Related papers: Sigma One
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
Anthropic models can give testable predictions, which can be confirmed or falsified at a specified confidence level. This is illustrated using the successful prediction of the cosmological constant as an example. The history and the nature…
This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between…
Sky surveys represent a fundamental data basis for astronomy. We use them to map in a systematic way the universe and its constituents, and to discover new types of objects or phenomena. We review the subject, with an emphasis on the…
Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…
Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…
We present a model where some proportion of extraterrestrial civilizations expand uniformly over time to reach a cosmological scale. We then ask what humanity could infer if a sky survey were to find zero, one, or more such civilizations.…
A general purpose fitting model for one-dimensional astrometric signals is developed, building on a maximum likelihood framework, and its performance is evaluated by simulation over a set of realistic image instances. The fit quality is…
The simplest model of a smart spatial redistribution of individuals is proposed. A single-species population is considered, to be composed of two discrete subpopulations inhabiting two stations; migration is a transfer between them. The…
This paper proposes a general family of estimators for estimating the population mean in systematic sampling in the presence of non-response adapting the family of estimators proposed by Khoshnevisan et al. (2007). In this paper we have…
Many datasets describing contacts in a population suffer from incompleteness due to population sampling and underreporting of contacts. Data-driven simulations of spreading processes using such incomplete data lead to an underestimation of…
We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
The paper analyzes how the enlarging of the sample affects to the mitigation of collinearity concluding that it may mitigate the consequences of collinearity related to statistical analysis but not necessarily the numerical instability. The…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…