carfima - Continuous-Time Fractionally Integrated ARMA Process for Irregularly Spaced Long-Memory Time Series Data

We provide a toolbox to fit a continuous-time fractionally integrated ARMA process (CARFIMA) on univariate and irregularly spaced time series data via both frequentist and Bayesian machinery. A general-order CARFIMA(p, H, q) model for p>q is specified in Tsai and Chan (2005) <doi:10.1111/j.1467-9868.2005.00522.x> and it involves p+q+2 unknown model parameters, i.e., p AR parameters, q MA parameters, Hurst parameter H, and process uncertainty (standard deviation) sigma. Also, the model can account for heteroscedastic measurement errors, if the information about measurement error standard deviations is known. The package produces their maximum likelihood estimates and asymptotic uncertainties using a global optimizer called the differential evolution algorithm. It also produces posterior samples of the model parameters via Metropolis-Hastings within a Gibbs sampler equipped with adaptive Markov chain Monte Carlo. These fitting procedures, however, may produce numerical errors if p>2. The toolbox also contains a function to simulate discrete time series data from CARFIMA(p, H, q) process given the model parameters and observation times.

Last updated 5 years ago

1.30 score 2 stars 4 scripts 254 downloads

Rdta - Data Transforming Augmentation for Linear Mixed Models

We provide a toolbox to fit univariate and multivariate linear mixed models via data transforming augmentation. Users can also fit these models via typical data augmentation for a comparison. It returns either maximum likelihood estimates of unknown model parameters (hyper-parameters) via an EM algorithm or posterior samples of those parameters via MCMC. Also see Tak et al. (2019) <doi:10.1080/10618600.2019.1704295>.

Last updated 10 months ago

1.00 score 156 downloads

h0 - A Robust Bayesian Meta-Analysis for Estimating the Hubble Constant via Time Delay Cosmography

We provide a toolbox to conduct a Bayesian meta-analysis for estimating the current expansion rate of the Universe, called the Hubble constant H0, via time delay cosmography. The input data are Fermat potential difference and time delay estimates. For a robust inference, we assume a Student's t error for these inputs. Given these inputs, the meta-analysis produces posterior samples of the model parameters including the Hubble constant via Metropolis-Hastings within Gibbs. The package provides an option to implement repelling-attracting Metropolis-Hastings within Gibbs in a case where the parameter space has multiple modes.

Last updated 1 years ago

1.00 score 318 downloads

Rdrw - Univariate and Multivariate Damped Random Walk Processes

We provide a toolbox to fit and simulate a univariate or multivariate damped random walk process that is also known as an Ornstein-Uhlenbeck process or a continuous-time autoregressive model of the first order, i.e., CAR(1) or CARMA(1, 0). This process is suitable for analyzing univariate or multivariate time series data with irregularly-spaced observation times and heteroscedastic measurement errors. When it comes to the multivariate case, the number of data points (measurements/observations) available at each observation time does not need to be the same, and the length of each time series can vary. The number of time series data sets that can be modeled simultaneously is limited to ten in this version of the package. We use Kalman-filtering to evaluate the resulting likelihood function, which leads to a scalable and efficient computation in finding maximum likelihood estimates of the model parameters or in drawing their posterior samples. Please pay attention to loading the data if this package is used for astronomical data analyses; see the details in the manual. Also see Hu and Tak (2020) <arXiv:2005.08049>.

Last updated 4 years ago

1.00 score 179 downloads

timedelay - Time Delay Estimation for Stochastic Time Series of Gravitationally Lensed Quasars

We provide a toolbox to estimate the time delay between the brightness time series of gravitationally lensed quasar images via Bayesian and profile likelihood approaches. The model is based on a state-space representation for irregularly observed time series data generated from a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian method adopts scientifically motivated hyper-prior distributions and a Metropolis-Hastings within Gibbs sampler, producing posterior samples of the model parameters that include the time delay. A profile likelihood of the time delay is a simple approximation to the marginal posterior distribution of the time delay. Both Bayesian and profile likelihood approaches complement each other, producing almost identical results; the Bayesian way is more principled but the profile likelihood is easier to implement. A new functionality is added in version 1.0.9 for estimating the time delay between doubly-lensed light curves observed in two bands. See also Tak et al. (2017) <doi:10.1214/17-AOAS1027>, Tak et al. (2018) <doi:10.1080/10618600.2017.1415911>, Hu and Tak (2020) <arXiv:2005.08049>.

Last updated 5 years ago

1.00 score 4 scripts 223 downloads