Preface |
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xv | |
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1 | (10) |
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1.1 Motivating example: mapping river-blindness in Africa |
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1 | (4) |
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1.2 Empirical or mechanistic models |
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5 | (2) |
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1.3 What is in this book? |
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7 | (4) |
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2 Regression modelling for spatially referenced data |
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11 | (18) |
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2.1 Linear regression models |
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11 | (5) |
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2.1.1 Malnutrition in Ghana |
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13 | (3) |
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2.2 Generalised linear models |
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16 | (5) |
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2.2.1 Logistic Binomial regression: river-blindness in Liberia |
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16 | (4) |
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2.2.2 Log-linear Poisson regression: abundance of Anopheles Gambiae mosquitoes in Southern Cameroon |
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20 | (1) |
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2.3 Questioning the assumption of independence |
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21 | (8) |
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2.3.1 Testing for residual spatial correlation: the empirical variogram |
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24 | (5) |
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29 | (26) |
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29 | (2) |
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3.2 Families of spatial correlation functions |
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31 | (6) |
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3.2.1 The exponential family |
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31 | (1) |
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32 | (2) |
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3.2.3 The spherical family |
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34 | (1) |
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3.2.4 The theoretical variogram and the nugget variance |
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35 | (2) |
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3.3 Statistical inference |
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37 | (5) |
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3.3.1 Likelihood-based inference |
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38 | (4) |
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42 | (1) |
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43 | (1) |
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3.6 Approximations to Gaussian processes |
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44 | (11) |
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3.6.1 Low-rank approximations |
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45 | (3) |
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3.6.2 Gaussian Markov random field approximations via stochastic partial differential equations |
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48 | (7) |
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4 The linear geostatistical model |
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55 | (28) |
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55 | (2) |
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57 | (5) |
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4.2.1 Likelihood-based inference |
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57 | (1) |
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4.2.1.1 Maximum likelihood estimation |
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58 | (1) |
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59 | (2) |
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4.2.3 Trans-Gaussian models |
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61 | (1) |
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62 | (4) |
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4.3.1 Scenario 1: omission of the nugget effect |
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63 | (1) |
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4.3.2 Scenario 2: miss-specification of the smoothness parameter |
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64 | (1) |
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4.3.3 Scenario 3: non-Gaussian data |
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64 | (2) |
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66 | (4) |
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70 | (13) |
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4.5.1 Heavy metal monitoring in Galicia |
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70 | (5) |
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4.5.2 Malnutrition in Ghana (continued) |
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75 | (3) |
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4.5.2.1 Spatial predictions for the target population |
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78 | (5) |
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5 Generalised linear geostatistical models |
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83 | (22) |
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84 | (5) |
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85 | (2) |
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87 | (1) |
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5.1.3 Negative binomial sampling? |
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88 | (1) |
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89 | (4) |
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5.2.1 Likelihood-based inference |
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89 | (1) |
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5.2.1.1 Laplace approximation |
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89 | (1) |
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5.2.1.2 Monte Carlo maximum likelihood |
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90 | (1) |
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91 | (2) |
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93 | (1) |
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94 | (1) |
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95 | (4) |
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5.5.1 River-blindness in Liberia (continued) |
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95 | (3) |
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5.5.2 Abundance of Anopheles Gambiae mosquitoes in Southern Cameroon (continued) |
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98 | (1) |
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5.6 A link between geostatistical models and point processes |
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99 | (3) |
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5.7 A link between geostatistical models and spatially discrete processes |
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102 | (3) |
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105 | (18) |
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105 | (2) |
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107 | (1) |
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107 | (10) |
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6.3.1 Two extremes: completely random and completely regular designs |
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108 | (1) |
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109 | (1) |
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6.3.3 Inhibitory-plus-close-pairs designs |
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109 | (3) |
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6.3.3.1 Comparing designs: a simple example |
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112 | (2) |
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6.3.4 Modified regular lattice designs |
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114 | (1) |
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6.3.5 Application: rolling malaria indicator survey sampling in the Majete perimeter, southern Malawi |
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115 | (2) |
