Astrostatistics aims to extract meaningful information from astronomical data to gain insights into the properties and behaviors of celestial objects.

The parallax method is a fundamental technique in astronomy for measuring the distance to nearby stars by observing their apparent shift in position as the Earth orbits the Sun.

The Hubble diagram is a graphical representation of the relationship between the redshift and distance of galaxies, which is crucial for understanding the expansion of the universe.

Bayesian inference is a powerful statistical technique that allows astronomers to estimate model parameters, make predictions, and quantify uncertainty in their results.

The log-normal distribution is often used to model the distribution of stellar masses because it can accommodate the observed skewed distribution with a long tail towards higher masses.

Astrostatistics plays a crucial role in exoplanet detection and characterization by analyzing transit light curves, estimating exoplanet properties, and searching for biomarkers in exoplanet atmospheres.

The CMB is a remnant radiation from the early universe and is crucial for studying the Big Bang theory, determining the age of the universe, and probing the conditions of the early universe.

Survival analysis is a statistical technique used to analyze the time until an event of interest occurs, making it applicable to various astrophysical phenomena such as stellar lifetimes, gamma-ray burst durations, and galaxy merger rates.

K-means clustering, hierarchical clustering, and density-based clustering are all statistical methods used for clustering galaxies based on their properties, such as their luminosities, colors, and morphologies.

Studying the distribution of dark matter is crucial for understanding galaxy formation and evolution, probing the nature of dark matter itself, and constraining cosmological models.

Power spectrum analysis, correlation function analysis, and Minkowski functionals are statistical techniques used to analyze the large-scale structure of the universe by quantifying the distribution and clustering of galaxies.

Astrostatistics plays a vital role in gravitational lensing studies by enabling astronomers to estimate the mass of lensing galaxies, reconstruct the distribution of dark matter, and study the properties of distant galaxies.

Time series analysis is a statistical technique used to analyze the variability of astronomical objects, detect periodic signals in astronomical data, and forecast future astronomical events.

Isochrone fitting, main sequence fitting, and color-magnitude diagram analysis are statistical methods used to estimate the age of stars by comparing their observed properties to theoretical models.

Astrostatistics plays a crucial role in the search for extraterrestrial life by analyzing data from SETI experiments, identifying potential biosignatures in exoplanet atmospheres, and assessing the habitability of exoplanets.