Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

Probability judgement from samples: accurate estimates and the conjunction fallacy

This paper investigates a fundamental conflict in the literature on people’s probability estimation. Research on ‘perception’ of probability shows that people are accurate in their estimates of probability of various simple events from samples. Equally, however, a large body of research shows that people’s probability estimates are fundamentally biased, and subject to reliable and striking fall...

Tail estimates for one-dimensional random walk in random environment

Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX k g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1 ? ! x. Solomon (1975) determined the almost-sure asymptotic speed (=rate of escape) ...

Computing Bounds for Entropy of Stationary Zd Markov Random Fields

For any stationary Zd Gibbs measure that satisfies strong spatial mixing, we obtain sequences of upper and lower approximations that converge to its entropy. In the case d = 2, these approximations are efficient in the sense that they are accurate to within ε and can be computed in time polynomial in 1/ε.

Computing tolerance interval for binomial random variable

Tolerance interval is a random interval that contains a proportion of the population with a determined confidence level and is applied in many application fields such as reliability and quality control. In this educational paper, we investigate different methods for computing tolerance interval for the binomial random variable using the package Tolerance in statistical software R. 

On Computing the Topological Entropy of One-sided Cellular Automata