Search results for "Bayesian Inference"
showing 10 items of 120 documents
Facilitating Effect of Natural Frequencies: Size Does Not Matter
2009
The question of whether humans are able to work in a Bayesian way is currently a topic of substantial investigation. An important finding, reported by Gigerenzer and Hoffrage in 1995 is that Bayesian reasoning is facilitated when the information format corresponds to natural frequencies. The present concern was whether the facilitating effect of frequencies persists when natural frequencies relate to samples which are not convenient multiples of 10. 150 undergraduates participated as volunteers (42 men, 108 women; M age = 23 yr.). Analysis showed the effect of natural frequency formats was not dependent on size of reference class. Theoretical and practical implications are discussed.
Thompson Sampling Guided Stochastic Searching on the Line for Non-stationary Adversarial Learning
2015
This paper reports the first known solution to the N-Door puzzle when the environment is both non-stationary and deceptive (adversarial learning). The Multi-Armed-Bandit (MAB) problem is the iconic representation of the exploration versus exploitation dilemma. In brief, a gambler repeatedly selects and play, one out of N possible slot machines or arms and either receives a reward or a penalty. The objective of the gambler is then to locate the most rewarding arm to play, while in the process maximize his winnings. In this paper we investigate a challenging variant of the MAB problem, namely the non-stationary N-Door puzzle. Here, instead of directly observing the reward, the gambler is only…
Conditional measures and their applications to fuzzy sets
1991
Abstract Given a ⊥-decomposable measure with respect to a continuous t-conorm, as introduced by the author in an earlier paper (see Section 1), we can construct ⊥-conditional measures as implications. These fulfil a ‘generalized product law’ replacing the product in the classical law by any other strict t-norm ⊥ and turn out to be decomposable with respect to an operation ⊥ V depending on ⊥, ⊥ and the condition set V (Section 2). More general, conditional measures are introduced axiomatically and are shown to be ⊥-conditional measures with respect to some ⊥-decomposable measure (Section 3). ‘Bayesian-like’ models are given which are alternatives to that presented by the author in a recent p…
Recent Advances in Bayesian Inference in Cosmology and Astroparticle Physics Thanks to the MultiNest Algorithm
2012
We present a new algorithm, called MultiNest, which is a highly efficient alternative to traditional Markov Chain Monte Carlo (MCMC) sampling of posterior distributions. MultiNest is more efficient than MCMC, can deal with highly multi-modal likelihoods and returns the Bayesian evidence (or model likelihood, the prime quantity for Bayesian model comparison) together with posterior samples. It can thus be used as an all-around Bayesian inference engine. When appropriately tuned, it also provides an exploration of the profile likelihood that is competitive with what can be obtained with dedicated algorithms.
The Bayesian Learning Automaton — Empirical Evaluation with Two-Armed Bernoulli Bandit Problems
2009
The two-armed Bernoulli bandit (TABB) problem is a classical optimization problem where an agent sequentially pulls one of two arms attached to a gambling machine, with each pull resulting either in a reward or a penalty. The reward probabilities of each arm are unknown, and thus one must balance between exploiting existing knowledge about the arms, and obtaining new information.
On incorporating the paradigms of discretization and Bayesian estimation to create a new family of pursuit learning automata
2013
Published version of an article in the journal: Applied Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/s10489-013-0424-x There are currently two fundamental paradigms that have been used to enhance the convergence speed of Learning Automata (LA). The first involves the concept of utilizing the estimates of the reward probabilities, while the second involves discretizing the probability space in which the LA operates. This paper demonstrates how both of these can be simultaneously utilized, and in particular, by using the family of Bayesian estimates that have been proven to have distinct advantages over their maximum likelihood counterparts. The success of LA-…
Bayesian Inference for the Exponential Power Function Parameters
2008
This paper addresses the problem of obtaining the marginal posterior distributions, via Gibbs Sampler, for the parameters of the well-known generalized error distribution called Exponential Power Function (E.P.F.). This density represents a family of unimodal symmetric distributions with shapes varying from leptokurtic to platikurtic.
What can chromosomes tell us about the origins of primates?
2010
What can chromosomes tell us about the origins of primates? Barbara Picone1, Luca Sineo1, Daniele Silvestro2,3, Massimiliano DelPero4 and Judith Masters5 1 Dipartimento di Biologia Animale “G. Reverberi”, Università degli Studi di Palermo, Via Archirafi 18, 90123 Palermo, Italy; 2 Senckenberg Research Institute, Frankfurt am Main, Germany ; 3 Biodiversity and Climate Research Centre (BiK-F), Frankfurt am Main, Germany;4 Dipartimento di Biologia Animale e dell’Uomo, Università degli Studi di Torino, Via Accademia Albertina 13, 10124 Torino, Italy; 5Department of Zoology and Entomology, University of Fort Hare, Private Bag X1314, Alice 5700, South Africa; Our study investigated the usefulness…
Bayesian Methodology in Statistics
2009
Bayesian methods provide a complete paradigm for statistical inference under uncertainty. These may be derived from an axiomatic system and provide a coherent methodology which makes it possible to incorporate relevant initial information, and which solves many of the difficulties that frequentist methods are known to face. If no prior information is to be assumed, the more frequent situation met in scientific reporting, a formal initial prior function, the reference prior, mathematically derived from the assumed model, is used; this leads to objective Bayesian methods, objective in the precise sense that their results, like frequentist results, only depend on the assumed model and the data…
Solving two‐armed Bernoulli bandit problems using a Bayesian learning automaton
2010
PurposeThe two‐armed Bernoulli bandit (TABB) problem is a classical optimization problem where an agent sequentially pulls one of two arms attached to a gambling machine, with each pull resulting either in a reward or a penalty. The reward probabilities of each arm are unknown, and thus one must balance between exploiting existing knowledge about the arms, and obtaining new information. The purpose of this paper is to report research into a completely new family of solution schemes for the TABB problem: the Bayesian learning automaton (BLA) family.Design/methodology/approachAlthough computationally intractable in many cases, Bayesian methods provide a standard for optimal decision making. B…