Applied statistical modeling and data analytics: a practical guide for the petroleum geosciences

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Cover Half-Title Page APPLIED STATISTICAL MODELING AND DATA ANALYTICS: A Practical Guide for the Petroleum Geosciences Copyright Dedication Contents Preface Acknowledgments 1: Basic Concepts Background and Scope What Is Statistics? What Is Big Data Analytics? Data Analysis Cycle Some Applications in the Petroleum Geosciences Data, Statistics, and Probability Outcomes and Events Probability Conditional Probability and Bayes Rule Random Variables Discrete Case Continuous Case Indicator Transform Summary Exercises References 2: Exploratory Data Analysis Univariate Data Measures of Center Measures of Spread Measures of Asymmetry Graphing Univariate Data Bivariate Data Covariance Correlation and Rank Correlation Graphing Bivariate Data Multivariate Data Summary Exercises References 3: Distributions and Models Thereof Empirical Distributions Histogram Quantile Plot Parametric Models Uniform Distribution Triangular Distribution Normal Distribution Lognormal Distribution Poisson Distribution Exponential Distribution Binomial Distribution Weibull Distribution Beta Distribution Working With Normal and Log-Normal Distributions Normal Distribution Normal Score Transformation Log-Normal Distribution Fitting Distributions to Data Probability Plots Parameter Estimation Techniques Linear Regression Analysis Method of Moments Nonlinear Least-Squares Analysis Other Properties of Distributions and Their Evaluation Central Limit Theorem and Confidence Limits Bootstrap Sampling Comparing Two Distributions Q-Q Plot Testing for Difference in Mean Testing for Difference in Distributions Other Methods for Comparing Distributions Summary Exercises References 4: Regression Modeling and Analysis Introduction Simple Linear Regression Formulating and Solving the Linear Regression Problem Evaluating the Linear Regression Model Properties of the Regression Parameters and Confidence Limits Estimating Confidence Intervals for the Mean Response and Forecast An Illustrative Example of Linear Regression Modeling and Analysis Multiple Regression Formulating and Solving the Multiple Regression Model Evaluating the Multiple Regression Model How Many Terms in the Regression Model? Analysis of Variance (ANOVA) Table An Illustrative Example of Multiple Regression Modeling and Analysis Nonparametric Transformation and Regression Conditional Expectation and Scatterplot Smoothers Generalized Additive Models Response Transformation Models: ACE Algorithm and Its Variations Data Correlation via Nonparametric Transformation Field Application for Nonparametric Regression: The Salt Creek Data Set Dataset Description Variable Selection Optimal Transformations and Optimal Correlation Summary Exercises References 5: Multivariate Data Analysis Introduction Principal Component Analysis Computing the Principal Components An Illustrative Example of the Principal Component Analysis Cluster Analysis k-Means Clustering An Illustrative Example of k-Means Clustering Hierarchical Clustering An Illustrative Example of Hierarchical Clustering Model-Based Clustering Discriminant Analysis An Illustrative Example of Discriminant Analysis Field Application: The Salt Creek Data Set Dataset Description PCA Cluster Analysis Data Correlation and Prediction Summary Exercises References Further Reading 6: Uncertainty Quantification Introduction Deterministic Versus Probabilistic Approach Elements of a Systematic Framework Role of Monte Carlo Simulation Uncertainty Characterization Screening for Key Uncertain Inputs Fitting Distributions to Data Maximum Entropy Distribution Selection Generation of Subjective Probability Distributions Problem of Scale Uncertainty Propagation Sampling Methods Random Sampling Latin Hypercube Sampling Correlation Control in LHS Computational Considerations Number of Samples Visualization of Results Uncertainty Importance Assessment Basic Concepts in Uncertainty Importance Scatter Plots and Rank Correlation Analysis Stepwise Regression and Partial Rank Correlation Analysis Other Measures of Variable Importance Entropy (Mutual Information) Analysis Classification Tree Analysis Moving Beyond Monte Carlo Simulation First-Order Second-Moment Method (FOSM) General Expressions for Mean and Variance Error Analysis in Additive and Multiplicative Models Point Estimate Method (PEM) Logic Tree Analysis (LTA) Treatment of Model Uncertainty Basic Concepts Moment-Matching Weighting Method for Geostatistical Models Example Field Application Elements of a Good Uncertainty Analysis Study Summary Exercises References 7: Experimental Design and Response Surface Analysis General Concepts Experimental Design Factorial Designs Plackett-Burman Central Composite and Box-Behnken Augmented Pairs Comparison of Factorial Designs Sampling Designs Purely Random Design Latin Hypercube Sampling Maximin LHS Maximum Entropy Design Comparison of Sampling Designs Metamodeling Techniques Quadratic Model Quadratic Model With LASSO Variable Selection Kriging Model Radial Basis Functions Metamodel Performance Evaluation Metric An Illustration of Experimental Design and Response Surface Modeling Field Application of Experimental Design and Response Surface Modeling Problem of Interest Proxy Construction and Application Strategy Field Case Study Summary Exercises References Further Reading 8: Data-Driven Modeling Introduction Preliminaries Data-Driven Models-What and Why? Our Philosophy Modeling Approaches Classification and Regression Trees Random Forest Gradient Boosting Machine Support Vector Machine Artificial Neural Network Model Strengths and Weaknesses Computational Considerations Model Evaluation Automatic Tuning of Model Parameters Variable Importance Model Aggregation Field Example Dataset Description Predictive Model Building Variable Importance and Conditional Sensitivity Classification Tree Analysis Summary Exercises References 9: Concluding Remarks The Path We Have Taken Recapitulation of Topics Style and Intended Use Resources Key Takeaways Which Variables? Simple Model, or Complex? One Model, or Many? Is Past Always Prolog? To Fit, or Overfit? Final Thoughts References Index Back Cover