Researchers in Statistics and Population Studies

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The analysis of indexed astronomical time series – X. Significance testing of O − C data
(Oxford University Press, 2006) Koen, Chris
It 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.
The analysis of indexed astronomical time series – XI. The statistics of oversampled white noise periodograms
(Oxford University Press, 2015) Koen, Chris
The 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.
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, Chris
With 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.
The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations
(Oxford University Press, 2005) Koen, Chris
The 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.
Confidence intervals for the correlation between the gamma-ray burst peak energy and the associated supernova peak brightness
(Oxford University Press, 2009) Koen, Chris
A 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.
Correcting CCD photometry of stars for seeing effects
(Oxford Univeristy Press, 2009) Koen, Chris
Systematic 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.
The detailed forms of the LMC Cepheid PL and PLC relations
(Oxford University Press, 2007) Koen, Chris; Kanbur, S; Ngeow, C
Possible 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.
Detection of an increasing orbital period in the subdwarf B eclipsing system NSVS 14256825
(Oxford University Press, 2012) Kilkenny, David; Koen, Chris
New 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.
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.
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.
Evidence for rapid evolution of periodic variations in an ultracool dwarf
(Oxford University Press, 2006) Koen, Chris
The 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.
An extensive search for rapid optical variability in ultracool dwarfs
(Oxford University Press, 2013) Koen, Chris
In 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.
Fitting power-law distributions to data with measurement errors
(Oxford University Press, 2009) Koen, Chris; Kondlo, L
If 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.
Fitting sinusoids to observations of rotating spotted stars
(Oxford University Press, 2007) Koen, Chris
It 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.
The “four sigma” limit for significant periodicities
(Springer Verlag, 2010) Koen, Chris
Most 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.
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.
HE 0230−4323 revisited: a new rapidly pulsating sdB star
(Oxford University Press, 2010) Kilkenny, David; Koen, Chris; Worters, H.
HE 0230−4323 is a hot sdB star in a binary system. An earlier work demonstrated that the light curve of the system shows a strong (∼4 per cent) reflection effect and also appears to exhibit photometric variations of the type associated with the slowly pulsating class of sdB star (multiple periods in the range ∼1–2 h). In this paper, we show that HE 0230−4323 is, in fact, a rapidly pulsating sdB with at least five frequencies between 3227 and 3532 μHz (periods between 310 and 283 s). The long periods previously claimed were the result of undersampling the light curve at a time interval very close to that of the short periods. The interpretation of the very slow variation (∼0.45 d) as a reflection effect in a close binary is unaffected by these new results.
HE0230–4323: an unusual pulsating hot subdwarf star
(Oxford University Press, 2007) Koen, Chris
HE 0230−4323 is a known binary, consisting of a subdwarf star and a companion which is not observable in the optical. Photometric measurements reported in this paper have shown it to be both a reflection-effect and a pulsating variable. The dominant pulsation frequencies changed over the course of several nights of observing, from ∼32–39 d−1 to ∼8–16 d−1. Observations were obtained through B and V filters, and the variations in the two wavebands appear to be approximately 180◦ out of phase.
IC and RC band time-series observations of some bright ultracool dwarfs
(Oxford University Press, 2005) Koen, Chris
The results of more than 100 h of CCD photometric monitoring of 10 L dwarfs and two T dwarfs are presented. Reasonable evidence is shown for IC band variability in DENIS 0255−4700, DENIS 1705−0516 and 2M 2104−1037. Substantial brightening of the T dwarf binary Indi Bab was observed over the course of 3.6 h; it is unlikely that this could have been caused by surface spots. No unequivocal variability could be detected in the RC band.
Improved SAAO–2MASS photometry transformations
(Oxford University Press, 2007) Koen, Chris; Marang, F.; Kilkenny, David; Jacobs, C.
Near-infrared photometry of 599 stars is used to calculate transformations from the South African Astronomical Observatory (SAAO) JHK system to the Two-Micron All-Sky Survey (2MASS) JHKS system. Both several-term formal regression relations and simplified transformations are presented. Inverse transformations (i.e. 2MASS to SAAO) are also given. The presence of non-linearities in some colour terms is highlighted.

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