Related papers: Resurrecting the One-Sided P-value as a Likelihood…
Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
The Cepheids' P-L relation got itself talked about again in the recent past due to claims of observed metallicity dependences of at least its zero point. The divergences of the observational results obtained by the different authors are…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
Laplace's method is used to approximate intractable integrals in a statistical problems. The relative error rate of the approximation is not worse than $O_p(n^{-1})$. We provide the first statistical lower bounds showing that the $n^{-1}$…
We point out that the traditional notion of test statistic is too narrow, and we propose a natural generalization that is arguably maximal. The study is restricted to simple statistical hypotheses.
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
This paper adresses the valuation of the Paris barrier options proposed by Yor, Jeanblanc-Picque, and Chesnay (Advances in Applied Probability, 29(1997), 165-184) using the Laplace transform approach. Based on suggestions by Pliska the…
In this study, we propose a two-stage procedure for hypothesis testing, where the first stage is conventional hypothesis testing and the second is an equivalence testing procedure using an introduced Empirical Equivalence Bound. In 2016,…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
As a classic parameter from the binomial distribution, the binomial proportion has been well studied in the literature owing to its wide range of applications. In contrast, the reciprocal of the binomial proportion, also known as the…
There are two main approach to probability, one of set-theoretic character where probability is the measure of a set, and another one of linguistic character where probability is the degree of confidence in a proposition. In this work we…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal…
Two sequential estimators are proposed for the odds p/(1-p) and log odds log(p/(1-p)) respectively, using independent Bernoulli random variables with parameter p as inputs. The estimators are unbiased, and guarantee that the variance of the…
Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not…
Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that…
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…