Markov Models: An Introduction to Markov Models

By Steven Taylor

Markov Models

This book will offer you an insight into the Hidden Markov Models as well as the Bayesian Networks. Additionally, by reading this book, you will also learn algorithms such as Markov Chain Sampling.

Furthermore, this book will also teach you how Markov Models are very relevant when a decision problem is associated with a risk that continues over time, when the timing of occurrences is vital as well as when events occur more than once. This book highlights several applications of Markov Models. 

Lastly, after purchasing this book, you will need to put in a lot of effort and time for you to reap the maximum benefits.

By Downloading This Book Now You Will Discover:

• Hidden Markov Models
• Dynamic Bayesian Networks
• Stepwise Mutations using the Wright Fisher Model
• Using Normalized Algorithms to Update the Formulas
• Types of Markov Processes
• Important Tools used with HMM
• Machine Learning
• And much much more!

Download this book now and learn more about Markov Models!

• Language: English
• Publisher: Steven Taylor
• Release date: Dec 25, 2017
• ISBN: 9781386066187

Steven Taylor

Dr. Steven Taylor is a Professor and Clinical Psychologist in the Department of Psychiatry at the University of British Columbia. For 10 years he was Associate Editor of Behavior Research and Therapy, and now is Associate Editor of the Journal of Cognitive Psychotherapy. He has published over 100 journal articles, over 35 book chapters, and 8 books on anxiety disorders and related topics. His most recent books are on the nature and treatment of hypochondriasis, which is commonly considered to be an OC spectrum disorder. He served as a consultant on the text revision of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV-TR), and is a member of the scientific advisory board of the Anxiety Disorders Association of Canada. He has received early career awards from the Canadian Psychological Association, the Association for Advancement of Behavior Therapy, and the Anxiety Disorders Association of America. He is also a Fellow of the Canadian Psychological Association and the Association of Cognitive Therapy. His clinical and research interests include cognitive-behavioral treatments and mechanisms of anxiety disordres and related conditions.

Book preview

Introduction

A Markov model refers to a stochastic model that is used to model systems that spontaneously change and where there is an assumption that future states rely on the current ones, and not on the events that happened before it. Markov models are used varying situations though the most models are categorized into four, and the categorizations mainly depends on whether each and every chronological condition is can or cannot be observed, and whether the model is to be attuned on the basis of the realized observations.

The most basic Markov model is the Markov chain. It is responsible for modelling the state of a system with a random variable that alters over time. This means that this concept is of the view that the distribution for this variable relies solely on the distribution of a previous state.

Markov models are valuable once a decision problem entails risk that is constant over time, when the scheduling of events is imperative. In addition, Markov models are also very valuable when vital events may take place more than once. Coming up with proper representations of such sensitive settings with traditional decision trees is complex and may call for impracticable simplifying assumptions. In medical settings, for instance, Markov models are based on an assumption that a patient is constantly in one of a limited number of distinct states of health, which are called Markov states. In that situation, all events are modeled as transitions coming from one health state to another health state.

Among techniques for evaluating a Markov model include the use of matrix algebra, the use of cohort simulation and the application of a Monte Carlo simulation. There is a recently emerging method for representing Markov models, which uses the Markov-cycle tree. This technique uses a tree depiction of clinical incidents. It can be either a Monte Carlo simulation of a cohort simulation when evaluated. The Markov model has the capacity of representing repetitive or recurring events and this is a powerful advantage. Moreover, the fact that time dependence of the two probabilities and utilities permits clinical settings to be more accurately represented.

There are various ways in which a decision analyst can assign values to these terminal nodes of the decision tree. In some cases the outcome measure is a crude life expectancy; in others it is a quality-adjusted life expectancy. One of the methods for approximation of life expectancy is the diminishing exponential estimation of life expectancy (DEALE). This works out a sick person’s or an individual’s specific mortality rate considering a particular permutation of patient features and comorbid diseases. Standard life tables or Gompertz schemes of survival can be used to obtain life expectancies. Besides the two sources of life expectancies, the Markov model, developed by Beck and Pauker in 1983 can also serve as an estimation of an individual’s life expectancy. It applies Markov chains and processes to depict prognosis for use in healthcare or medical applications. Since its introduction in the 1980s, many Markov models have surfaced and have been used with increasing regularity in published decision evaluations. The advent of the computer has bolstered the effective application of these models by making development, construction and evaluation of the models easier and feasible. These reasons justify a re-examination of the Markov model. This book serves both as a review of the theory behind the Markov model of prognosis and as a practical guide for the construction of Markov models using microcomputer decision-analytic software.

Markov models are particularly useful when a decision problem involves a risk that is ongoing over time. Some clinical examples are the risk of hemorrhage while on anticoagulant therapy, the risk of rupture of an abdominal aortic aneurysm, and the risk of mortality in any person, whether sick or healthy. There are two important consequences of events that have ongoing risk. First, the times at which the events will occur are uncertain. This has important implications because the utility of an outcome often depends on when it occurs. For example, a stroke that occurs immediately may have a different impact on the patient than one that occurs ten years later. For economic analyses, both costs and utilities are discounted; such that later events have less impact than earlier ones. The