Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide...

This book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The...

This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III pr...

This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of ...

This book summarizes the vast amount of research related to teaching and learning probability that has been conducted for more than 50 years in a variety of disciplines. It begins with a synthesis of the most important probability interpretations throughout history: intuitive, classical, frequentist, subjective, logical propensity and axiomatic vie...

This book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear,...

This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them...

If you know how to program with Python and also know a little about probability, you're ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the ...

This book is aimed at computer science undergraduates late in sophomore or early in junior year, supplying a comprehensive background in qualitative and quantitative data analysis, probability, random variables, and statistical methods, including machine learning.With careful treatment of topics that fill the curricular needs for the course, Probab...

The ideal reader for this book will be quantitatively literate and has a basic understanding of statistical concepts and R programming. The book gives a rigorous treatment of the elementary concepts in statistical inference from a classical frequentist perspective. After reading this book and performing the exercises, the student will understand th...

This is a free textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University - Pueblo in the spring semester of 2017....

Statistics is quickly becoming the most important and multi-disciplinary field of mathematics. According to the American Statistical Association, statistician is one of the top ten fastest-growing occupations and statistics is one of the fastest-growing bachelor degrees. Statistical literacy is essential to our data driven society.
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