding region. HMMs are especially good for problems where the biological “truth” is hidden but tends to change gradually across the sequence, like exons and introns transitioning along a genome.

Tools like CNVnator use HMMs to detect copy number variations (CNVs) by modelling the coverage depth along the genome and identifying regions where it deviates significantly from expectation. Similarly, methylation state detection across regions often relies on HMMs to infer consistent patterns from variable coverage, like the tool Nanopolish does.

This tutorial review is a good technical breakdown.

3. Likelihood-Based Models

These models estimate the parameters that make the observed data most probable under a given model. In this context, likelihood refers to the probability of observing the data given a specific model and its parameters. Since different parameter values will give different likelihoods, the typical approach is to find the values that maximise this likelihood; that is, produce the highest likelihood. That’s known as maximum likelihood estimation (MLE).

In bioinformatics, a practical example of MLE in action is in genotype and variant calling. Tools like samtools mpileup and the accompanying BCFtools variant caller use MLE to determine whether a variant exists at a particular genomic site. For each site, the model calculates the likelihood of the sequencing data under different possible genotypes and picks the one with the highest likelihood.

These models generally assume that sequencing errors are random and independent, and they incorporate information like base quality scores and read depth to help calculate likelihoods accurately.

MLE-based methods are often faster and simpler than Bayesian approaches, since they don’t require specifying prior probabilities. However, they can be more sensitive to noise, especially in low-coverage regions, because they rely solely on the observed data.

4. Multiple Testing Corrections

In a genome-wide analysis, testing thousands or millions of sites for association with a trait or molecular change leads to a serious problem of assuming something is positive when it is, in fact, not. That problem is known as false positives. If you test 1 million hypotheses at p < 0.05 with chi-square or t-tests, depending on your variables, you’d expect 50,000 “significant” results just by chance.

To avoid this, researchers use corrections like the Benjamini-Hochberg False Discovery Rate (FDR) or the stricter Bonferroni correction, which adjust p-values to account for the number of comparisons. Thankfully, these methods are already standardised in many programming languages, so all it requires is implementing the function that accounts for multiple tests.

This is particularly critical in differential gene expression (e.g., using tools like DESeq2), methylation QTL (meQTL) mapping, and genome-wide association studies (GWAS).

5. Regression Models

Regression models help define the relationship between a dependent variable (the outcome) and one or more independent variables (features). Many variant impact predictions rely on regression, e.g., logistic regression, to estimate whether a given feature (e.g., a mutation in a gene) is likely to be functional or not.

Tools like PolyPhen-2 use models trained on labelled datasets, such as known benign or pathogenic variants, to predict how a new mutation might affect protein structure or function. In methylation studies, regression models help detect meQTLs, sites where genetic variants influence methylation levels. These analyses model methylation as a continuous variable and test whether SNPs significantly predict changes in it, sometimes adjusting for covariates like age or tumour purity.

Regression assumes a fairly clean, often straightforward relationship between input features and outcomes. And biological interactions are often far from clean or simple. So, when the true underlying relationship is more complex, a regression model might oversimplify things, leading to biased or overly confident predictions.

Still, regression remains popular because it’s interpretable, computationally efficient, and often good enough to reveal useful signals, especially when you’re dealing with large datasets. Plus, it sets a solid baseline for more complex models to improve upon.

6. Principal Component Analysis (PCA)

PCA is a technique that reduces complex data into a few summary components through a process called dimensionality reduction. In genomics and biomedical sciences, available data almost always have more features than the actual data points, which makes it difficult to determine what features are relevant to the analyses. PCA helps select the best features without necessarily losing other features, and it’s often used to visualise patterns in gene expression, methylation, or population structure.

PCA works by finding the directions, called principal components, in which the data varies the most. The top few components often capture meaningful biology or confounding technical noise. Like most statistical methods, PCA is an established technique that only requires a few lines of code and the right function.

7. Machine Learning Models

Modern bioinformatics tools use machine learning to classify variants, predict phenotypes, group patients by molecular subtypes, and make sense of complex multi-omics data. These approaches can be supervised, unsupervised, or semi-supervised, depending on whether the data includes known labels, like disease status or variant effect.

Supervised learning is the most common in bioinformatics. It’s used when we have labelled datasets; for example, variants classified as pathogenic or benign, or patients with known clinical outcomes. Tools like DeepVariant (for variant calling) and MuRaL (for predicting local mutation rates) are trained on large, high-quality datasets and often outperform traditional statistical methods, especially in challenging settings like noisy tumour samples or low-coverage sequencing.

Unsupervised learning, on the other hand, doesn’t rely on labelled data. It’s useful when we want to discover hidden patterns or groupings in the data without pre-defined categories. Clustering techniques are used to identify molecular subtypes of diseases, e.g., stratification of cancer patients based on gene expression or methylation profiles.

Then there’s semi-supervised learning, which sits in the middle. It’s especially handy in genomics, where labelled data are scarce, but unlabeled data are plentiful.

Machine learning models have unique challenges. Supervised models, in particular, depend heavily on the quality and balance of training data. Biases in the dataset can lead to biased predictions. And then there’s the black box problem in deep models, especially neural networks, where it is often hard to interpret why a model is making a certain decision. In a clinical context, this lack of transparency can be a dealbreaker, since decisions about patient care demand accuracy and trust.

P.S. The term “model” comes up a lot here, so you might want to check out this fun piece I wrote on biological models.

Where Is It All Going?

As sequencing becomes cheaper and multi-omics datasets grow, statistical techniques in bioinformatics are evolving to handle:

• Integration: Combining genomics, transcriptomics, epigenomics, and proteomics in the same model.
• Causal inference: Moving beyond correlation to infer what’s driving what, because we have all agreed that correlation does not equal causation. “We” being the scientific community.
• Real-time analysis: Streaming large datasets from clinical workflows to models for immediate insights.

This is definitely not an attempt to teach biostatistics, but as I said earlier, biology is data now, so every little thing you can remember about the math or statistical principle counts, especially for interpretation.

Finally, as I read through this before hitting publish, I realise how much variant discovery and explanation make up the bulk of my examples for these methods. That either speaks to my bias toward variant-focused research or to how much resources are continuously devoted to spotting and understanding differences in the context of medicine.