Related papers: A crash course on data analysis in asteroseismolog…
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…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.
It is well known that asteroseismology is the unique technique permitting the study of the internal structure of pulsating stars using their pulsational frequencies, which is per se very important. It acquires an additional value when the…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the…
The recent asteroseismic data from the CoRoT and Kepler missions have provided an entirely new basis for investigating stellar properties. This has led to a rapid development in techniques for analysing such data, although it is probably…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
Asteroseismology involves probing the interiors of stars and quantifying their global properties, such as radius and age, through observationsof normal modes of oscillation. The technical requirements for conducting asteroseismology include…
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…
Asteroseismology is the determination of the interior structures of stars by using their oscillations as seismic waves. Simple explanations of the astrophysical background and some basic theoretical considerations needed in this rapidly…
Over the past decade and a half, adoption of Bayesian inference in pulsar timing analysis has led to increasingly sophisticated models. The recent announcement of evidence for a stochastic background of gravitational waves by various pulsar…
We introduce a few of the key ideas of statistical analysis using two real-world examples to illustrate how these ideas are used in practice.
Bayesian methods are becoming more widely used in asteroseismic analysis. In particular, they are being used to determine oscillation frequencies, which are also commonly found by Fourier analysis. It is important to establish whether the…
A fundamental problem in the practice and teaching of data science is how to evaluate the quality of a given data analysis, which is different than the evaluation of the science or question underlying the data analysis. Previously, we…
Frequentist statistical methods, such as hypothesis testing, are standard practice in papers that provide benchmark comparisons. Unfortunately, these methods have often been misused, e.g., without testing for their statistical test…
This article studies the financial time series data processing for machine learning. It introduces the most frequent scaling methods, then compares the resulting stationarity and preservation of useful information for trend forecasting. It…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next,…
The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis,…
A flood of reliable seismic data will soon arrive. The migration to larger telescopes on the ground may free up 4-m class instruments for multi-site campaigns, and several forthcoming satellite missions promise to yield nearly uninterrupted…