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Vor 2 Tagen · Set Theory: The Language of Probability. The mathematics of probability is expressed most naturally in terms of sets. This chapter lays out the basic terminology and reviews naive set theory: how to define and manipulate sets of things, operations on sets that yield other sets, special relationships among sets, and so on.
Vor 3 Tagen · We also introduce the notion of prediction methods and argue that all probabilities are outputs of such prediction methods. This helps to explain how the calibration criterion can be satisfied and to show that also supposedly objective probabilities are model-dependent. We compare our account of probability with common interpretations and show that it recovers key intuitions behind the latter ...
Vor 3 Tagen · Deductive reasoning—if logical—is as certain as mathematics can be. Much of the meat of Statistics, covered in other chapters, concerns inductive reasoning. Exceptional care is needed to draw reliable conclusions by inductive reasoning. And good inductive reasoning requires correct deductive reasoning, the subject of this chapter.
Vor 5 Tagen · Epistemology. Philosophy Of Language. Philosophy Of Religion. Logic. Research interests. Hájek's research interests include the philosophical foundations of probability and decision theory, epistemology, the philosophy of science, metaphysics, and the philosophy of religion.
Vor 5 Tagen · Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and elsewhere. Imprecise probability can be modelled in various ways, including by convex sets of probability distributions. We look at programming language models for imprecise probability. Our desiderata are that we would like our model to support all ...
Vor 6 Tagen · This course covers several fundamental topics in probability, providing a solid and broad foundation across the spectrum of the subject. The course reviews the foundations of probability theory, discusses random variables, conditional expectations, martingales, and Markov chains.
Vor einem Tag · Definition: Simple Rules of Probability. For any event 𝐴, if 𝑃 ( 𝐴) is the probability of event 𝐴 occurring, we have the following: The probability of event 𝐴 occurring is given by 𝑃 ( 𝐴) = 𝑛 ( 𝐴) 𝑛 ( 𝑆), where 𝑛 ( 𝐴) is the number of elements in event 𝐴 and 𝑛 ( 𝑆) is the number of elements in the sample space 𝑆.
