202 research outputs found
Reconstructing Probability Distributions with Gaussian Processes
Modern cosmological analyses constrain physical parameters using Markov Chain
Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques
are computationally expensive to run and require up to thousands of CPU hours
to complete. Here we present a method for reconstructing the log-probability
distributions of completed experiments from an existing MCMC chain (or any set
of posterior samples). The reconstruction is performed using Gaussian process
regression for interpolating the log-probability. This allows for easy
resampling, importance sampling, marginalization, testing different samplers,
investigating chain convergence, and other operations. As an example use-case,
we reconstruct the posterior distribution of the most recent Planck 2018
analysis. We then resample the posterior, and generate a new MCMC chain with
forty times as many points in only thirty minutes. Our likelihood
reconstruction tool can be found online at
https://github.com/tmcclintock/AReconstructionTool.Comment: 7 pages, 4 figures, repository at
https://github.com/tmcclintock/AReconstructionToo
A Systematic Study of Projection Biases in Weak Lensing Analysis
We present a systematic study of projection biases in the weak lensing
analysis of the first year of data from the Dark Energy Survey (DES)
experiment. In the analysis we used a CDM model and three two-point
correlation functions. We show that these biases are a consequence of
projecting, or marginalizing, over parameters like , , and
that are both poorly constrained and correlated with the
parameters of interest like , and . Covering the
relevant parameter space we show that the projection biases are a function of
where the true values of the poorly constrained parameters lie with respect to
the parameter priors. For example, biases in the position of the posteriors can
exceed the 1.5 level if the true values of and are close to
the top of the prior's range and the true values of and are close to the bottom of the range of their priors. We also show that in
some cases the 1D credible intervals can be over-specified by as much as 30%
and coverage can be as low as 27%. Finally we estimate these projection biases
for the analysis of three and six years worth of DES data
Solving high-dimensional parameter inference: marginal posterior densities & Moment Networks
High-dimensional probability density estimation for inference suffers from the "curse of dimensionality". For many physical inference problems, the full posterior distribution is unwieldy and seldom used in practice. Instead, we propose direct estimation of lower-dimensional marginal distributions, bypassing high-dimensional density estimation or high-dimensional Markov chain Monte Carlo (MCMC) sampling. By evaluating the two-dimensional marginal posteriors we can unveil the full-dimensional parameter covariance structure. We additionally propose constructing a simple hierarchy of fast neural regression models, called Moment Networks, that compute increasing moments of any desired lower-dimensional marginal posterior density; these reproduce exact results from analytic posteriors and those obtained from Masked Autoregressive Flows. We demonstrate marginal posterior density estimation using high-dimensional LIGO-like gravitational wave time series and describe applications for problems of fundamental cosmology
Parameter inference and model comparison using theoretical predictions from noisy simulations
When inferring unknown parameters or comparing different models, data must be
compared to underlying theory. Even if a model has no closed-form solution to
derive summary statistics, it is often still possible to simulate mock data in
order to generate theoretical predictions. For realistic simulations of noisy
data, this is identical to drawing realizations of the data from a likelihood
distribution. Though the estimated summary statistic from simulated data
vectors may be unbiased, the estimator has variance which should be accounted
for. We show how to correct the likelihood in the presence of an estimated
summary statistic by marginalizing over the true summary statistic in the
framework of a Bayesian hierarchical model. For Gaussian likelihoods where the
covariance must also be estimated from simulations, we present an alteration to
the Sellentin-Heavens corrected likelihood. We show that excluding the proposed
correction leads to an incorrect estimate of the Bayesian evidence with JLA
data. The correction is highly relevant for cosmological inference that relies
on simulated data for theory (e.g. weak lensing peak statistics and simulated
power spectra) and can reduce the number of simulations required.Comment: 9 pages, 6 figures, published by MNRAS. Changes: matches published
version, added Bayesian hierarchical interpretation and probabilistic
graphical mode
Relativistic spin precession in the binary PSR J11416545
PSR J11416545 is a precessing binary pulsar that has the rare potential to
reveal the two-dimensional structure of a non-recycled pulsar emission cone. It
has undergone of relativistic spin precession in the
years since its discovery. In this paper, we present a detailed Bayesian
analysis of the precessional evolution of the width of the total intensity
profile, to understand the changes to the line-of-sight impact angle ()
of the pulsar using four different physically motivated prior distribution
models. Although we cannot statistically differentiate between the models with
confidence, the temporal evolution of the linear and circular polarisations
strongly argue that our line-of-sight crossed the magnetic pole around MJD
54000 and that only two models remain viable. For both these models, it appears
likely that the pulsar will precess out of our line-of-sight in the next
years, assuming a simple beam geometry. Marginalising over suggests
that the pulsar is a near-orthogonal rotator and provides the first
polarization-independent estimate of the scale factor () that
relates the pulsar beam opening angle () to its rotational period ()
as : we find it to be at 1.4
GHz with 99\% confidence. If all pulsars emit from opposite poles of a dipolar
magnetic field with comparable brightness, we might expect to see evidence of
an interpulse arising in PSR J11416545, unless the emission is patchy.Comment: Accepted for publication in Astrophysical Journal Letter
Complete parameter inference for GW150914 using deep learning
The LIGO and Virgo gravitational-wave observatories have detected many exciting events over the past five years. As the rate of detections grows with detector sensitivity, this poses a growing computational challenge for data analysis. With this in mind, in this work we apply deep learning techniques to perform fast likelihood-free Bayesian inference for gravitational waves. We train a neural-network conditional density estimator to model posterior probability distributions over the full 15-dimensional space of binary black hole system parameters, given detector strain data from multiple detectors. We use the method of normalizing flows---specifically, a neural spline normalizing flow---which allows for rapid sampling and density estimation. Training the network is likelihood-free, requiring samples from the data generative process, but no likelihood evaluations. Through training, the network learns a global set of posteriors: it can generate thousands of independent posterior samples per second for any strain data consistent with the prior and detector noise characteristics used for training. By training with the detector noise power spectral density estimated at the time of GW150914, and conditioning on the event strain data, we use the neural network to generate accurate posterior samples consistent with analyses using conventional sampling techniques
Do pulsar timing arrays observe merging primordial black holes?
In this letter we evaluate whether the gravitational wave background recently
observed by a number of different pulsar timing arrays could be due to merging
primordial supermassive black hole binaries. We find that for homogeneously
distributed primordial black holes this possibility is inconsistent with strong
cosmological and astrophysical constraints on their total abundance. If the
distribution exhibits some clustering, however, the merger rate will in general
be enhanced, opening the window for a consistent interpretation of the PTA data
in terms of merging primordial black holes.Comment: 8 pages, 3 figure
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