5 - Parametric Inference

Summary

Graphical models are powerful statistical tools that have been applied to a wide variety of problems in computational biology: sequence alignment, ancestral genome reconstruction, etc. A graphical model consists of a graph whose vertices have associated random variables representing biological objects, such as entries in a DNA sequence, and whose edges have associated parameters that model transition or dependence relations between the random variables at the nodes. In many cases we will know the contents of only a subset of the model vertices, the observed random variables, and nothing about the contents of the remaining ones, the hidden random variables. A common example is a phylogenetic tree on a set of current species with given DNA sequences, but with no information about the DNA of their extinct ancestors. The task of finding the most likely set of values of the hidden random variables (also known as the explanation) given the set of observed random variables and the model parameters, is known as inference in graphical models.

Clearly, inference drawn about the hidden data is highly dependent on the topology and parameters (transition probabilities) of the graphical model. The topology of the model will be determined by the biological process being modeled, while the assumptions one can make about the nature of evolution, site mutation and other biological phenomena, allow us to restrict the space of possible transition probabilities to certain parameterized families. This raises several questions.