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piazza r invitation probability data analysis physicists 2025

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Textbook in PDF format Preface Digging Into Data: a Primer in Statistics An (Apparent) Oxymoron, to Begin with A Kick-Off Meeting with Randomness The Passwords of Statistics Frequency Distributions Histograms Outlining a Distribution Mean Moments of a Distribution Standard Deviation and Skewness Statistics by Classes and Weighted Parameters A First Encounter with Brownian Motion Correlations Characteristic Scales and Scale Invariance Probability Basics Rules of Calculation Independent Events Conditional Probability Bayes' Theorem The Art of Combinatorics Counting Distinguishable Stuff Counting Indistinguishable Objects The Stirling Approximation Generalizing the Factorial: The Gamma Function Random Variables Probability Distributions for Discrete RVs Expectation, Variance and Higher Moments The Binomial Distribution The Poisson Distribution Probability Density for Continuous RVs Probability Density The Normal (or Gaussian) Distribution Cumulative Normal Distribution A Selection of Useful Distributions The Negative Binomial Distribution The Hypergeometric Distribution The Beta Distribution The Log-Normal Distribution The Weibull and Pareto Distributions A Multifaceted Distribution: The Generalized Gamma Extreme Values Probability: Accessories for Use Functions of a Random Variable Bivariate Distributions Joint and Marginal Distributions Independent Variables Conditional Distributions Expectation Values and Correlation Coefficients Continuous Variables Bivariate Normal Distribution Probability Distribution for a Function of Two RVs Complex Random Variables and Distributions Characteristic Function Some Properties of the Characteristic Function Characteristic Functions of Noteworthy Distributions A (Poor) Relative of \widetilde{f}(k)widetildef(k): The Moment Generating Function Cumulants: Why the Gaussian Is So ``Special'' The Central Limit Theorem (CLT) Probability and Information Statistical Entropy The Principle of Maximum Entropy Relative Entropy and Mutual Information The Problem of Continuous Variables Statistical Versus Thermodynamic Entropy Elements of Random Processes Mathematical Tools for Random Processes The Mean Function Correlation Functions Wide-Sense Stationarity and Ergodicity Spectral Density and the Wiener-Khinchine Theorem Random Pulse Sequences Noise Thermal Noise Shot Noise Colored Noise From Random Walk to Brownian Motion The Diffusion Limit The Langevin Equation Markov Processes The Master Equation The Fokker-Planck Equation The Ornstein-Uhlenbeck Process What Is Probability? Probability for the Theorist: Equiprobability and Beyond Probability for the Experimentalist: the Tormented Story of Frequentism The Law of Large Numbers Randomness and Algorithmic Complexity Subjective ma Non Troppo The Bayes Theorem, Cross and Delight of the Predictor From Bayes' Theorem to Subjective and Logical Probability Probability in Quantum Mechanics Noise and Bias in Measurements A Theorist's Little Guide to the Lab Measurement Setup Specs and Features of an Experimental Setup Noise Versus Errors Precision Versus Accuracy Is Noise Gaussian? Outliers Parameter Assessment Why Is It Worth Taking More Measurements? The Mean as an Estimator of the Expectation Estimating \sigma_xσx: The ``Adjusted'' Standard Deviation How to Report a Result Estimating Correlations Indirect Measurements Expectation of Y= f(X)Y= f(X) Functions of a Single Variable Functions of Several Variables Significant Figures Weighted Averages Small Samples Data Analysis and Model Testing The Maximum Likelihood (ML) Principle Chi-Squared Test Degrees of Freedom Distribution of the Chi-Squared Chi-Squared Test for a Distribution Maximum Likelihood or Maximum Entropy? Testing, Comparing, or Guessing a Relationship The Method of Least Squares Linear Relationships (or Reducible to Them) Regression Polynomial and Nonlinear Fits Chi-Squared Test for a Fit Benefits and Limits of the \chi^2χ Test Reversed Chi-Squared Test Hypotheses Non Fingo Is There a Signal? The Null Hypothesis The Neyman-Pearson Test Appendix Suggested Readings Appendix A Mathematical Notes Useful Functions (and False Friends) The Gamma Function The Beta Function The Dirac Delta Useful Integrals Numeric Tables Index

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Piazza R. An Invitation to Probability and Data Analysis for Physicists 2025.pdf 12.3 MB

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piazza r invitation probability data analysis physicists 2025

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