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Elorrieta, F., Eyheramendy, S., & Palma, W. (2019). Discretetime autoregressive model for unequally spaced timeseries observations. Astron. Astrophys., 627, 11 pp.
Abstract: Most timeseries models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuoustime autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discretetime process. We show that the model is weakly stationary and that it can be represented as a statespace system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.
Keywords: methods: statistical; methods: data analysis; stars: general

Elorrieta, F., Eyheramendy, S., Palma, W., & Ojeda, C. (2021). A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series. Mon. Not. Roy. Astron. Soc., 505(1), 1105–1116.
Abstract: In several disciplines, it is common to find time series measured at irregular observational times. In particular, in astronomy there are a large number of surveys that gather information over irregular time gaps and in more than one passband. Some examples are PanSTARRS, ZTF, and also the LSST. However, current commonly used time series models that estimate the time dependence in astronomical light curves consider the information of each band separately (e.g, CIAR, IAR, and CARMA models) disregarding the dependence that might exist between different passbands. In this paper, we propose a novel bivariate model for irregularly sampled time series, called the Bivariate Irregular Autoregressive (BIAR) model. The BIAR model assumes an autoregressive structure on each time series; it is stationary, and it allows to estimate the autocorrelation, the crosscorrelation and the contemporary correlation between two unequally spaced time series. We implemented the BIAR model on light curves, in the g and r bands, obtained from the ZTF alerts processed by the ALeRCE broker. We show that if the light curves of the two bands are highly correlated, the model has more accurate forecast and prediction using the bivariate model than a similar method that uses only univariate information. Further, the estimated parameters of the BIAR are useful to characterize longperiod variable stars and to distinguish between classes of stochastic objects, providing promising features that can be used for classification purposes.

Fierro, R., & Leiva, V. (2017). A stochastic methodology for risk assessment of a large earthquake when a long time has elapsed. Stoch. Environ. Res. Risk Assess., 31(9), 2327–2336.
Abstract: We propose a stochastic methodology for risk assessment of a large earthquake when a long time has elapsed from the last large seismic event. We state an approximate probability distribution for the occurrence time of the next large earthquake, by knowing that the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a nonhomogeneous Poisson process. As it is not possible to obtain an empirical cumulative distribution function of the waiting time for the next large earthquake, an estimator of its cumulative distribution function based on existing data is derived. We conduct a simulation study for detecting scenario in which the proposed methodology would perform well. Finally, a realworld data analysis is carried out to illustrate its potential applications, including a homogeneity test for the times between earthquakes.

GarciaPapani, F., UribeOpazo, M. A., Leiva, V., & Aykroyd, R. G. (2017). BirnbaumSaunders spatial modelling and diagnostics applied to agricultural engineering data. Stoch. Environ. Res. Risk Assess., 31(1), 105–124.
Abstract: Applications of statistical models to describe spatial dependence in georeferenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In nonspatial applications, where the data are unimodal and positively skewed, the BirnbaumSaunders (BS) distribution has excelled. This paper proposes a spatial loglinear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a realworld agricultural data set, where the spatial variability of phosphorus concentration in the soil is consideredwhich is extremely important for agricultural management.

Khosravi, M., Leiva, V., Jamalizadeh, A., & Porcu, E. (2016). On a nonlinear BirnbaumSaunders model based on a bivariate construction and its characteristics. Commun. Stat.Theory Methods, 45(3), 772–793.
Abstract: The BirnbaumSaunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Studentt distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skewt distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.

Leiva, V., Ferreira, M., Gomes, M. I., & Lillo, C. (2016). Extreme value BirnbaumSaunders regression models applied to environmental data. Stoch. Environ. Res. Risk Assess., 30(3), 1045–1058.
Abstract: Extreme value models are widely used in different areas. The BirnbaumSaunders distribution is receiving considerable attention due to its physical arguments and its good properties. We propose a methodology based on extreme value BirnbaumSaunders regression models, which includes model formulation, estimation, inference and checking. We further conduct a simulation study for evaluating its performance. A statistical analysis with realworld extreme value environmental data using the methodology is provided as illustration.

