Related papers: Sigma One
Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and…
Observational astronomy is plagued with selection effects that must be taken into account when interpreting data from astronomical surveys. Because of the physical limitations of observing time and instrument sensitivity, datasets are…
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation $\, X \sim {\cal{N}}(\mu , \, \sigma^2) \,$. Here we extend this result to obtaining 1-sample confidence…
We give an elementary proof of the known fact that every probability measure, defined on an arbitrary $\sigma$-field on a countable sample space $\Omega$, may in fact be extended to a probability measure on the power set of $\Omega$. This…
There has been significant recent progress in observational cosmology. This, in turn, has provided an unprecedented picture of the early universe and its evolution. In this review I will present a (biased) view of how one can use these…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
We use weighted mean and median statistics techniques to combine individual estimates of Omega_m0, the present mean mass density in non-relativistic matter, and determine the observed values and ranges of Omega_m0 from different…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
Comparing population-synthesis models to the results of hierarchical Bayesian inference in gravitational-wave astronomy requires a careful understanding of the domain of validity of the models fitted to data. This comparison is usually done…
The sample median is often used in statistical analyses of physical or astronomical data wherein a central value must be found from samples polluted by elements which do not belong to the population of interest or when the underlying…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is…
We have measured a velocity dispersion for the foreground galaxy in this gravitationally lensed system. Our dispersion confirms the prediction from lens models, provided that the source is distant enough ($z_{_S}>0.2$). Current…
In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…
In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found…
Observational data about human behavior is often heterogeneous, i.e., generated by subgroups within the population under study that vary in size and behavior. Heterogeneity predisposes analysis to Simpson's paradox, whereby the trends…
We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…
We present the first cosmological constraints using only the observed photometry of galaxies. Villaescusa-Navarro et al. (2022; arXiv:2201.02202) recently demonstrated that the internal physical properties of a single simulated galaxy…
Human groups can perform extraordinary accurate estimations compared to individuals by simply using the mean, median or geometric mean of the individual estimations [Galton 1907, Surowiecki 2005, Page 2008]. However, this is true only for…