Statistical eyeglasses : the math behind scientific knowledge, The
Mathematical physics Physics Science
IOP Publishing
2018
EISBN 9781643271507
1. Models of nature.
2. Randomness.
2.1. What is random?.
2.2. How does randomness show up in nature?.
2.3. Random and deterministic signals.
2.4. From noisy data to the likelihood function
3. Bayesian and frequentist approaches to scientific inference.
3.1. Bayes' theorem.
3.2. The same game, and a mysterious result.
3.3. Statistical descriptors
4. The principles of inferential statistics.
4.1. Bayes and the likelihood function.
4.2. The 'least informative prior'.
4.3. The principles of inferential statistics
5. Parametric inference.
5.1. Bayesian parametric inference.
5.2. Frequentist parametric inference
6. Prior distributions and equiprobable events in the physical sciences.
6.1. Elementary Monte Carlo method.
6.2. Transformations of random variables by Monte Carlo.
6.3. Bertrand's paradox.
7. Conclusions : the statistical nature of scientific knowledge.
Science often deals with hard-to-see phenomena, and they only stand out and become real when viewed through the lens of complex statistical tools. This book is not a textbook about statistics applied to science--there are already many excellent books to choose from--rather, it gives an overview of the basic principles that physical scientists use to analyze their data and bring out the order of Nature from the fog of background noise.
2. Randomness.
2.1. What is random?.
2.2. How does randomness show up in nature?.
2.3. Random and deterministic signals.
2.4. From noisy data to the likelihood function
3. Bayesian and frequentist approaches to scientific inference.
3.1. Bayes' theorem.
3.2. The same game, and a mysterious result.
3.3. Statistical descriptors
4. The principles of inferential statistics.
4.1. Bayes and the likelihood function.
4.2. The 'least informative prior'.
4.3. The principles of inferential statistics
5. Parametric inference.
5.1. Bayesian parametric inference.
5.2. Frequentist parametric inference
6. Prior distributions and equiprobable events in the physical sciences.
6.1. Elementary Monte Carlo method.
6.2. Transformations of random variables by Monte Carlo.
6.3. Bertrand's paradox.
7. Conclusions : the statistical nature of scientific knowledge.
Science often deals with hard-to-see phenomena, and they only stand out and become real when viewed through the lens of complex statistical tools. This book is not a textbook about statistics applied to science--there are already many excellent books to choose from--rather, it gives an overview of the basic principles that physical scientists use to analyze their data and bring out the order of Nature from the fog of background noise.
