Related papers: Probability Distributions of Positioning Errors fo…
The center of gravity is a widespread algorithm for position reconstruction in particle physics. For track fitting, its standard use is always accompanied by an easy guess for the probability distribution of the positioning errors. This is…
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…
To complete a previous paper, the probability density functions of the center-of-gravity as positioning algorithm are derived with classical methods. These methods, as suggested by the textbook of Probability, require the preliminary…
The construction of a well tuned probability distributions is illustrated in synthetic way, these probability distributions produce faithful realizations of the impact point distributions for particles in silicon strip detector. Their use…
A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…
The realistic probability distributions of a previous article are applied to the reconstruction of tracks in constant magnetic field. The complete forms and their schematic approximations produce excellent momentum estimations, drastically…
In our paper published earlier we discussed forecasts of earthquake focal mechanism and ways to test the forecast efficiency. Several verification methods were proposed, but they were based on ad-hoc, empirical assumptions, thus their…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…
The optimizations of the track fittings require complex simulations of silicon strip detectors to be compliant with the fundamental properties of the hit heteroscedasticity. Many different generations of random numbers must be available…
Likelihood ratios are used for a variety of applications in particle physics data analysis, including parameter estimation, unfolding, and anomaly detection. When the data are high-dimensional, neural networks provide an effective tools for…
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular,…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
In this paper we derive an exact full expression for the 2D probability distribution of the ellipticity of an object measured from data, only assuming Gaussian noise in pixel values. This is a generalisation of the probability distribution…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling…
The likelihood ratio is a crucial quantity for statistical inference in science that enables hypothesis testing, construction of confidence intervals, reweighting of distributions, and more. Many modern scientific applications, however,…
The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its…