Preface |
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xi | |
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1 | (1) |
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Descriptive and Inferential Statistics |
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2 | (1) |
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Uncertainty about the Atmosphere |
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2 | (2) |
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4 | (2) |
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6 | (1) |
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The Elements of Probability |
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7 | (2) |
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7 | (1) |
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7 | (1) |
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The Axioms of Probability |
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8 | (1) |
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The Meaning of Probability |
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9 | (1) |
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9 | (1) |
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Bayesian (Subjective) Interpretation |
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9 | (1) |
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Some Properties of Probability |
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10 | (11) |
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Domain, Subsets, Complements, and Unions |
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10 | (2) |
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12 | (2) |
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14 | (2) |
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16 | (1) |
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17 | (2) |
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19 | (2) |
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Empirical Distributions and Exploratory Data Analysis |
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21 | (3) |
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Robustness and Resistance |
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21 | (1) |
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22 | (2) |
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Numerical Summary Measures |
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24 | (3) |
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24 | (1) |
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25 | (1) |
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26 | (1) |
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Graphical Summary Techniques |
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27 | (9) |
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27 | (2) |
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29 | (1) |
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30 | (3) |
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33 | (1) |
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33 | (1) |
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Cumulative Frequency Distributions |
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34 | (2) |
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36 | (8) |
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37 | (4) |
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41 | (3) |
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Exploratory Techniques for Paired Data |
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44 | (10) |
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44 | (1) |
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Pearson (``Ordinary'') Correlation |
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45 | (5) |
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50 | (1) |
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51 | (2) |
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53 | (1) |
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Exploratory Techniques for Higher-Dimensional Data |
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54 | (10) |
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55 | (2) |
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57 | (2) |
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59 | (3) |
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62 | (2) |
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Theoretical Probability Distributions |
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64 | (2) |
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What Is a Theoretical Distribution? |
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65 | (1) |
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Parameters versus Statistics |
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65 | (1) |
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Discrete versus Continuous Distributions |
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66 | (1) |
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66 | (8) |
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66 | (4) |
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70 | (1) |
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71 | (3) |
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74 | (2) |
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Expected Value of a Random Variable |
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74 | (1) |
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Expected Value of a Function of a Random Variable |
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74 | (2) |
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76 | (23) |
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Distribution Functions and Expected Values |
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76 | (3) |
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79 | (7) |
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86 | (7) |
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93 | (2) |
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95 | (1) |
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95 | (2) |
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97 | (2) |
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Multivariate Probability Distributions |
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99 | (5) |
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Bivariate Normal Distribution |
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99 | (3) |
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Multivariate Normal Distribution |
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102 | (2) |
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Qualitative Assessments of the Goodness of Fit |
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104 | (4) |
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Superposition of a Fitted Theoretical Distribution and Data Histogram |
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104 | (2) |
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106 | (2) |
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Parameter Fitting Using Maximum Likelihood |
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108 | (6) |
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111 | (3) |
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114 | (7) |
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Parametric versus Nonparametric Tests |
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114 | (1) |
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The Sampling Distribution |
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115 | (1) |
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The Elements of Any Hypothesis Test |
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115 | (1) |
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116 | (1) |
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Error Types and the Power of a Test |
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116 | (1) |
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One-Sided versus Two-Sided Tests |
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117 | (1) |
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Confidence Intervals: Inverting Hypothesis Tests |
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118 | (3) |
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121 | (16) |
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121 | (1) |
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Tests for Differences of Mean under Independence |
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122 | (3) |
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Tests for Differences of Mean under Serial Dependence |
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125 | (4) |
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129 | (6) |
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135 | (2) |
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137 | (14) |
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``Classical'' Nonparametric Tests for Location |
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138 | (7) |
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145 | (6) |
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Field Significance and Multiplicity |
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151 | (8) |
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The Multiplicity Problem for Independent Tests |
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151 | (1) |
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Field Significance Given Spatial Correlation |
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152 | (5) |
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157 | (2) |
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Statistical Weather Forecasting |
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159 | (1) |
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Review of Least-Squares Regression |
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160 | (21) |
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160 | (3) |
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Distribution of the Residuals |
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163 | (2) |
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The Analysis-of-Variance Table |
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165 | (1) |
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166 | (2) |
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Sampling Distributions of the Regression Coefficients |
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168 | (3) |
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171 | (4) |
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175 | (6) |
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Objective Forecasts---Without NWP |
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181 | (18) |
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Stratification and Compositing |
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182 | (1) |
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When the Predictand Is a Probability |
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182 | (3) |
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185 | (3) |
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188 | (1) |
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189 | (5) |
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194 | (4) |
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198 | (1) |
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Objective Forecasts---With NWP |
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199 | (11) |
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200 | (1) |
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Model Output Statistics (MOS) Forecasts |
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201 | (1) |
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Comparisons between the Classical, Perfect Prog, and MOS Approaches |
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202 | (7) |
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Operational MOS Forecasts |
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209 | (1) |
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Probabilistic Field (Ensemble) Forecasts |
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210 | (11) |
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Stochastic Dynamic Forecasts |
