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"A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics--origin, rates, and frequencies--of these phenomena. This comprehensive text introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine. Gidon Eshel begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. He then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams"--

Spatial analysis (Statistics) --- Analysis, Spatial (Statistics) --- Correlation (Statistics) --- Spatial systems --- EOF analysis. --- EOF. --- GramГchmidt orthogonalization. --- SVD analysis. --- SVD. --- astrophysics. --- autocorrelation functions. --- autocovariance. --- autoregressive model. --- climate science. --- column space. --- covariability matrix. --- data analysis. --- data matrices. --- degrees of freedom. --- deterministic science. --- ecology. --- eigen-decomposition. --- eigen-techniques. --- eigenanalysis. --- eigenvalues. --- empirical orthogonal functions. --- empirical science. --- empiricism. --- exercises. --- forward problem. --- geophysics. --- inverse problem. --- linear algebra. --- linear regression. --- matrices. --- matrix structure. --- matrix. --- medicine. --- multidimensional data sets. --- multidimensional data. --- nondeterministic phenomena. --- null space. --- phenomena. --- probability distribution. --- row space. --- singular value decomposition. --- spatiotemporal data. --- spectral representation. --- square matrices. --- statistics. --- stochastic processes. --- subjective decisions. --- theoretical science. --- time series. --- timescale. --- tornado. --- variables. --- vectors.

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This Special Issue of Entropy, titled “Recent Advances in Single-Particle Tracking: Experiment and Analysis”, contains a collection of 13 papers concerning different aspects of single-particle tracking, a popular experimental technique that has deeply penetrated molecular biology and statistical and chemical physics. Presenting original research, yet written in an accessible style, this collection will be useful for both newcomers to the field and more experienced researchers looking for some reference. Several papers are written by authorities in the field, and the topics cover aspects of experimental setups, analytical methods of tracking data analysis, a machine learning approach to data and, finally, some more general issues related to diffusion.

Research & information: general --- Physics --- diauxic growth --- replicator equation --- mesoscopic model --- integro-differential equations --- anomalous diffusion --- statistical analysis --- single-particle tracking --- trajectory classification --- fractional Brownian motion --- estimation --- autocovariance function --- neural network --- Monte Carlo simulations --- multifractional Brownian motion --- power of the statistical test --- machine learning classification --- feature engineering --- confinement --- information theory --- Brownian particle --- stochastic thermodynamics --- CTRW --- diffusing-diffusivity --- occupation time statistics --- wound healing dynamics --- single pseudo-particle tracking --- phase contrast image segmentation --- 3D single-particle tracking --- Fisher information --- non-uniform illumination --- SPT --- deep learning --- residual neural networks --- random walk --- heterogeneous --- endosomes --- single particle trajectory --- stochastic processes --- trapping --- diauxic growth --- replicator equation --- mesoscopic model --- integro-differential equations --- anomalous diffusion --- statistical analysis --- single-particle tracking --- trajectory classification --- fractional Brownian motion --- estimation --- autocovariance function --- neural network --- Monte Carlo simulations --- multifractional Brownian motion --- power of the statistical test --- machine learning classification --- feature engineering --- confinement --- information theory --- Brownian particle --- stochastic thermodynamics --- CTRW --- diffusing-diffusivity --- occupation time statistics --- wound healing dynamics --- single pseudo-particle tracking --- phase contrast image segmentation --- 3D single-particle tracking --- Fisher information --- non-uniform illumination --- SPT --- deep learning --- residual neural networks --- random walk --- heterogeneous --- endosomes --- single particle trajectory --- stochastic processes --- trapping

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The last decade has brought dramatic changes in the way that researchers analyze economic and financial time series. This book synthesizes these recent advances and makes them accessible to first-year graduate students. James Hamilton provides the first adequate text-book treatments of important innovations such as vector autoregressions, generalized method of moments, the economic and statistical consequences of unit roots, time-varying variances, and nonlinear time series models. In addition, he presents basic tools for analyzing dynamic systems (including linear representations, autocovariance generating functions, spectral analysis, and the Kalman filter) in a way that integrates economic theory with the practical difficulties of analyzing and interpreting real-world data. Time Series Analysis fills an important need for a textbook that integrates economic theory, econometrics, and new results. The book is intended to provide students and researchers with a self-contained survey of time series analysis. It starts from first principles and should be readily accessible to any beginning graduate student, while it is also intended to serve as a reference book for researchers.

