Farhan Feroz

I briefly describe my research areas below.



Statistical Inference Methods

In recent years, it has become increasingly apparent that a great deal could be gained from interdisciplinary research linking the areas of statistical inference, machine learning, astrophysics and particle physics. Although the observational techniques in astrophysics vary widely from planets to galaxy clusters, the statistical foundations for extracting information from noisy data-sets remain the same. Prof. Mike Hobson and I have developed the MultiNest algorithm which can efficiently explore complex parameter spaces and also perform model selection between competing theories. MultiNest has reduced the computational cost of statistical inference in astrophysics typically by a factor of 100 as compared to Markov Chain Monte Carlo (MCMC) methods, and has been applied in many diverse areas including gravitational wave astronomy, exoplanet detection, galaxy cluster modelling, Cosmological model selection and supersymmetry (SUSY) studies in particle physics. Following figure shows an application of MultiNest in extracting galaxy clusters from weak lensing data-set.

Cluster extraction from simulated weak lensing data-set. Left panel shows the true mass map, middle panel, the noisy mass map and right panel, the mass map inferred using MultiNest. See [3] for more details.

I have also developed and applied artificial neural network (ANN) methods in astroparticle physics and shown that ANN can accelerate statistical analyses by a factor of million [12]. More recently, along with Phil Graff and Prof. Mike Hobson, I have combined ANN with MultiNest in a complementary manner to construct a Blind Accelerated Multimodal Bayesian Inference engine (BAMBI), which can be applied to generic inference problems in an automated manner to yield rapidly generated parameter estimates, as well as a trained ANN for likelihood evaluation that can be used to replace original likelihood codes in any subsequent analyses.



Particle Physics Phenomenology

With the forthcoming high quality data from LHC, the particle physics community is keen to move from ruling out parts of model parameters to do a systematic model comparison between several proposed fundamental underlying theories and estimate their parameters. This has resulted in a great deal of effort being put in the development and application of efficient statistical and computational tools to carry out robust statistical inference using all the available data for supersymmetry (SUSY) models. Statistical inference of SUSY models is particularly challenging. The parameter space is inherently fragmented due to the presence of unphysical points throughout the parameter space. Moreover, a particularly important constraint comes from the cold dark matter (DM) relic density, as determined by WMAP. DM is assumed to consist solely of the lightest supersymmetric particle (LSP). The accuracy of the DM constraint results in the regions in parameter space favoured by the data being very narrow and steep as the system is rather under-constrained. This makes the global fit to all the relevant SUSY parameters potentially difficult with prior dependence still present.

2D posterior distributions for the CMSSM parameters using log priors and all presently available constraints. The contours represent the 68% and 95% Bayesian credible regions. See [12] for more details.

I have been involved in several studies of SUSY models within the Minimal Supersymmetric Standard Model (MSSM) framework using MultiNest. Prompted by the results of these studies, I participated in a study to assess the coverage properties of confidence and credible intervals on the Constrained MSSM (CMSSM) parameter space inferred from a Bayesian posterior and the frequentist profile likelihood [12] based on an ATLAS sensitivity study, using MultiNest in combination with artificial neural networks to approximate the mapping between CMSSM parameters and weak-scale particle masses. We concluded that both the Bayesian posterior and the frequentist profile likelihood intervals can significantly over-cover and identified the origin of this effect to physical boundaries in the parameter space.



Gravitational Wave Astronomy

Gravitational waves (GW) are extremely weak ripples of spacetime that propagate at the speed of light. The strongest sources of GW emission are concentrations of highly relativistic masses: white dwarfs, neutron stars, supermassive black holes (SMBH), cosmic strings and the early universe itself. Although, GW have been indirectly detected through monitoring of the orbital decay of pulsars in binary systems, their direct detection is still elusive. Planned improvements in the sensitivity of the ground-based GW laser interferometers like advanced-LIGO (aLIGO), make the first ever direct detection of GW plausible. The key difficulty in analysing GW data-sets is the presence of many secondary maxima in the likelihood surfaces of several sources and therefore standard inference algorithms like MCMC tend to get stuck in secondary maxima and are unable to find the primary mode. It is therefore desirable to have algorithms that can simultaneously identify and characterize all the modes of the likelihood surface.

I have worked on the detection and accurate characterization of SMBH and cosmic strings from simulated GW data-sets, even in the presence of multiple modes [21, 17]. I have also taken part in the Mock Data Challenges for the proposed Laser Interferometer Space Antenna (LISA) in which our results were highly competitive with all the other entries submitted [16].

Along with a few colleagues at Cambridge, I am a member of the LIGO Scientific Collaboration where we have been working with the Compact Binary Coalescence group, analysing real data using our algorithms and testing them against existing LIGO algorithms.



Extrasolar Planet Detection

Extrasolar planetary searches have made great advances in the last decade as a result of the data gathered by several telescopes. So far more than 500 exoplanets have been discovered. Extreme faintness of planets at interstellar distances makes their direct observations very difficult. However, there are indirect ways of detecting exoplanets, the most successful of which are the radial velocity (RV) and transit methods. The RV method measures the doppler shifts in the spectrum of the host star according to its RV, the velocity along the line-of-sight to the observer, caused by the revolution of the star around the common centre of mass of the system due to the gravitational force between the planets and their host star. Several such measurements, usually over an extended period of time, can then be used to detect exoplanets. Transit method relies on continuous measurements of the brightness of stars. If a planet transits in front of the starís disk then the observed brightness of the star drops by an amount which depends on the orbital parameters of the planet.

RV measurements, with 68% errorbars, and the mean fitted RV curve with 1 (red solid line) and 2-companions (green dashed line) for HIP 5158. See [7] for more details.
Traditionally, the number of planets and their orbital parameters have been obtained from RV measurements by searching for periodicity in the RV data using the periodogram. Bayesian methods have several advantages over traditional methods, for example when the data do not cover a complete orbital phase of the planet. Bayesian inference also provides a rigorous way of performing model selection which is required to decide the number of planets favoured by the data. However, finding the correct number of planets in a RV or transit data-set is very challenging, as the number of modes in the likelihood increase exponentially with the number of planets. Moreover, calculating the probability of data-set supporting n planets, requires the evaluation of a multi-dimensional integral which can become prohibitive for as few as 3 planets. With Prof. Mike Hobson and Sreekumar Balan, I have recently introduced a new general approach to Bayesian object detection that is applicable to exoplanet studies, even for systems with a large number of planets [8]. We have analysed several RV data-sets and discovered a companion orbiting star HIP 5158 with period at least 10 years [7].

My current research is focused on the development of fully automated transit analysis method for the analysis of Kepler data-sets.



Others

My other research interests include studies of galaxy clusters through gravitational lensing and Sunyaev-Zelídovich (SZ) effect and topological defects in the early universe, in particular cosmic textures and cosmic strings. Clusters of galaxies are the most massive gravitationally bound objects in the universe and, as such, are critical tracers of the formation of large-scale structure. Having helped develop the analysis software for Arcminute Microkelvin Imager (AMI) (SZ telescope built by Cavendish Lab) [25], I have been involved in several studies of galaxy clusters [3, 5, 6, 9, 10], including a detection of previously unknown galaxy cluster [6]. I have recently developed a method to do detailed modelling of the triaxial structure of clusters for studies through lensing [4] and shown that erroneously assuming spherical symmetry can lead to the mistaken conclusion that some substructure is present in the galaxy clusters or, even worse, that multiple galaxy clusters are present in the field.





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