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The value of the likelihood is occasionally used by high energy physicists as a statistic to measure goodness-of-fit in unbinned maximum likelihood fits. Simple examples are presented that illustrate why this (seemingly intuitive) method…

Parameter estimation via unbinned maximum likelihood fits is central for many analyses performed in high energy physics. Unbinned maximum likelihood fits using event weights, for example to statistically subtract background contributions…

When a measurement of a physical quantity is reported, the total uncertainty is usually decomposed into statistical and systematic uncertainties. This decomposition is not only useful to understand the contributions to the total…

Unbinned maximum likelihood is a common procedure for parameter estimation. After parameters have been estimated, it is crucial to know whether the fit model adequately describes the experimental data. Univariate Goodness of Fit procedures…

The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…

The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…

Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned…

We present a universal method to include residual un-modeled background shape uncertainties in likelihood based statistical tests for high energy physics and astroparticle physics. This approach provides a simple and natural protection…

When fitting theory to data in the presence of background uncertainties, the question of whether the spectral shape of the background happens to be similar to that of the theoretical model of physical interest has not generally been…

Reliable uncertainty estimation is one of the major challenges for medical classification tasks. While many approaches have been proposed, recently the statistical framework of conformal predictions has gained a lot of attention, due to its…

When reading peer-reviewed scientific literature describing any analysis of empirical data, it is natural and correct to proceed with the underlying assumption that experiments have made good faith efforts to ensure that their analyses…

Maximum likelihood fits to data can be performed using binned data and unbinned data. The likelihood fits in either case produce only the fitted quantities but not the goodness of fit. With binned data, one can obtain a measure of the…

Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted…

The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…

The possibility of strong biases in a multicomponent Maximum Likelihood fits with component-dependent templates has been demonstrated in some toy problems. We discuss here in detail a problem of practical interest, particle identification…

In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…

Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the…

We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…

Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…

A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…