Browsing by Author "Koen, Chris"
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Item The analysis of indexed astronomical time series – X. Significance testing of O − C data(Oxford University Press, 2006) Koen, ChrisIt is assumed that O − C (‘observed minus calculated’) values of periodic variable stars are determined by three processes, namely measurement errors, random cycle-to-cycle jitter in the period, and possibly long-term changes in the mean period. By modelling the latter as a random walk, the covariances of all O − C values can be calculated. The covariances can then be used to estimate unknown model parameters, and to choose between alternative models. Pseudo-residuals which could be used in model fit assessment are also defined. The theory is illustrated by four applications to spotted stars in eclipsing binaries.Item The analysis of indexed astronomical time series – XI. The statistics of oversampled white noise periodograms(Oxford University Press, 2015) Koen, ChrisThe distribution of the maxima of periodograms is considered in the case where the time series is made up of regularly sampled, uncorrelated Gaussians. It is pointed out that if there is no oversampling, then for large data sets, the known distribution of maxima tends to a oneparameter Gumbel distribution. Simulations are used to demonstrate that for oversampling by large factors, a two-parameter Gumbel distribution provides a highly accurate representation of the simulation results. As the oversampling approaches the continuous limit, the twoparameter Gumbel distribution takes on a simple form which depends only on the logarithm of the number of data. Subsidiary results are the autocorrelation function of the oversampled periodogram; expressions for the accuracy of simulated percentiles; and the relation between percentiles of the periodogram and the amplitude spectrum.Item The analysis of indexed astronomical time series – XII. The statistics of oversampled Fourier spectra of noise plus a single sinusoid(Oxford University Press, 2015) Koen, ChrisWith few exceptions, theoretical studies of periodogram properties focus on pure noise time series. This paper considers the case in which the time series consists of noise together with a single sinusoid, observed at regularly spaced time points. The distribution of the periodogram ordinates in this case is shown to be of exponentially modified Gaussian form. Simulations are used to demonstrate that if the periodogram is substantially oversampled (i.e. calculated in a dense grid of frequencies), then the distribution of the periodogram maxima can be accurately approximated by a simple form (at least at moderate signal-to-noise ratios). This result can be used to derive a calculation formula for the probability of correct signal frequency identification at given values of the time series length and (true) signal-to-noise ratio. A set of curves is presented which can be used to apply the theory to, for example, asteroseismic data. An illustrative application to Kepler data is given.Item The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations(Oxford University Press, 2005) Koen, ChrisThe theory of low-order linear stochastic differential equations is reviewed. Solutions to these equations give the continuous time analogues of discrete time autoregressive time-series. Explicit forms for the power spectra and covariance functions of first- and second-order forms are given. A conceptually simple method is described for fitting continuous time autoregressive models to data. Formulae giving the standard errors of the parameter estimates are derived. Simulated data are used to verify the performance of the methods. Irregularly spaced observations of the two hydrogen-deficient stars FQ Aqr and NO Ser are analysed. In the case of FQ Aqr the best-fitting model is of second order, and describes a quasi-periodicity of about 20 d with an e-folding time of 3.7 d. The NO Ser data are best fitted by a first-order model with an e-folding time of 7.2 d.Item Confidence intervals for the correlation between the gamma-ray burst peak energy and the associated supernova peak brightness(Oxford University Press, 2009) Koen, ChrisA strong correlation between the gamma-ray burster peak energy and the peak luminosity of the associated supernova was discovered by Li for four GRBs. Despite the fact that the formal significance level of the correlation is 0.3 per cent, the smallness of the data set requires careful further evaluation of the result. Subject to the assumption that the data are bivariate Gaussian, a 95 per cent confidence interval of (−0.9972, 0.02) for the correlation is derived. Using data from the literature, it is shown that the distribution of known peak GRB