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117 | (3) |
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6.4.1 An adaptive design algorithm |
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118 | (2) |
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6.5 Application: sampling for malaria prevalence in the Majete perimeter (continued) |
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120 | (2) |
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122 | (1) |
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123 | (18) |
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123 | (2) |
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7.2 Preferential sampling methodology |
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125 | (5) |
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7.2.1 Non-uniform designs need not be preferential |
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126 | (1) |
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7.2.2 Adaptive designs need not be strongly preferential |
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126 | (1) |
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7.2.3 The Diggle, Menezes and Su model |
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127 | (1) |
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7.2.4 The Pati, Reich and Dunson model |
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127 | (1) |
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7.2.4.1 Monte Carlo maximum likelihood using stochastic partial differential equations |
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128 | (2) |
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7.3 Lead pollution in Galicia |
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130 | (4) |
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7.4 Mapping ozone concentration in Eastern United States |
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134 | (4) |
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138 | (3) |
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141 | (16) |
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8.1 Models with zero-inflation |
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141 | (3) |
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144 | (1) |
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145 | (1) |
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146 | (11) |
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8.4.1 River blindness mapping in Sudan and South Sudan |
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146 | (4) |
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8.4.2 Loa loa: mapping prevalence and intensity of infection |
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150 | (7) |
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9 Spatio-temporal geostatistical analysis |
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157 | (26) |
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158 | (2) |
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9.2 Is the sampling design preferential? |
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160 | (3) |
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9.3 Geostatistical methods for spatio-temporal analysis |
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163 | (8) |
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9.3.1 Exploratory analysis: the spatio-temporal variogram |
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164 | (2) |
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9.3.2 Diagnostics and novel extensions |
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166 | (1) |
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9.3.2.1 Example: a model for disease prevalence with temporally varying variance |
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167 | (1) |
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9.3.3 Defining targets for prediction |
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168 | (1) |
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9.3.4 Accounting for parameter uncertainty using classical methods of inference |
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168 | (2) |
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170 | (1) |
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9.4 Historical mapping of malaria prevalence in Senegal from 1905 to 2014 |
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171 | (9) |
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180 | (3) |
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10 Further topics in model-based geostatistics |
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183 | (16) |
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10.1 Combining data from multiple surveys |
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183 | (5) |
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10.1.1 Using school and community surveys to estimate malaria prevalence in Nyanza province, Kenya |
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184 | (4) |
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10.2 Combining multiple instruments |
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188 | (3) |
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10.2.1 Case I: Predicting prevalence for a gold-standard diagnostic |
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189 | (1) |
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10.2.2 Case II: Joint prediction of prevalence from two complementary diagnostics |
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190 | (1) |
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191 | (8) |
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191 | (4) |
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195 | (1) |
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10.3.2.1 Modelling of the sampling design |
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196 | (3) |
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199 | (32) |
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A Background statistical theory |
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201 | (1) |
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A.1 Probability distributions |
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201 | (22) |
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A.1.1 The Binomial distribution |
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202 | (1) |
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A.1.2 The Poisson distribution |
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202 | (1) |
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A.1.3 The Normal distribution |
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203 | (1) |
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A.1.4 Independent and dependent random variables |
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204 | (2) |
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A.2 Statistical models: responses, covariates, parameters and random effects |
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206 | (2) |
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A.3 Statistical inference |
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208 | (1) |
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A.3.1 The likelihood and log-likelihood functions |
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208 | (2) |
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A.3.2 Estimation, testing and prediction |
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210 | (1) |
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A.3.3 Classical inference |
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211 | (4) |
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215 | (1) |
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216 | (1) |
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217 | (1) |
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218 | (1) |
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A.4.2 Markov chain Monte Carlo |
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218 | (2) |
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A.4.3 Monte Carlo maximum likelihood |
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220 | (3) |
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223 | (8) |
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B.1 Handling vector data in R |
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223 | (4) |
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B.2 Handling raster data in R |
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227 | (4) |
References |
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231 | (12) |
Index |
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243 | |