ALBERT

Description / Table of Contents: Contents: PART 1 FUNDAMENTAL CONCEPTS. - 1 Introduction. - 1.1 Climate archives, variables and dating. - 1.2 Noise and statistical distribution. - 1.3 Persistence. - 1.4 Spacing. - 1.5 Aim and structure of this book. - 1.6 Background material. - 2 Persistence models. - 2.1 First-Order Autoregressive Model. - 2.1.1 Even spacing. - 2.1.2 Uneven Spacing. - 2.2 Second-Order Autoregressive Model. - 2.3 Mixed Autoregressive Moving Average Model. - 2.4 Other models. - 2.4.1 Long-memory process. - 2.4.2 Nonlinear and non-gaussian models. - 2.5 Climate theory. - 2.5.1 Stochastic climate models. - 2.5.2 Long memory of temperature fluctuations?. - 2.5.3 Long memory of river runoff. - 2.6 Background material. - 2.7 Technical issues. - 3 Bootstrap confidence intervals. - 3.1 Error bars and confidence intervals. - 3.1.1 Theoretical example: Mean estimation of Gaussian White Noise. - 3.1.2 Theoretical example: Standard deviation estimation of Gaussian White Noise. - 3.1.3 Real world. - 3.2 Bootstrap principle. - 3.3 Bootstrap resampling. - 3.3.1 Nonparametric: Moving block bootstrap. - 3.3.2 Parametric: Autoregressive Bootstrap. - 3.3.3 Parametric: Surrogate Data. - 3.4 Bootstrap Confidence Intervals. - 3.4.1 Normal confidence interval. - 3.4.2 Student's t confidence interval. - 3.4.3 Percentile confidence interval. - 3.4.4 BCa Confidence Interval. - 3.5 Examples. - 3.6 Bootstrap hypothesis tests. - 3.7 Notation. - 3.8 Background material. - 3.9 Technical issues. - PART 2 UNIVARIATE TIME SERIES. - 4 Regression I. - 4.1 Linear regression. - 4.1.1 Weighted least-squares and ordinary least-squares estimation. - 4.1.2 Generalized least-squares estimation. - 4.1.3 Other estimation types. - 4.1.4 Classical confidence intervals. - 4.1.5 Bootstrap confidence intervals. - 4.1.6 Monte Carlo Experiments: Ordinary least-squares estimation. - 4.1.7 Timescale errors. - 4.2 Nonlinear regression. - 4.2.1 Climate Transition Model: Ramp. - 4.2.2 Trend-Change Model: Break. - 4.3 Nonparametric regression or smoothing. - 4.3.1 Kernel estimation. - 4.3.2 Bootstrap confidence intervals and bands. - 4.3.3 Extremes or outlier detection. - 4.4 Background material. - 4.5 Technical issues. - 5 Spectral analysis. - 5.1 Spectrum. - 5.1.1 Example: AR(1) process, discrete time. - 5.1.2 Example: AR(2) process, discrete time. - 5.1.3 Physical meaning. - 5.2 Spectral estimation. - 5.2.1 Periodogram. - 5.2.2 Welch's overlapped segment averaging. - 5.2.3 Multitaper estimation. - 5.2.4 Lomb-Scargle estimation. - 5.2.5 Peak detection: red-noise hypthesis. - 5.2.6 Example: Peaks in monsoon spectrum. - 5.2.7 Aliasing. - 5.2.8 Timescale errors. - 5.2.9 Example: Peaks in monsoon spectrum (continued). - 5.3 Background material. - 5.4 Technical Issues. - 6 Extreme value time series. - 6.1 Data types. - 6.1.1 Event times. - 6.1.2 Peaks over threshold. - 6.1.3 Block extremes. - 6.1.4 Remarks on data selection. - 6.2 Stationary models. - 6.2.1 Generalized extreme value distribution. - 6.2.2 Generalized pareto distribution. - 6.2.3 Bootstrap confidence intervals. - 6.2.4 Example: Elbe summer floods, 1852-2002. - 6.2.5 Persisitence. - 6.2.6 Remark: Tail estimation. - 6.2.7 Remark: Optimal estimation. - 6.3 Nonstationary models. - 6.3.1 Time-dependent generalized extreme value distribution. - 6.3.2 Inhomogenous poisson process. - 6.3.3 Hybrid: Poisson-Extreme value distribution. - 6.4 Sampling and time spacing. - 6.5 Background material. - 6.6 Technical issues. - PART 3 BIVARIATE TIME SERIES. - 7. Correlation. - 7.1 Pearson's Correlation Coefficient. - 7.1.1 Remark: Alternative correlation measures. - 7.1.2 Classical confidence intervals, nonpersistent processes. - 7.1.3 Bivariate time series models. - 7 .1.4 Classical Confidence Intervals, Persistent Processes. - 7.1.5 Bootstrap Confidence Intervals. - 7.2 Spearman's Rank Correlation Coefficient. - 7.2.1 Classical Confidence Intervals, Nonpersistent Processes. - 7.2.2 Classical Confidence Intervals, Persistent Processes. - 7.2.3 Bootstrap Confidence Intervals. - 7.3 Monte Carlo Experiments. - 7.4 Example: Elbe Runoff Variations. - 7.5 Unequal Timescales. - 7.5.1 Binned Correlation. - 7.5.2 Synchrony Correlation. - 7.5.3 Monte Carlo Experiments. - 7.5.4 Example: Vostok Ice Core Records. - 7.6 Background Material. - 7. 7 Technical Issues. - 8 Regression II. - 8.1 Linear Regression. - 8.1.1 Ordinary Least-Squares Estimation. - 8.1.2 Weighted Least-Squares for Both Variables Estimation. - 8.1.3 Wald-Bartlett Procedure. - 8.2 Bootstrap Confidence lntervals. - 8.2.1 Simulating Incomplete Prior Knowledge. - 8.3 Monte Carlo Experiments. - 8.3.1 Easy Setting. - 8.3.2 Realistic Setting: Incomplete Prior Knowledge. - 8.3.3 Dependence on Accuracy of Prior Knowledge. - 8.3.4 Mis-Specified Prior Knowledge. - 8.4 Example: Climate Sensitivity. - 8.5 Prediction. - 8.5.1 Example: Calibration of a Proxy Variable. - 8.6 Lagged Regression. - 8.6.1 Example: CO2 and Temperature Variations in the Pleistocene. - 8.7 Background Material. - 8.8 Technical Issues. - PART 4 OUTLOOK. - 9 Future Directions. - 9 .1 Timescale Modeling. - 9.2 Novel Estimation Problems. - 9.3 Higher Dimensions. - 9.4 Climate Models. - 9.4.1 Fitting Climate Models to Observations. - 9.4.2 Forecasting with Climate Models. - 9.4.3 Design of the Cost Function. - 9.4.4 Climate Model Bias. -9.5 Optimal Estimation. - 9.6 Background Material. - References. - Author Index. - Subject Index.

Description / Table of Contents: Climate is a paradigm of a complex system. Analysing climate data is an exciting challenge, which is increased by non-normal distributional shape, serial dependence, uneven spacing and timescale uncertainties. This book presents bootstrap resampling as a computing-intensive method able to meet the challenge. It shows the bootstrap to perform reliably in the most important statistical estimation techniques: regression, spectral analysis, extreme values and correlation. This book is written for climatologists and applied statisticians. It explains step by step the bootstrap algorithms (including novel adaptions) and methods for confidence interval construction. It tests the accuracy of the algorithms by means of Monte Carlo experiments. It analyses a large array of climate time series, giving a detailed account on the data and the associated climatological questions.