energies is not Gaussian if X-ray flashes are included in the sample. This leads to a proposed alternative to the bivariate Gaussian model, which entails describing the dependence between the two variables by a Gaussian copula. The copula is still characterized by a correlation coefficient. The Bayesian posterior distribution of the correlation coefficient is evaluated using a Markov chain Monte Carlo method. The mean values of the posterior distributions range from −0.33 to about zero, depending on the specifics of the supernova (SN) peak brightness distribution. The implication is that the existing data favour a modest correlation between the GRB peak energy and the SN peak brightness; confidence intervals are very wide and include zero.Item Correcting CCD photometry of stars for seeing effects(Oxford Univeristy Press, 2009) Koen, ChrisSystematic variability in stellarmagnitudes, as derived from profile fitting to CCD images,may in some instances be due to variable seeing. It is suggested that this happens in cases where the stars are unresolved pairs, typically with sub-arcsecond separation between the components. It is shown that the fitting of suitable Generalised Additive Models to time series photometry can disentangle intrinsic stellar variability and seeing-induced brightness changes. It is possible that there will be a fixed seeing response associated with a given star which exhibits the effect: estimation of this response from several long photometric runs is demonstrated.Item The detailed forms of the LMC Cepheid PL and PLC relations(Oxford University Press, 2007) Koen, Chris; Kanbur, S; Ngeow, CPossible deviations from linearity of the Large Magellanic Cloud Cepheid period–luminosity (PL) and period–luminosity–colour (PLC) relations are investigated. Two data sets are studied, respectively from the Optical Gravitational Lensing Experiment (OGLE) and MACHO projects. A non-parametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for, then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These findings are confirmed by fitting ‘Generalized Additive Models’ (non-parametric regression functions) to the two data sets. Colour dependence is shown to be non-linear in both data sets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and the colour functions in the MACHO data.Item Detection of an increasing orbital period in the subdwarf B eclipsing system NSVS 14256825(Oxford University Press, 2012) Kilkenny, David; Koen, ChrisNew timings of eclipses made in 2010 and 2011 are presented for the hot subdwarf B (sdB) eclipsing binary NSVS 14256825. Composed of an sdB star and a much cooler companion, with a period near 0.1104 days, this system is very similar to the prototype sdB eclipsing binary HW Vir. The new observations show that the binary period of NSVS 14256825 is rapidly increasing at a rate of about 12 × 10−12 days orbit−1.Item A detection threshold in the amplitude spectra calculated from Kepler data obtained during K2 mission.(Oxford University Press, 2015) Baran, A.C.; Koen, Chris; Pokrzywka, B.We present our analysis of simulated data in order to derive a detection threshold which can be used in the pre-whitening process of amplitude spectra. In case of ground-based data of pulsating stars, this threshold is conventionally taken to be four times the mean noise level in an amplitude spectrum. This threshold is questionable when space-based data are analysed. Our effort is aimed at revising this threshold in the case of continuous 90-d Kepler K2 phase observations. Our result clearly shows that a 95 per cent confidence level, common for ground observations, can be reached at 5.4 times the mean noise level and is coverage dependent. In addition, this threshold varies between 4.8 and 5.7, if the number of cadences is changed. This conclusion should secure further pre-whitening and helps to avoid over-interpretation of spectra of pulsating stars observed with the Kepler spacecraft during K2 phase. We compare our results with the standard approach widely used in the literature.Item The Edinburgh-Cape Blue Object Survey - III. Zone 2; galactic latitudes -30? > b > -40?