# Modeling Stochastic Variability in Multiband Time-series Data

@article{Hu2020ModelingSV, title={Modeling Stochastic Variability in Multiband Time-series Data}, author={Zhirui Hu and Hyungsuk Tak}, journal={arXiv: Instrumentation and Methods for Astrophysics}, year={2020} }

In preparation for the era of the time-domain astronomy with upcoming large-scale surveys, we propose a state-space representation of a multivariate damped random walk process as a tool to analyze irregularly-spaced multi-filter light curves with heteroscedastic measurement errors. We adopt a computationally efficient and scalable Kalman-filtering approach to evaluate the likelihood function, leading to maximum $O(k^3n)$ complexity, where $k$ is the number of available bands and $n$ is the…

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#### References

SHOWING 1-10 OF 57 REFERENCES

Time Series Analysis by State Space Methods

- Computer Science
- 2001

This excellent text provides a comprehensive treatment of the state space approach to time series analysis, where observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbence terms, each of which is modelled separately.

Improving Exoplanet Detection Power: Multivariate Gaussian Process Models for Stellar Activity

- Physics, Mathematics
- 2017

The radial velocity method is one of the most successful techniques for detecting exoplanets. It works by detecting the velocity of a host star induced by the gravitational effect of an orbiting…

Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations

- Physics
- 2009

We analyze a sample of optical light curves for 100 quasars, 70 of which have black hole mass estimates. Our sample is the largest and broadest used yet for modeling quasar variability. The sources…

The Time Variability of SDSS Stripe 82 Quasars as a Damped Random Walk

- Physics
- 2010

We model the time variability of ~9000 spectroscopically confirmed quasars in SDSS Stripe 82 as a damped random walk (DRW). Using 2.7 million photometric measurements collected over 10 yr, we confirm…

Stochastic Methods (Berlin Heidelberg: Springer-Verlag

- 2009

Bayesian estimates of astronomical time delays between gravitationally lensed stochastic light curves

- Physics, Mathematics
- 2017

The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object such as a quasar. If the galaxy is a strong gravitational lens, it can produce multiple…

Rgbp: An R Package for Gaussian, Poisson, and Binomial Random Effects Models with Frequency Coverage Evaluations

- Mathematics
- 2016

Rgbp is an R package that provides estimates and verifiable confidence intervals for random effects in two-level conjugate hierarchical models for overdispersed Gaussian, Poisson, and binomial data.…

A Repelling–Attracting Metropolis Algorithm for Multimodality

- Computer Science, MathematicsJournal of Computational and Graphical Statistics
- 2018

The RAM algorithm is a Metropolis-Hastings algorithm that maintains the simple-to-implement nature of the Metropolis algorithm, but is more likely to jump between modes, and introduces an auxiliary variable which creates a term in the acceptance probability that cancels with the intractable ratio.

How proper are Bayesian models in the astronomical literature?

- PhysicsMonthly Notices of the Royal Astronomical Society
- 2018

The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior…

Alternative way to derive the distribution of the multivariate Ornstein–Uhlenbeck process

- MathematicsAdvances in Difference Equations
- 2019

In this paper, we solve the Fokker–Planck equation of the multivariate Ornstein–Uhlenbeck process to obtain its probability density function. This approach allows us to ascertain the distribution…