相关论文: How to Use Experimental Data to Compute the Probab…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
Mathematical models connect theory with the real world through data, enabling us to interpret, understand, and predict complex phenomena. However, scientific knowledge often extends beyond what can be empirically measured, offering valuable…
We report on a first experiment about an email based course that connects learning Python basics and introductory probability theory. In the experiment 7 short sequences of homework were sent out to prospective mathematics teachers who did…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
When eliciting probability models from experts, knowledge engineers may compare the results of the model with expert judgment on test scenarios, then adjust model parameters to bring the behavior of the model more in line with the expert's…
Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models…
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…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
In this paper we propose a procedure to evaluate Bayesian confidence intervals in counting experiments where both signal and background fluctuations are described by the Poisson statistics. The results obtained when the method is applied to…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
This paper introduces and reviews some of the principles and methods used in Bayesian reliability. It specifically discusses methods used in the analysis of success/no-success data and then reminds the reader of a simple Monte Carlo…
Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…
In a Bayesian context, theoretical parameters are correlated random variables. Then, the constraints on one parameter can be improved by either measuring this parameter more precisely - or by measuring the other parameters more precisely.…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
These three lectures provide an introduction to the main concepts of statistical data analysis useful for precision measurements and searches for new signals in High Energy Physics. The frequentist and Bayesian approaches to probability…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…