519.246 --- Time-series analysis --- modeles economiques --- AA / International- internationaal --- 303.0 --- 304.0 --- 306.5 --- 519.55 --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Probabilities --- Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- economische modellen --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken). --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen. --- Statistische analyse (methodologie). --- 519.246 Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- Time-series analysis. --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen --- Statistische analyse (methodologie) --- Stochastic processes --- Statistical science --- Série chronologique --- Absolute summability. --- Autocovariance. --- Bartlett kernel. --- Block exogeneity. --- Cointegrating vector. --- Consumption spending. --- Cospectrum. --- Dickey-Fuller test. --- EM algorithm. --- Exchange rates. --- Filters. --- Fundamental innovation. --- Gamma distribution. --- Global identification. --- Gross national product. --- Hessian matrix. --- Inequality constraints. --- Invertibility. --- Jacobian matrix. --- Joint density. --- Khinchine's theorem. --- Kronecker product. --- Lagrange multiplier. --- Loss function. --- Mean-value theorem. --- Mixingales. --- Monte Carlo method. --- Newton-Raphson. --- Order in probability. --- Orthogonal. --- Permanent income. --- Quadrature spectrum. --- Recessions. --- Reduced form. --- Sample periodogram. --- Stock prices. --- Taylor series. --- Vech operator. --- Time series analysis

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Written by one of the leading experts in the field, this book focuses on the interplay between model specification, data collection, and econometric testing of dynamic asset pricing models. The first several chapters provide an in-depth treatment of the econometric methods used in analyzing financial time-series models. The remainder explores the goodness-of-fit of preference-based and no-arbitrage models of equity returns and the term structure of interest rates; equity and fixed-income derivatives prices; and the prices of defaultable securities. Singleton addresses the restrictions on t

Capital assets pricing model. --- Pricing --- Econometric models. --- Arbitrage. --- Asymptotic distribution. --- Autocorrelation. --- Autocovariance. --- Autoregressive conditional heteroskedasticity. --- Bayesian inference. --- Bayesian probability. --- Bond Yield. --- Capital asset pricing model. --- Central limit theorem. --- Collateral Value. --- Conditional expectation. --- Conditional probability distribution. --- Conditional variance. --- Consistent estimator. --- Correlation and dependence. --- Covariance function. --- Covariance matrix. --- Credit risk. --- Credit spread (options). --- Discount function. --- Discrete time and continuous time. --- Doubly stochastic model. --- Dynamic pricing. --- Econometric model. --- Economic equilibrium. --- Economics. --- Equity premium puzzle. --- Ergodic process. --- Estimation theory. --- Estimation. --- Estimator. --- Expectations hypothesis. --- Expected value. --- Forecasting. --- Forward price. --- Forward rate. --- General equilibrium theory. --- Generalized method of moments. --- High-yield debt. --- Inference. --- Interest rate risk. --- Interest rate. --- Investment Horizon. --- Investment strategy. --- Investor. --- Joint probability distribution. --- LIBOR market model. --- Leverage (finance). --- Likelihood function. --- Liquidity premium. --- Liquidity risk. --- Margin (finance). --- Marginal rate of substitution. --- Marginal utility. --- Market Risk Premium. --- Market capitalization. --- Market liquidity. --- Market portfolio. --- Market price. --- Market value. --- Markov model. --- Markov process. --- Mathematical finance. --- Monetary policy. --- Objective Probability. --- Option (finance). --- Parameter. --- Partial equilibrium. --- Portfolio insurance. --- Precautionary savings. --- Predictability. --- Preference (economics). --- Present value. --- Price index. --- Pricing. --- Principal component analysis. --- Probability. --- Real interest rate. --- Repurchase agreement. --- Revaluation of fixed assets. --- Risk aversion. --- Risk management. --- Risk premium. --- Skewness. --- Special case. --- Standard deviation. --- State variable. --- Statistic. --- Stochastic differential equation. --- Stochastic volatility. --- Supply (economics). --- Time series. --- Underlying Security. --- Utility maximization problem. --- Utility. --- Variable (mathematics). --- Vector autoregression. --- Yield curve. --- Yield spread.