AN INTRODUCTION TO STATISTICAL INFERENCE AND DATA ANALYSIS
CONTENTS I BASIC CONCEPTS 1 1 BACKGROUND AND SCOPE 1 2 DATA, STATISTICS, AND PROBABILITY 1 3 R<LNDOM VARI<1BLCS 1 4 SUMMARY REFERENCES 2 EXPLORATORY DATA ANALYSIS 2 1 UNIVARIATE DATA 2 2 BIVARIME DAM 2 3 MU\RIVMIARC DAM 2 4 SUMMARY 3 DISTRIBUTIONS AND MODELS THEREOF 3 \ EMPIRICAL DIS(FIBMIONS 3 2 PARAMETRIC MODELS 3 3 WORKING WITH NORMAL AND LOGÓNORNWL DISTRIBUTIONS 3 4 FITTING DISR RIBUCIONS TO DAM 3 5 OTHER PROPERTIES OF DISTRIBUTIONS AND THEIR EVALUATION 3 6 SUMMARY 4 REGRESSION MODELING AND ANALYSIS 4 1 INTRODUCTION 4 2 SIMPLE LINEAR REGRESSION 4 3 MULTIPLE REGRESSION 4 4 NONPARAMCRRIC TRANSFORMATION AND REGRESSION 4 5 FIELD APPLICATION FOR NONPARAMETRIC REGRESSION: THE SALT CREEK DATA SEC 4 6 SUMMARY 1 MULTIVARIATE DATA ANALYSIS 5 1 INTRODUCTION 5 2 PRINCIPTLL COMPONENT ANALYSIS 5 3 CLUSTER ANALYSIS 5 4 DISCRIMINANT ANTILYSIS 5 5 FIDD APPLICATION: THE SALT CREEK DAM SET 5 6 SUMMARY FUNHER READING 6 UNCERTAINTY QUANTIFICATION 6 1 INTRODUCTION 6 2 UNCERR AINTY CHARACRERIWTION 6 3 UNCERTAINTY PROPAGATION 6 4 UNCERTAINTY IMPORTANCE ASSESSMENT 6 5 MOVING BEYOND MONTE CARLO SIMULATION 6 6 TREATMENT OF MODEL UNCENAINTY 6 7 ELEMENTS OF A GOOD UNCERTAINTY ANALYSIS STUDY 6 8 SUMMARY 7 EXPERIMENTAL DESIGN AND RESPONSE SURFACE ANALYSIS 7 1 GENERAL CONCEPTS 7 2 EXPERIMENTAL DESIGN 7 3 MEWMODELING TECHNIQUES 7 4 AN ILLUSTRATION OF EXPERIMENTAL DESIGN AND RESPONSE SURFACE MODELING 7 5 FIELD APPLICATION OF EXPERIMENTAL DESIGN AND RESPONSE SURFACE MODELING 7 6 SUMMARY FURTHER READING S DATA-DRIVEN MODELING 8 1 INTRODUCTION 8 2 MODELING APPROACHES 8 3 COMPUTATIONAL CONSIDERATIONS 8 4 FIELD EXAMPLE 8 5 SUMMARY 9 CONCLUDING REMARKS 9 1 THE PATH WE HAVE TAKEN 9 2 KEY TAKEAWAYS 9 3 FINAL THOUGHTS C H A P T E R BASIC CONCEPTS O U T L I N E 1 1 BACKGROUND AND SCOPE 1 1 1 WHAT IS STATISTICS? 1 1 2 WHAT IS BIG DATA ANALYTICS? 1 1 3 DATA ANALYSIS CYCLE 1 1 4 SOME APPLICATIONS IN THE PETROLEUM GEOSCIENCES 1 2 DATA, STATISTICS, AND PROBABILITY 1 2 1 OUTCOMES AND EVENTS 1 2 2 PROBABILITY 1 2 3 CONDITIONAL PROBABILITY AND BAYES RULE 1 3 RANDOM VARIABLES 1 3 1 DISCRETE CASE 1 3 2 CONTINUOUS CASE 1 3 3 INDICATOR TRANSFORM EXERCISES 1 1 BACKGROUND AND SCOPE WE INTRODUCE THE READER TO SOME FUNDAMENTAL CONCEPTS OF CLASSICAL STATISTICS SUCH AS PROB- ABILITY AND RANDOM VARIABLES, ALONG WITH BASIC CONCEPTS FROM THE EMERGING FIELD OF DATA ANALYTICS AND BIG-DATA TECHNOLOGIES WE ALSO LIST SOME TYPICAL APPLICATIONS OF THE RELEVANT TECHNIQUES FOR DATA ANALYSIS IN THE PETROLEUM GEOSCIENCES 1 1 1 WHAT IS STATISTICS? STATISTICS IS THE SCIENCE OF ACQUIRING AND UTILIZING DATA IT PROVIDES US WITH THE TOOLS FOR DATA COLLECTION, SUMMARIZATION, AND INTERPRETATION—WITH THE GOAL OF IDENTIFYING THE UNDERLYING STRUCTURE, TRENDS, AND RELATIONSHIPS INHERENT IN THE DATA THIS IS HOW WE CONVERT DATA INTO INFORMATION FUNDAMENTAL TO STATISTICS ARE THE CONCEPTS OF POPULATION AND SAMPLE A POPULATION IS THE UNIVERSE OF ALL POSSIBLE OUTCOMES AND EVENTS, WHEREAS A SAMPLE IS A FINITE SUBSET EXTRACTED SCHEMATIC SHOWING POPULATION—SAMPLE RELATIONSHIP