Search results for "Beta distribution"
showing 10 items of 10 documents
Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions
2022
Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simula…
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.
The design of absorbing Bayesian pursuit algorithms and the formal analyses of their ε-optimality
2016
The fundamental phenomenon that has been used to enhance the convergence speed of learning automata (LA) is that of incorporating the running maximum likelihood (ML) estimates of the action reward probabilities into the probability updating rules for selecting the actions. The frontiers of this field have been recently expanded by replacing the ML estimates with their corresponding Bayesian counterparts that incorporate the properties of the conjugate priors. These constitute the Bayesian pursuit algorithm (BPA), and the discretized Bayesian pursuit algorithm. Although these algorithms have been designed and efficiently implemented, and are, arguably, the fastest and most accurate LA report…
A Bayesian Learning Automaton for Solving Two-Armed Bernoulli Bandit Problems
2008
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. In the last decades, several computationally efficient algorithms for tackling this problem have emerged, with learning automata (LA) being known for their ?-optimality, and confidence interval based for logarithmically growing regret. Applications include treatment selection in clinical trials, route selection in …
What Does Objective Mean in a Dirichlet-multinomial Process?
2017
Summary The Dirichlet-multinomial process can be seen as the generalisation of the binomial model with beta prior distribution when the number of categories is larger than two. In such a scenario, setting informative prior distributions when the number of categories is great becomes difficult, so the need for an objective approach arises. However, what does objective mean in the Dirichlet-multinomial process? To deal with this question, we study the sensitivity of the posterior distribution to the choice of an objective Dirichlet prior from those presented in the available literature. We illustrate the impact of the selection of the prior distribution in several scenarios and discuss the mo…
Moments for Some Kumaraswamy Generalized Distributions
2014
Explicit expansions for the moments of some Kumaraswamy generalized (Kw-G) distributions (Cordeiro and de Castro, 2011) are derived using special functions. We explore the Kw-normal, Kw-gamma, Kw-beta, Kw-t, and Kw-F distributions. These expressions are given as infinite weighted linear combinations of well-known special functions for which numerical routines are readily available.
On achieving near-optimal “Anti-Bayesian” Order Statistics-Based classification fora asymmetric exponential distributions
2013
Published version of a Chapter in the book: Computer Analysis of Images and Patterns. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-40261-6_44 This paper considers the use of Order Statistics (OS) in the theory of Pattern Recognition (PR). The pioneering work on using OS for classification was presented in [1] for the Uniform distribution, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean - which is distinct from the optimal Bayesian paradigm. In [2], we showed that the results could be extended for a few sym…
“Anti-Bayesian” parametric pattern classification using order statistics criteria for some members of the exponential family
2013
This paper submits a comprehensive report of the use of order statistics (OS) for parametric pattern recognition (PR) for various distributions within the exponential family. Although the field of parametric PR has been thoroughly studied for over five decades, the use of the OS of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented earlier for the uniform distribution and for some members of the exponential family, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. A…
Generalized Bayesian pursuit: A novel scheme for multi-armed Bernoulli bandit problems
2011
Published version of a chapter in the book: IFIP Advances in Information and Communication Technology. Also available from the publisher at: http;//dx.doi.org/10.1007/978-3-642-23960-1_16 In the last decades, a myriad of approaches to the multi-armed bandit problem have appeared in several different fields. The current top performing algorithms from the field of Learning Automata reside in the Pursuit family, while UCB-Tuned and the ε -greedy class of algorithms can be seen as state-of-the-art regret minimizing algorithms. Recently, however, the Bayesian Learning Automaton (BLA) outperformed all of these, and other schemes, in a wide range of experiments. Although seemingly incompatible, in…
The Bayesian Pursuit Algorithm: A New Family of Estimator Learning Automata
2011
Published version of a chapter in the book: Modern Approaches in Applied Intelligence. Also available from the publisher at http://dx.doi.org/10.1007/978-3-642-21827-9_53 The fastest Learning Automata (LA) algorithms currently available come from the family of estimator algorithms. The Pursuit algorithm (PST), a pioneering scheme in the estimator family, obtains its superior learning speed by using Maximum Likelihood (ML) estimates to pursue the action currently perceived as being optimal. Recently, a Bayesian LA (BLA) was introduced, and empirical results that demonstrated its advantages over established top performers, including the PST scheme, were reported. The BLA scheme is inherently …