(Oxford University Press, 2013) Kilkenny, David; Koen, Chris; Hambly, N.; MacGillivray, H.; Stobie, R. S.; O’Donoghue, D.The Edinburgh–Cape Blue Object Survey seeks to identify point sources with an ultraviolet excess. Results for zone 2 of the survey are presented here, covering that part of the South Galactic Cap between 30◦ and 40◦ from the Galactic plane and south of about −12. ◦ 3 of declination. Edinburgh–Cape zone 2 comprises 66 UK Schmidt Telescope fields covering about 1730 deg2, in which we find some 892 blue objects, including 423 hot subdwarfs (∼47 per cent); 128 white dwarfs (∼14 per cent); 25 cataclysmic variables (∼3 per cent); 119 binaries (∼13 per cent), mostly composed of a hot subdwarf and a main-sequence F or G star; 66 horizontal branch stars (∼7 per cent) and 48 ‘star-like’ extragalactic objects (∼5 per cent). A further 362 stars observed in the survey, mainly low-metallicity F- and G-type stars, are also listed. Both low-dispersion spectroscopic classification and UBV photometry are presented for almost all of the hot objects and either spectroscopy or photometry (or both) for the cooler ones.Item Estimation of Pareto Distribution Functions from Samples Contaminated by Measurement Errors(University of the Western Cape, 2010) Kondlo, Lwando Orbet; Koen, ChrisEstimation of population distributions, from samples that are contaminated by measurement errors, is a common problem. This study considers the problem of estimating the population distribution of independent random variables Xi, from error-contaminated samples ~i (.j = 1, ... , n) such that Yi = Xi + f·.i, where E is the measurement error, which is assumed independent of X. The measurement error ( is also assumed to be normally distributed. Since the observed distribution function is a convolution of the error distribution with the true underlying distribution, estimation of the latter is often referred to as a deconvolution problem. A thorough study of the relevant deconvolution literature in statistics is reported. We also deal with the specific case when X is assumed to follow a truncated Pareto form. If observations are subject to Gaussian errors, then the observed Y is distributed as the convolution of the finite-support Pareto and Gaussian error distributions. The convolved probability density function (PDF) and cumulative distribution function (CDF) of the finite-support Pareto and Gaussian distributions are derived. The intention is to draw more specific connections bet.ween certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher's information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available. Simulated data are used to validate the methodology. A real-life application of the methodology is illustrated by fitting convolved distributions to astronomical dataItem Estimation of Pareto distribution functions from samples contaminated by measurement errors(University of the Western Cape, 2010) Kondlo, Lwando Orbet; Koen, Chris; Faculty of ScienceThe intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher’s information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available.Item Estimation of the coherence time of stochastic oscillations from modest samples(Oxford University Press, 2012) Koen, Chris‘Quasi-periodic’ or ‘solar-like’ oscillations can be described by three parameters – a characteristic frequency, a coherence time (or ‘quality factor’) and the variance of the random driving process. This paper is concerned with the estimation of these quantities, particularly the coherence time, from modest sample sizes (observations covering of the order of a hundred or fewer oscillation periods). Under these circumstances, finite sample properties of the periodogram (bias and covariance) formally invalidate the commonly used maximum-likelihood procedure. It is shown that it none the less gives reasonable results, although an appropriate covariance matrix should be used for the standard errors of the estimates. Tailoring the frequency interval used, and oversampling the periodogram, can substantially improve parameter estimation. Maximum-likelihood estimation in the time-domain has simpler statistical properties, and generally performs better for the parameter values considered in this paper. The effects of added measurement errors are also studied. An example analysis of pulsating star data is given.Item Evidence for rapid evolution of periodic variations in an ultracool dwarf(Oxford University Press, 2006) Koen, ChrisThe results of three short photometric monitoring runs on the L0 dwarf 2MASS J06050196−2342270, during three consecutive nights, are presented. The observations show the persistent presence of a 2.4-h period, with an IC band amplitude which decreased from 27 to 11 mmag over the three nights. The amplitude in the RC band appeared to be substantially smaller than in the IC band.Item An extensive search for rapid optical variability in ultracool dwarfs(Oxford University Press, 2013) Koen, ChrisIn this paper, a summary of optical time-series photometry of 125 ultracool dwarfs is given. The observing strategy was to monitor each object continuously for 2–3 h in order to ascertain whether itwas rapidly variable. Many of the targetswere observed atmultiple epochs, to follow up possible short time-scale variability, or to test for slow brightness changes on longer