Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling

Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for nanosecond gravitational waves. As for other applications of Gaussian distributions, outliers in timing measurements pose a significant challenge to statistical inference, since they can bias the estimation of timing and noise parameters, and affect reported parameter uncertainties. We describe and demonstrate a practical end-to-end approach to perform Bayesian inference of timing and noise parameters robustly in the presence of outliers, and to identify these probabilistically. The method is fully consistent (i.e., outlier-ness probabilities vary in tune with the posterior distributions of the timing and noise parameters), and it relies on the efficient sampling of the hierarchical form of the pulsar-timing likelihood. Such sampling has recently become possible with a "no-U-turn" Hamiltonian sampler coupled to a highly customized reparametrization of the likelihood; this code is described elsewhere, but it is already available online. We recommend our method as a standard step in the preparation of pulsar-timing-array datasets: even if statistical inference is not affected, follow-up studies of outlier candidates can reveal unseen problems in radio observations and timing measurements; furthermore, confidence in the results of gravitational-wave searches will only benefit from stringent statistical evidence that datasets are clean and outlier-free.Comment: 6 pages, 2 figures, RevTeX 4.

An Efficient Approximation to the Likelihood for Gravitational Wave Stochastic Background Detection Using Pulsar Timing Data

Direct detection of gravitational waves by pulsar timing arrays will become feasible over the next few years. In the low frequency regime ($10^{-7}$ Hz -- $10^{-9}$ Hz), we expect that a superposition of gravitational waves from many sources will manifest itself as an isotropic stochastic gravitational wave background. Currently, a number of techniques exist to detect such a signal; however, many detection methods are computationally challenging. Here we introduce an approximation to the full likelihood function for a pulsar timing array that results in computational savings proportional to the square of the number of pulsars in the array. Through a series of simulations we show that the approximate likelihood function reproduces results obtained from the full likelihood function. We further show, both analytically and through simulations, that, on average, this approximate likelihood function gives unbiased parameter estimates for astrophysically realistic stochastic background amplitudes.Comment: 10 pages, 3 figure

BMI1 and KAP1 interaction and function: BMI1 capped by KAP1?

The Polycomb-repressive complex 1 (PRC1) protein BMI1 is of major importance in the epigenetic regulation of gene expression. The repression of important tumour suppressor genes (such a P16INK4a and P14ARF) by means of chromatin remodeling has marked BMI1 as a proto-oncoprotein. We previously found evidence that posttranslational modification by phosphorylation may be implicated in the stability and functioning of BMI1. Furthermore, we found that KAP1, through direct interaction with BMI1, may be implicated in regulation of BMI1 functioning. I here begin to elucidate how phosphorylation affects BMI1 and how KAP1 regulates BMI1. Several U2OS or TIG3ER cell lines were created that overexpressed BMI1 wild type and mutants that either contain phospho-mimic or phospho-null mutations. shRNA’s were used to effectively knockdown KAP1 expression. The effect of BMI1 mutant overexpression and/or KAP1 knock down on proliferation was measured under cell stress conditions induced by arsenite, selenite or etoposide. The effect of KAP1 knock down and mutant KAP1 lacking the RingFinger domain (KAP1-DeltaRF) on sub-cellular localization was assessed in U2OS cells. Finally functional interaction between KAP1 and PRC1 was measured by analysis of transcriptional induction of the PRC1-target gene ATF3 upon mitogenic stimulation. BMI1 overexpression partially rescues arsenite induced senescence; this rescue activity is affected by its phosphorylation status. KAP1 knockdown increases the effect of BMI1 overexpression on proliferation under arsenite induced cell stress but ablates the differences observed between different BMI1 phospho-mutants. KAP1 induced increases of ATF3 induction point towards a functional interaction between KAP1 and PRC1. My experiments provide experimental indication that BMI1 affects proliferation under arsenite induced cell stress condition. This effect was enhanced by KAP1 knockdown suggesting that KAP1 inhibits the pro-proliferative effects of BMI1. Increased ATF3 induction in the presence of KAP1-DeltaRF mutant protein suggests that the KAP1 negatively controls expression of ATF3 in a RF-dependent manner. Further research is required to elucidate the exact molecular mechanisms underlying the function interaction of BMI1 and KAP1.

