19 research outputs found

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

We propose a Bayesian meta-analysis to infer the current expansion rate of
the Universe, called the Hubble constant ($H_0$), via time delay cosmography.
Inputs of the meta-analysis are estimates of two properties for each pair of
gravitationally lensed images; time delay and Fermat potential difference
estimates with their standard errors. A meta-analysis can be appealing in
practice because obtaining each estimate from even a single lens system
involves substantial human efforts, and thus estimates are often separately
obtained and published. This work focuses on combining these estimates from
independent studies to infer $H_0$ in a robust manner. For this purpose, we
adopt Student's $t$ error for the inputs of the meta-analysis. We investigate
properties of the resulting $H_0$ estimate via two simulation studies with
realistic imaging data. It turns out that the meta-analysis can infer $H_0$
with sub-percent bias and about 1 percent level of coefficient of variation,
even when 30 percent of inputs are manipulated to be outliers. We also apply
the meta-analysis to three gravitationally lensed systems, and estimate $H_0$
by $75.632 \pm 6.918$ (km/second/Mpc), which covers a wide range of $H_0$
estimates obtained under different physical processes. An R package, h0, is
publicly available for fitting the proposed meta-analysis

### A Repelling-Attracting Metropolis Algorithm for Multimodality

Although the Metropolis algorithm is simple to implement, it often has
difficulties exploring multimodal distributions. We propose the
repelling-attracting Metropolis (RAM) algorithm that maintains the
simple-to-implement nature of the Metropolis algorithm, but is more likely to
jump between modes. The RAM algorithm is a Metropolis-Hastings algorithm with a
proposal that consists of a downhill move in density that aims to make local
modes repelling, followed by an uphill move in density that aims to make local
modes attracting. The downhill move is achieved via a reciprocal Metropolis
ratio so that the algorithm prefers downward movement. The uphill move does the
opposite using the standard Metropolis ratio which prefers upward movement.
This down-up movement in density increases the probability of a proposed move
to a different mode. Because the acceptance probability of the proposal
involves a ratio of intractable integrals, we introduce an auxiliary variable
which creates a term in the acceptance probability that cancels with the
intractable ratio. Using several examples, we demonstrate the potential for the
RAM algorithm to explore a multimodal distribution more efficiently than a
Metropolis algorithm and with less tuning than is commonly required by
tempering-based methods

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

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. Rgbp models aggregate data from k independent groups summarized by observed sufficient statistics for each random effect, such as sample means, possibly with covariates. Rgbp uses approximate Bayesian machinery with unique improper priors for the hyper-parameters, which leads to good repeated sampling coverage properties for random effects. A special feature of Rgbp is an option that generates synthetic data sets to check whether the interval estimates for random effects actually meet the nominal confidence levels. Additionally, Rgbp provides inference statistics for the hyper-parameters, e.g., regression coefficients

### TD-CARMA: Painless, accurate, and scalable estimates of gravitational-lens time delays with flexible CARMA processes

Cosmological parameters encoding our current understanding of the expansion
history of the Universe can be constrained by the accurate estimation of time
delays arising in gravitationally lensed systems. We propose TD-CARMA, a
Bayesian method to estimate cosmological time delays by modelling the observed
and irregularly sampled light curves as realizations of a Continuous
Auto-Regressive Moving Average (CARMA) process. Our model accounts for
heteroskedastic measurement errors and microlensing, an additional source of
independent extrinsic long-term variability in the source brightness. The CARMA
formulation admits a linear state-space representation, that allows for
efficient and scalable likelihood computation using the Kalman Filter. We
obtain a sample from the joint posterior distribution of the model parameters
using a nested sampling approach. This allows for "painless" Bayesian
Computation, dealing with the expected multi-modality of the posterior
distribution in a straightforward manner and not requiring the specification of
starting values or an initial guess for the time delay, unlike existing
methods. In addition, the proposed sampling procedure automatically evaluates
the Bayesian evidence, allowing us to perform principled Bayesian model
selection. TD-CARMA is parsimonious, and typically includes no more than a
dozen unknown parameters. We apply TD-CARMA to three doubly lensed quasars HS
2209+1914, SDSS J1001+5027 and SDSS J1206+4332, estimating their time delays as
$-21.96 \pm 1.448$ (6.6$\%$ precision), $120.93 \pm 1.015$ (0.8$\%$), and
$111.51 \pm 1.452$ (1.3$\%$), respectively. A python package, TD-CARMA, is
publicly available to implement the proposed method