timescales. The 353 data sets obtained contain nearly 22 000 individual measurements. Optical (IC) magnitudes, accurate to roughly 0.1–0.2 mag, were derived for 21 objects for which there is no optical photometry in the literature. It is shown that photometry is affected by variable seeing in a large percentage of the time-series observations. Since this could give the appearance of variability intrinsic to the objects, magnitudes are modelled as functions of both time and seeing. Several ultracool dwarfs which had not been monitored before are variable, according to certain model-fitting criteria. A number of objects with multi-epoch observations appear to be variable on longer time-scales. Since testing for variability is far from being straightforward, the time-series data are made available so that interested readers can perform their own analyses.Item Fitting extreme value distributions to the Zambezi River flood water levels recorded at Katima Mulilo in Namibia (1965-2003)(University of the Western Cape, 2005) Kamwi, Innocent Silibelo; Koen, Chris; Blignaut, Renette JThis study sought to identify and fit the appropriate extreme value distribution to flood data, using the method of maximum likelihood. To examine the uncertainty of the estimated parameters and evaluate the goodness of fit of the model identified. The study revealed that the three parameter Weibull and the generalised extreme value (GEV) distributions fit the data very well. Standard errors for the estimated parameters were calculated from the empirical information matrix. An upper limit to the flood levels followed from the fitted distribution.Item Fitting power-law distributions to data with measurement errors(Oxford University Press, 2009) Koen, Chris; Kondlo, LIf X, which follows a power-law distribution, is observed subject to Gaussian measurement error e, thenX+e is distributed as the convolution of the power-lawand Gaussian distributions. Maximum-likelihood estimation of the parameters of the two distributions is considered. Large-sample formulae are given for the covariance matrix of the estimated parameters, and implementation of a small-sample method (the jackknife) is also described. Other topics dealt with are tests for goodness of fit of the posited distribution, and tests whether special cases (no measurement errors or an infinite upper limit to the power-law distribution) may be preferred. The application of the methodology is illustrated by fitting convolved distributions to masses of giant molecular clouds in M33 and the Large Magellanic Cloud (LMC), and to HI cloud masses in the LMC.Item Fitting sinusoids to observations of rotating spotted stars(Oxford University Press, 2007) Koen, ChrisIt is assumed that K blocks (e.g. seasons) of observations are available, and the parameters characterizing a fixed-frequency sinusoidal variability (mean light level, amplitude, phase) are constant within each of the blocks. The paper is concerned with estimation when any combination of these parameters varies between blocks of observations. This allows observations subject to changes in mean light level, spot sizes and/or spot locations to be modelled. Objective choices between competing models, and the calculation of the standard errors of model parameters, are also dealt with. Illustrative applications to simulated and real data are given.Item The “four sigma” limit for significant periodicities(Springer Verlag, 2010) Koen, ChrisMost of the pulsations which have been observed in sdB stars have very low amplitudes. Detection of modes from photometric observations is usually performed by noting the most prominent peaks in a periodogram or, equivalently, an amplitude spectrum. A common strategy is to assume that peaks which exceed four times the mean noise level correspond to significant periodicities. The efficiency of the assumption is investigated by simulation. It is found that the actual significance levels corresponding to the four sigma limit may vary by orders of magnitude, depending on the exact data configuration.Item Further observations of Hipparcos red stars and standards for UBV(RI)C photometry(Oxford University Press, 2007) Kilkenny, David; Koen, Chris; van Wyk, F.; Marang, F.; Cooper, D.We present homogeneous and standardized UBV(RI)C JHK photometry for over 100 M stars selected from an earlier paper on the basis of apparent photometric constancy. L photometry has been obtained for stars brighter than about L = 6. Most of the stars have a substantial number of UBV(RI)C observations and, it is hoped, will prove useful as red supplementary standards. Additionally,we list JHK photometry for nearly 300 Hipparcos red stars not selected as standards, as well as L photometry for the brightest stars.