Study of aging properties of a binary random variable

1996 ◽  
Vol 32 (4) ◽  
pp. 609-614
Author(s):  
V. Yu. Kotlyar
Keyword(s):  
Random Variable ◽  
Binary Random Variable ◽  
Aging Properties

scholarly journals Inferences About the Probability of Success, Given the Value of a Covariate, Using a Nonparametric Smoother

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Rand Wilcox
Keyword(s):  
Logistic Regression ◽  
Confidence Interval ◽  
Regression Model ◽  
Goodness Of Fit ◽  
Logistic Regression Model ◽  
Random Variable ◽  
Goodness Of Fit Test ◽  
Binary Random Variable ◽  
Alternative Approach ◽  
Probability Of Success

For a binary random variable Y, let p(x) = P(Y = 1 | X = x) for some covariate X. The goal of computing a confidence interval for p(x) is considered. In the logistic regression model, even a slight departure difficult to detect via a goodness-of-fit test can yield inaccurate results. The accuracy of a confidence interval can deteriorate as the sample size increases. The goal is to suggest an alternative approach based on a smoother, which provides a more flexible approximation of p(x).

Using numerical methods to design simulations: revisiting the balancing intercept

2021 ◽  
Author(s):  
Sarah E Robertson ◽  
Issa J Dahabreh ◽  
Jon A Steingrimsson
Keyword(s):  
Regression Model ◽  
Logistic Model ◽  
Numerical Approximation ◽  
Basic Problem ◽  
Random Variable ◽  
Analytical Approximation ◽  
Simulation Studies ◽  
Linear Predictor ◽  
Binary Random Variable ◽  
A Value

Abstract We consider methods for generating draws of a binary random variable whose expectation conditional on covariates follows a logistic regression model with known covariate coefficients. We examine approximations for finding a “balancing intercept,” that is, a value for the intercept of the logistic model that leads to a desired marginal expectation for the binary random variable. We show that a recently proposed analytical approximation can produce inaccurate results, especially when targeting more extreme marginal expectations or when the linear predictor of the regression model has high variance. We describe and implement a numerical approximation based on Monte Carlo methods that appears to work well in practice. Our approach to the basic problem of the balancing intercept provides an example of a broadly applicable strategy for formulating and solving problems that arise in the design of simulation studies used to evaluate or teach epidemiologic methods.

Relative Aging of Distributions

1998 ◽  
Vol 12 (4) ◽  
pp. 469-478 ◽  
Author(s):  
Ginger Rowell ◽  
Kyle Siegrist
Keyword(s):  
Partial Order ◽  
Equivalence Relation ◽  
Random Variable ◽  
Aging Properties ◽  
Aging Property ◽  
Parametric Families

We consider the reliability of one random variable relative to another, when the variables are continuous and take values in an interval [a, b). We give definitions and characterizations for the exponential property and the standard aging properties IFR, IFRA, and NBU. The exponential property defines an equivalence relation on the distributions, and then each of these aging properties defines a partial order on the distributions, modulo the exponential equivalence. We give a set of conditions that must be satisfied for a general aging property to define such a partial order and show that these conditions are not satisfied by the NBUE property. Several parametric families of distributions are considered.

scholarly journals A Regularized Opponent Model with Maximum Entropy Objective

2019 ◽  
Author(s):  
Zheng Tian ◽  
Ying Wen ◽  
Zhichen Gong ◽  
Faiz Punakkath ◽  
Shihao Zou ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Maximum Entropy ◽  
Single Agent ◽  
Exact Algorithm ◽  
Random Variable ◽  
Matrix Game ◽  
Inference Problem ◽  
Opponent Modeling ◽  
Binary Random Variable ◽  
Multi Agent

In a single-agent setting, reinforcement learning (RL) tasks can be cast into an inference problem by introducing a binary random variable o, which stands for the "optimality". In this paper, we redefine the binary random variable o in multi-agent setting and formalize multi-agent reinforcement learning (MARL) as probabilistic inference. We derive a variational lower bound of the likelihood of achieving the optimality and name it as Regularized Opponent Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel perspective on opponent modeling and show how it can improve the performance of training agents theoretically and empirically in cooperative games. To optimize ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of convergence. We extend the exact algorithm to complex environments by proposing an approximate version, ROMMEO-AC. We evaluate these two algorithms on the challenging iterated matrix game and differential game respectively and show that they can outperform strong MARL baselines. 

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

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