posterior
Definition
In Bayesian statistics and probabilistic modeling, the posterior (or posterior probability) represents the updated probability of a hypothesis after observing new evidence or data. It combines prior knowledge with observed data through Bayes' theorem: posterior ∝ likelihood × prior. In biological network analysis, posterior probabilities quantify confidence in network structures, edge weights, or pathway activities after integrating experimental data. This approach is crucial for inferring gene regulatory networks, protein-protein interactions, and causal relationships where uncertainty must be explicitly modeled. Posterior distributions provide not just point estimates but full probability distributions, enabling researchers to assess confidence intervals and make statistically rigorous decisions about biological mechanisms.
Visualize posterior in Nodes Bio
Researchers can visualize posterior probabilities as edge weights or confidence scores in biological networks. In Nodes Bio, edges with high posterior probabilities can be highlighted to show the most confident regulatory relationships or protein interactions. Node colors or sizes can represent posterior probabilities of gene activity states or pathway involvement, helping researchers focus on statistically supported connections while filtering uncertain relationships from complex multi-omics datasets.
Visualization Ideas:
- Gene regulatory networks with edge thickness proportional to posterior probabilities of regulatory relationships
- Protein interaction networks colored by posterior confidence scores from Bayesian integration of multiple experimental datasets
- Pathway activity networks where node sizes represent posterior probabilities of pathway activation states across conditions
Example Use Case
A systems biology team investigating cancer drug resistance integrates RNA-seq, proteomics, and ChIP-seq data to infer gene regulatory networks. Using Bayesian network inference, they calculate posterior probabilities for each potential regulatory edge between transcription factors and target genes. Edges with posterior probability >0.8 reveal high-confidence regulatory mechanisms driving resistance. The posterior distribution for a key transcription factor's activity shows 95% probability of upregulation in resistant cells, providing statistical support for targeting this factor in combination therapy development.