Estimation in the Mixture Transition Distribution Model for High Order Markov Chains

Abstract

The mixture transition distribution (MTD) model was introduced by Raftery (1985) as a parsimonious model for high-order Markov chains. It is flexible, can represent a wide range of dependence patterns, can be physically motivated, fits data well, and appears to be a discrete-valued analogue for the class of autoregressive time series models. However, estimation has presented difficulties because the parameter space is highly nonconvex, being defined by a large number of nonlinear constraints. Here we propose an efficient computational algorithm for maximum likelihood estimation which is based on a way of reducing the large number of constraints. This also allows more structured versions of the model, for example those involving structural zeros, to be fit quite easily. A way of fitting the model using GLIM is also discussed. The algorithm is applied to a sequence of wind directions, and also to two sequences of DNA bases from introns from genes of the mouse. In each case, the MTD model fits better than the conventional Markov chain model.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1991
Accession Number
ADA241341

Entities

People

  • Adrian Raftery
  • Simon Tavare

Organizations

  • University of Washington

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Biological Sciences
  • Computer Programming
  • Data Analysis
  • Data Sets
  • Information Science
  • Lymphocytes
  • Markov Chains
  • Markov Models
  • Numbers
  • Probability
  • Sequence Analysis
  • Statistical Analysis
  • Statistical Inference
  • Statistics
  • Wind Direction
  • Wind Turbines

Fields of Study

  • Mathematics

Readers

  • Distributed Systems and Data Platform Development
  • Statistical inference.

Technology Areas

  • Space