Theory of Probability: A Critical Introductory Treatment

  title={Theory of Probability: A Critical Introductory Treatment},
  author={Bruno de Finetti and Antonio Machi and Adrian J. Smith},
Part 7 A preliminary survey: heads and tails - preliminary considerations heads and tails - the random process laws of "large numbers" the "central limit theorem". Part 8 Random processes with independent increments: the case of asymptotic normality the Wiener-Levy process behaviour and asymptotic behaviour ruin problems ballot problems. Part 9 An introduction to other types of stochastic process: Markov processes stationary processes. Part 10 Problems in higher dimensions: second-order… 
Subjectivist (Bayesian) Theory
This chapter presents the third major view of probability and statistics, the subjectivist or Bayesian theory, which heavily depends on the use of data, or facts, that permit the Bayesians to contend that they have used facts in order to obtain adequate solutions to problems.
Scalable Gaussian process inference using variational methods
Various theoretical issues arising from the application of variational inference to the infinite dimensional Gaussian process setting are settled decisively and a new argument for existing approaches to variational regression that settles debate about their applicability is given.
Robust Simulation for Mega-Risks: The Path from Single-Solution to Competitive, Multi-Solution Methods for Mega-Risk Management
The Deductivist Theory of Probability and Statistics and Bayesian Theory are discussed, as well as some examples of Quantitative and Qualitative Examples, of how these theories can be applied to decision-making.
Practical Semiparametric Inference With Bayesian Nonparametric Ensembles
This thesis proposes Bayesian Nonparametric Ensemble (BNE), a general modeling approach that combines the a priori information encoded in candidate models using ensemble methods, and then addresses the systematic bias in the candidate models use Bayesian nonparametric machinery.
Decision making under partial information using precise and imprecise probabilistic models
This work recalls and discusses optimality criteria for decision making under uncertainty with respect to different assumptions concerning the structure of the information available and demonstrates how linear optimization theory can be used to construct algorithms for determining optimal decisions in finite decision problems.
Lectures on Statistics in Theory: Prelude to Statistics in Practice.
This is a writeup of lectures on "statistics" that have evolved from the 2009 Hadron Collider Physics Summer School at CERN to the forthcoming 2018 school at Fermilab. The emphasis is on foundations,
Exchangeable models of financial correlations matrices. Bayesian nonparametric models and network derived measures of financial assets
Abstract De Finetti theorem establishes the conceptual basis of Bayesian inference replacing the independent and identically distributed sampling hypothesis prevalent in frequentist statistics with
Statistical physics of inference: thresholds and algorithms
The connection between inference and statistical physics is currently witnessing an impressive renaissance and the current state-of-the-art is reviewed, with a pedagogical focus on the Ising model which, formulated as an inference problem, is called the planted spin glass.
"Take the Middle" - Averaging Prior and Evidence as Effective Heuristic in Bayesian Reasoning
This work investigates the adequacy of a cognitively plausible heuristic strategy, which amounts to approximately averaging the probability information on prior hypotheses and evidence, and compares this strategy to optimal Bayesian reasoning and to information-neglecting strategies by exploring the situational parameter space.
Deciding Koopman's qualitative probability
  • D. Mundici
  • Computer Science, Mathematics
    Artif. Intell.
  • 2021
The scope of this paper is much larger than that of PSAT, because Koopman's conjunctions K also formalize the key notion of independence, and also inferences in Koop man's probability theory are shown to be computable.