Hidden Markov Models with Applications to DNA Sequence Analysis
Christopher Nemeth · 2011
The Hidden Markov Model (HMM) is a model with a finite number of states, each associated with a probability distribution. The transitions between states cannot be directly measured (hidden), but in a particular state an observation can be generated. It is the observations and not the states themselves which are visible to an outside observer. However, by applying a series of statistical techniques it is possible to gain insight into the hidden states via the observations they generate. In the case of DNA analysis, we observe a strand of DNA which we believe can be segmented into homogeneous regions to identify the specific functions of the DNA strand. Through the use of HMMs we can determine which parts of the strand belong to which segments by matching segments to hidden states. HMMs have been applied to a wide range of applications including speech recognition, signal processing and econometrics to name a few. Here we will discuss the theory behind HMMs and the applications that they have in DNA sequence analysis. We shall be specifically interested in discussing “how can we determine from which state our observations are being generated?”, “how do we determine the parameters of our model?” and “how do we determine the sequence of hidden states given our observations?” While there are many applications of HMMs we shall only be concerned with their use in terms of DNA sequence analysis and shall cover examples in this literature where HMMs have been successfully used. In this area we shall compare approaches to using HMMs for DNA segmentation. Firstly, the approach taken when the number of hidden states is known and secondly, how it is possible to segment a DNA sequence when the number of hidden states is unknown?