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211 | (2) |
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213 | (2) |
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Choosing Initial Ensemble Members |
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215 | (1) |
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216 | (1) |
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Dispersion of the Ensemble |
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217 | (4) |
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Subjective Probability Forecasts |
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221 | (12) |
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The Subjective Distribution |
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223 | (2) |
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Credible Interval Forecasts |
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225 | (2) |
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Assessing Discrete Probabilities |
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227 | (2) |
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Assessing Continuous Distributions |
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229 | (1) |
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230 | (3) |
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233 | (5) |
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Purposes of Forecast Verification |
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233 | (1) |
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Factorization of the Joint Distribution of Forecasts and Observations |
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234 | (1) |
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Scalar Attributes of Forecast Performance |
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235 | (2) |
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237 | (1) |
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Categorical Forecasts of Discrete Predictands |
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238 | (12) |
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238 | (1) |
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Accuracy Measures for Binary Forecasts |
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239 | (2) |
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241 | (1) |
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Accuracy Measures for Multicategory Forecasts |
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242 | (2) |
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Conversion of Probabilistic to Categorical Forecasts |
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244 | (4) |
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Skill Measures for Contingency Tables |
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248 | (2) |
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Categorical Forecasts of Continuous Predictands |
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250 | (8) |
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Conditional Quantile Plots |
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251 | (1) |
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251 | (4) |
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255 | (2) |
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Skill in Probability Space |
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257 | (1) |
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258 | (14) |
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259 | (1) |
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259 | (1) |
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Algebraic Decomposition of the Brier Score |
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260 | (3) |
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263 | (2) |
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265 | (2) |
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Hedging and Strictly Proper Scoring Rules |
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267 | (1) |
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Probability Forecasts for Multicategory Events |
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268 | (1) |
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269 | (3) |
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Categorical Forecasts of Fields |
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272 | (12) |
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274 | (1) |
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275 | (2) |
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277 | (4) |
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281 | (3) |
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284 | (3) |
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284 | (1) |
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285 | (1) |
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Time-Domain versus Frequency-Domain Approaches |
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286 | (1) |
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Time Domain. I. Discrete Data |
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287 | (15) |
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287 | (1) |
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Two-State, First-Order Markov Chains |
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288 | (4) |
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Test for Independence versus First-Order Serial Dependence |
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292 | (3) |
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Some Applications of Two-State Markov Chains |
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295 | (2) |
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297 | (1) |
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Higher-Order Markov Chains |
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298 | (2) |
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Deciding among Alternative Orders of Markov Chains |
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300 | (2) |
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Time Domain. II. Continuous Data |
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302 | (23) |
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First-Order Autoregression |
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302 | (6) |
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Higher-Order Autoregression |
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308 | (5) |
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313 | (2) |
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The Variance of a Time Average |
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315 | (3) |
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Autoregressive Moving-Average Models |
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318 | (1) |
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Simulation and Forecasting with Time-Domain Models |
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319 | (4) |
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Multivariate Autoregressions |
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323 | (2) |
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Frequency Domain. I. Harmonic Analysis |
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325 | (16) |
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Cosine and Sine Functions |
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325 | (1) |
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Representing a Simple Time Series with a Harmonic Function |
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326 | (4) |
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Estimation of the Amplitude and Phase of a Single Harmonic |
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330 | (3) |
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333 | (3) |
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336 | (3) |
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The Harmonic Functions as Uncorrelated Regression Predictors |
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339 | (2) |
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Frequency Domain. II. Spectral Analysis |
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341 | (18) |
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The Periodogram or Fourier Line Spectrum |
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341 | (5) |
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346 | (1) |
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347 | (3) |
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Sampling Properties of Spectral Estimates |
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350 | (2) |
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Theoretical Spectra of Autoregressive Models |
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352 | (5) |
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357 | (2) |
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Methods for Multivariate Data |
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359 | (1) |
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360 | (13) |
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360 | (2) |
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362 | (11) |
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Principal-Component (EOF) Analysis |
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373 | (25) |
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374 | (4) |
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Truncation of the Principal Components |
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378 | (2) |
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How Many Principal Components Should Be Retained? |
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380 | (3) |
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PCA Based on the Covariance Matrix versus the Correlation Matrix |
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383 | (3) |
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Application of PCA to Fields |
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386 | (7) |
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Rotation of the Eigenvectors |
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393 | (1) |
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The Varied Terminology of PCA |
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394 | (3) |
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Scaling Conventions in PCA |
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397 | (1) |
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Canonical Correlation Analysis |
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398 | (10) |
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399 | (1) |
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400 | (3) |
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403 | (1) |
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403 | (5) |
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408 | (11) |
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Linear Discriminant Analysis |
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409 | (6) |
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Multiple Discriminant Analysis |
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415 | (4) |
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419 | (10) |
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Distance Measures and Clustering Methods |
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420 | (3) |
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The Dendrogram, or Tree Diagram |
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423 | (1) |
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424 | (3) |
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427 | (2) |
Appendix A: Example Data Sets |
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429 | (3) |
Appendix B: Probability Tables |
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432 | (7) |
Appendix C: Answers to Exercises |
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439 | (5) |
References |
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444 | (11) |
Index |
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455 | (10) |
International Geophysics Series |
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465 | |