multivariate poisson hidden markov models for analysis of spatial ...

TABLE OF CONTENTS
PERMISSION TO USE ................................................................................i
ABSTRACT ..................................................................................................ii
ACKNOWLEDGEMENT.............................................................................iv
DEDICATION ..............................................................................................v
TABLE OF CONTENTS ..............................................................................vi
LIST OF TABLES ........................................................................................ix
LIST OF FIGURES.......................................................................................xi
LIST OF ACRONYMS.................................................................................xiii
1 GENERAL INTRODUCTION
1.1 Introduction .................................................................................1
1.2 Literature review .........................................................................2
1.2.1 Introduction to finite mixture models...........................2
1.2.2 History of hidden Markov models................................3
1.2.3 Hidden Markov model and
hidden Markov random field model .............................5
1.3 Outline of the thesis.....................................................................8
2 HIDDEN MARKOV MODELS ( HMM’s) AND HIDDEN
MARKOV RANDOM FIELDS (HMRF’s)
2.1 Discrete time finite space Markov chain .....................................9
2.2 Examples of hidden Markov models...........................................10
2.3 Definition of the hidden Markov model......................................17
2.4 Definition of the hidden Markov random field model ................20
2.4.1 Markov random fields ..................................................20
2.4.2 Hidden Markov random field (HMRF) model .............26
3 INFERENCE IN HIDDEN MARKOV MODELS
3.1 Introduction .................................................................................29
3.2 Solutions to three estimation problems .......................................30
3.2.1 Problem 1 and its solution ............................................30
3.2.2 Problem 2 and its solution ............................................35
3.2.3 Problem 3 and its solution ............................................37
4 HIDDEN MARKOV MODEL AND THEIR APPLICATIONS
TO WEED COUNTS
4.1 Introduction .................................................................................43
4.2 Weed species composition ..........................................................44
4.2.1 Wild Oats......................................................................45
4.2.1.1 Effects on crop quality...................................45
4.2.2 Wild Buckwheat ...........................................................46
4.2.2.1 Effects on crop quality...................................47
4.2.3 Dandelion .....................................................................47
4.2.3.1 Effects on crop quality...................................47
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