Accelerating pulsar timing data analysis

The analysis of pulsar timing data, especially in pulsar timing array (PTA) projects, has encountered practical difficulties: evaluating the likelihood and/or correlation-based statistics can become prohibitively computationally expensive for large datasets. In situations where a stochastic signal of interest has a power spectral density that dominates the noise in a limited bandwidth of the total frequency domain (e.g. the isotropic background of gravitational waves), a linear transformation exists that transforms the timing residuals to a basis in which virtually all the information about the stochastic signal of interest is contained in a small fraction of basis vectors. By only considering such a small subset of these "generalised residuals", the dimensionality of the data analysis problem is greatly reduced, which can cause a large speedup in the evaluation of the likelihood: the ABC-method (Acceleration By Compression). The compression fidelity, calculable with crude estimates of the signal and noise, can be used to determine how far a dataset can be compressed without significant loss of information. Both direct tests on the likelihood, and Bayesian analysis of mock data, show that the signal can be recovered as well as with an analysis of uncompressed data. In the analysis of IPTA Mock Data Challenge datasets, speedups of a factor of three orders of magnitude are demonstrated. For realistic PTA datasets the acceleration may become greater than six orders of magnitude due to the low signal to noise ratio

Analysis of the first IPTA Mock Data Challenge by the EPTA timing data analysis working group

This is a summary of the methods we used to analyse the first IPTA Mock Data Challenge (MDC), and the obtained results. We have used a Bayesian analysis in the time domain, accelerated using the recently developed ABC-method which consists of a form of lossy linear data compression. The TOAs were first processed with Tempo2, where the design matrix was extracted for use in a subsequent Bayesian analysis. We used different noise models to analyse the datasets: no red noise, red noise the same for all pulsars, and individual red noise per pulsar. We sampled from the likelihood with four different samplers: "emcee", "t-walk", "Metropolis-Hastings", and "pyMultiNest". All but emcee agreed on the final result, with emcee failing due to artefacts of the high-dimensionality of the problem. An interesting issue we ran into was that the prior of all the 36 (red) noise amplitudes strongly affects the results. A flat prior in the noise amplitude biases the inferred GWB amplitude, whereas a flat prior in log-amplitude seems to work well. This issue is only apparent when using a noise model with individually modelled red noise for all pulsars. Our results for the blind challenges are in good agreement with the injected values. For the GWB amplitudes we found h_c = 1.03 +/- 0.11 [10^{-14}], h_c = 5.70 +/- 0.35 [10^{-14}], and h_c = 6.91 +/- 1.72 [10^{-15}], and for the GWB spectral index we found gamma = 4.28 +/- 0.20, gamma = 4.35 +/- 0.09, and gamma = 3.75 +/- 0.40. We note that for closed challenge 3 there was quite some covariance between the signal and the red noise: if we constrain the GWB spectral index to the usual choice of gamma = 13/3, we obtain the estimates: h_c = 10.0 +/- 0.64 [10^{-15}], h_c = 56.3 +/- 2.42 [10^{-15}], and h_c = 4.83 +/- 0.50 [10^{-15}], with one-sided 2 sigma upper-limits of: h_c <= 10.98 [10^{-15}], h_c <= 60.29 [10^{-15}], and h_c <= 5.65 [10^{-15}].Comment: 10 pages, 5 figure

Pluraliteit wordt Vitaliteit. Een kritisch filosofisch maatschappelijk onderzoek vanuit het boek 'Identiteit' (2012) van Paul Verhaeghe; met Dansen als enige antwoord.

In deze scriptie wordt onderzocht wat de hedendaagse kapitalistische, neoliberale samenleving voor uitwerking heeft op het leven van het individu, en hoe dit mogelijk verbeterd kan worden. De scriptie begint met een contextuele analyse van het ontstaan van deze kapitalistische, neoliberale samenleving, en de uitwerkingen daarvan. Paul Verhaeghe schreef hier het boek ‘Identiteit’ (2012) over, dit boek zal semimonografisch besproken worden. Aan het eind zal de contextuele analyse, het boek van Verhaeghe en het maatschappelijk debat dat dit boek losmaakte verbonden worden in de zoektocht naar een antwoord. Via een filosofische denkexercitie beschrijft deze scriptie uiteindelijk de ontoereikendheid van deze antwoorden, en gaat op zoek naar een antwoord dat daadwerkelijk het dagelijks leven van het individu kan verbeteren; en komt uit bij dansen