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Register a new userMonte Carlo Markov Chain Parameter Estimation in Semi-Analytic Models of Galaxy Formation
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[abridged] We present a statistical exploration of the parameter space of the De Lucia and Blaizot version of the Munich semi-analytic model built upon the millennium dark matter simulation. This is achieved by applying a Monte Carlo Markov Chain method to constrain the 6 free parameters that define the stellar and black-hole mass functions at redshift zero. The model is tested against three different observational data sets, including the galaxy K-band luminosity function, B-V colours, and the black hole-bulge mass relation, separately and combined, to obtain mean values, confidence limits and likelihood contours for the best fit model. Using each observational data set independently, we discuss how the SA model parameters affect each galaxy property and to what extent the correlations between them can lead to improved understandings of the physics of galaxy formation. When all the observations are combined, we find reasonable agreement between the majority of the previously published parameter values and our confidence limits. However, the need to suppress dwarf galaxy formation requires the strength of the supernova feedback to be significantly higher in our best-fit solution than in previous work. To balance this, we require the feedback to become ineffective in halos of lower circular velocity than before, so as to permit the formation of sufficient high-luminosity galaxies: unfortunately, this leads to an excess of galaxies around L*. Although the best-fit is formally consistent with the data, there is no region of parameter space that reproduces the shape of galaxy luminosity function across the whole magnitude-range. We discuss modifications to the semi-analytic model that might simultaneously improve the fit to the observed luminosity function and reduce the reliance on excessive supernova feedback in small halos.
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We introduce a fast Markov Chain Monte Carlo (MCMC) exploration of the astrophysical parameter space using a modified version of the publicly available code CIGALE (Code Investigating GALaxy emission). The original CIGALE builds a grid of theoretical Spectral Energy Distribution (SED) models and fits to photometric fluxes from Ultraviolet (UV) to Infrared (IR) to put contraints on parameters related to both formation and evolution of galaxies. Such a grid-based method can lead to a long and challenging parameter extraction since the computation time increases exponentially with the number of parameters considered and results can be dependent on the density of sampling points, which must be chosen in advance for each parameter. Markov Chain Monte Carlo methods, on the other hand, scale approximately linearly with the number of parameters, allowing a faster and more accurate exploration of the parameter space by using a smaller number of efficiently chosen samples. We test our MCMC version of the code CIGALE (called CIGALEMC) with simulated data. After checking the ability of the code to retrieve the input parameters used to build the mock sample, we fit theoretical SEDs to real data from the well known and studied SINGS sample. We discuss constraints on the parameters and show the advantages of our MCMC sampling method in terms of accuracy of the results and optimization of CPU time.
We present a Markov-chain Monte-Carlo (MCMC) technique to study the source parameters of gravitational-wave signals from the inspirals of stellar-mass compact binaries detected with ground-based gravitational-wave detectors such as LIGO and Virgo, for the case where spin is present in the more massive compact object in the binary. We discuss aspects of the MCMC algorithm that allow us to sample the parameter space in an efficient way. We show sample runs that illustrate the possibilities of our MCMC code and the difficulties that we encounter.
An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point. This paper removes the need to solve this optimisation problem by, instead, selecting each new point based on a Markov chain sample path. This significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement. The new algorithms are illustrated on a set of challenging Bayesian inference problems, and rigorous theoretical guarantees of consistency are established.
We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improvements in mixing rates relative to both non-interacting PMCMC samplers, and a single PMCMC sampler with an equivalent memory and computational budget. An additional advantage of the iPMCMC method is that it is suitable for distributed and multi-core architectures.
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a deterministic dynamics which is modified using a Markov transition kernel at random event times. These methods enjoy remarkable features including the ability to update only a subset of the state components while other components implicitly keep evolving and the ability to use an unbiased estimate of the gradient of the log-target while preserving the target as invariant distribution. However, they also suffer from important limitations. The deterministic dynamics used so far do not exploit the structure of the target. Moreover, exact simulation of the event times is feasible for an important yet restricted class of problems and, even when it is, it is application specific. This limits the applicability of these techniques and prevents the development of a generic software implementation of them. We introduce novel MCMC methods addressing these shortcomings. In particular, we introduce novel continuous-time algorithms relying on exact Hamiltonian flows and novel non-reversible discrete-time algorithms which can exploit complex dynamics such as approximate Hamiltonian dynamics arising from symplectic integrators while preserving the attractive features of continuous-time algorithms. We demonstrate the performance of these schemes on a variety of applications.
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