Data Analysis and Statistics for Geography, Environmental Science, and Engineering By Miguel F. Acevedo (informative)

Free download Data Analysis and Statistics for Geography, Environmental Science, and Engineering By Miguel F. Acevedo
Authors of: Data analysis and statistics for Geography, Environmental Science, and Engineering By Miguel F. Acevedo
Miguel F. Acevedo
Table of Contents in Data analysis and statistics for Geography, Environmental Science, and Engineering By Miguel F. Acevedo
Chapter 1 – Introduction
* Overview of statistical methods and their applications.
* Importance of data analysis in various fields.
* Objectives and scope of the book.
Chapter 2 – Probability Theory
* Basic concepts: probability, outcomes, events, and sample spaces.
* Rules of probability, including addition and multiplication rules.
* Conditional probability and Bayes’ theorem.
* Discrete and continuous probability distributions.
* Applications of probability theory in data analysis.
Chapter 3 – Random Variables, Distributions, Moments, and Statistics
* Definition and types of random variables (discrete and continuous).
* Common probability distributions (e.g., Binomial, Poisson, Normal).
* Moments: mean, variance, skewness, and kurtosis.
* Descriptive statistics and their role in data summarization.
Chapter 4 – Exploratory Analysis and Introduction to Inferential Statistics
* Techniques for summarizing and visualizing data (e.g., histograms, box plots).
* Measures of central tendency and variability.
* Introduction to hypothesis testing and confidence intervals.
* Significance levels and p-values.
Chapter 5 – More on Inferential Statistics: Goodness of Fit, Contingency Analysis, and Analysis of Variance
* Goodness-of-fit tests: Chi-square and Kolmogorov-Smirnov.
* Contingency tables and association tests.
* Analysis of variance (ANOVA) and its assumptions.
* Comparing multiple group means.
Chapter 6 – Regression
* Simple and multiple linear regression models.
* Estimating coefficients and interpreting results.
* Diagnostic checks: residual analysis and multicollinearity.
* Applications in predicting and modeling relationships.
Chapter 7 – Stochastic or Random Processes and Time Series
* Definition and types of stochastic processes.
* Stationarity and ergodicity concepts.
* Time series analysis: trend, seasonality, and noise.
* Autoregressive (AR), Moving Average (MA), and ARIMA models.
Chapter 8 – Spatial Point Patterns
* Definition and types of spatial point processes.
* Analyzing spatial distributions: clustering, dispersion, and randomness.
* Methods for detecting spatial patterns (e.g., Ripley’s K-function).
* Applications in geographical and environmental studies.
Chapter 9 – Matrices and Linear Algebra
* Basic matrix operations: addition, multiplication, and inversion.
* Eigenvalues and eigenvectors.
* Solving linear systems and applications in multivariate statistics.
* Decompositions: LU, QR, and Singular Value Decomposition (SVD).
Chapter 10 – Multivariate Models
* Overview of multivariate data and analysis.
* Multivariate normal distribution and its properties.
* Methods for modeling multiple dependent variables.
* Applications in pattern recognition and classification.
Chapter 11 – Dependent Stochastic Processes and Time Series
* Modeling time-dependent data with stochastic processes.
* Covariance and correlation structures in time series.
* Multivariate time series models (e.g., Vector Autoregression – VAR).
* Forecasting methods and model validation.
Chapter 12 – Geostatistics: Kriging
* Introduction to geostatistical methods.
* Kriging: basic concepts and assumptions.
* Variogram analysis and model fitting.
* Spatial interpolation techniques.
* Applications in environmental and geospatial data analysis.
Chapter 13 – Spatial Auto-Correlation and Auto-Regression
* Measuring spatial dependence: Moran’s I and Geary’s C.
* Spatial autoregressive models (SAR).
* Spatial error models (SEM).
* Testing for spatial autocorrelation.
Chapter 14 – Multivariate Analysis I: Reducing Dimensionality
* Principal Component Analysis (PCA) and its interpretation.
* Factor analysis: identifying latent variables.
* Multidimensional scaling (MDS) for data visualization.
* Applications in reducing noise and simplifying complex data.
Chapter 15 – Multivariate Analysis II: Identifying and Developing Relationships among Observations and Variables
* Canonical correlation analysis for examining linear relationships.
* Discriminant analysis for classification.
* Cluster analysis to group similar observations.
* Structural equation modeling (SEM) for complex relationship analysis.
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