Mancini, L., Sarkis, P., Henning, T., Bakos, G. A., Bayliss, D., Bento, J., et al. (2020). The highly inflated giant planet WASP174b. Astron. Astrophys., 633, 12 pp.
Abstract: Context. The transiting exoplanetary system WASP174 was reported to be composed by a mainsequence F star (V = 11.8 mag) and a giant planet, WASP174b (orbital period Porb = 4.23 days). However only an upper limit was placed on the planet mass (<1.3 MJup), and a highly uncertain planetary radius (0.71.7 RJup) was determined.Aims. We aim to better characterise both the star and the planet and precisely measure their orbital and physical parameters.Methods. In order to constrain the mass of the planet, we obtained new measurements of the radial velocity of the star and joined them with those from the discovery paper. Photometric data from the HATSouth survey and new multiband, highquality (precision reached up to 0.37 mmag) photometric followup observations of transit events were acquired and analysed for getting accurate photometric parameters. We fit the model to all the observations, including data from the TESS space telescope, in two different modes: incorporating the stellar isochrones into the fit, and using an empirical method to get the stellar parameters. The two modes resulted to be consistent with each other to within 2<sigma>.Results. We confirm the grazing nature of the WASP174b transits with a confidence level greater than 5 sigma, which is also corroborated by simultaneously observing the transit through four optical bands and noting how the transit depth changes due to the limbdarkening effect. We estimate that approximate to 76% of the disk of the planet actually eclipses the parent star at midtransit of its transit events. We find that WASP174b is a highlyinflated hot giant planet with a mass of Mp = 0.330 +/ 0.091 MJup and a radius of Rp = 1.435 +/ 0.050 RJup, and is therefore a good target for transmissionspectroscopy observations. With a density of rho (p) = 0.135 +/ 0.042 g cm(3), it is amongst the lowestdensity planets ever discovered with precisely measured mass and radius.

Marchant, C., Leiva, V., Cysneiros, F. J. A., & Vivanco, J. F. (2016). Diagnostics in multivariate generalized BirnbaumSaunders regression models. J. Appl. Stat., 43(15), 2829–2849.
Abstract: BirnbaumSaunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with realworld multivariate data to show their potential applications.

Salinas, H., Pichara, K., Brahm, R., PerezGalarce, F., & Mery, D. (2023). Distinguishing a planetary transit from false positives: a Transformerbased classification for planetary transit signals. Mon. Not. Roy. Astron. Soc., 522(3), 3201–3216.
Abstract: Current spacebased missions, such as the Transiting Exoplanet Survey Satellite (TESS), provide a large database of light curves that must be analysed efficiently and systematically. In recent years, deep learning (DL) methods, particularly convolutional neural networks (CNN), have been used to classify transit signals of candidate exoplanets automatically. However, CNNs have some drawbacks; for example, they require many layers to capture dependencies on sequential data, such as light curves, making the network so large that it eventually becomes impractical. The selfattention mechanism is a DL technique that attempts to mimic the action of selectively focusing on some relevant things while ignoring others. Models, such as the Transformer architecture, were recently proposed for sequential data with successful results. Based on these successful models, we present a new architecture for the automatic classification of transit signals. Our proposed architecture is designed to capture the most significant features of a transit signal and stellar parameters through the selfattention mechanism. In addition to model prediction, we take advantage of attention map inspection, obtaining a more interpretable DL approach. Thus, we can identify the relevance of each element to differentiate a transit signal from false positives, simplifying the manual examination of candidates. We show that our architecture achieves competitive results concerning the CNNs applied for recognizing exoplanetary transit signals in data from the TESS telescope. Based on these results, we demonstrate that applying this stateoftheart DL model to light curves can be a powerful technique for transit signal detection while offering a level of interpretability.

Sanchez, L., Leiva, V., CaroLopera, F. J., & Cysneiros, F. J. A. (2015). On matrixvariate BirnbaumSaunders distributions and their estimation and application. Braz. J. Probab. Stat., 29(4), 790–812.
Abstract: Diverse phenomena from the realworld can be modeled using random matrices, allowing matrixvariate distributions to be considered. The normal distribution is often employed in this modeling, but usually the mentioned random matrices do not follow such a distribution. An asymmetric nonnormal model that is receiving considerable attention due to its good properties is the BirnbaumSaunders (BS) distribution. We propose a statistical methodology based on matrixvariate BS distributions. This methodology is implemented in the statistical software R. A simulation study is conducted to evaluate its performance. Finally, an application with realworld matrixvariate data is carried out to illustrate its potentiality and suitability.

SanchezSaez, P., Reyes, I., Valenzuela, C., Forster, F., Eyheramendy, S., Elorrieta, F., et al. (2021). Alert Classification for the ALeRCE Broker System: The Light Curve Classifier. Astron. J., 161(3), 141.
Abstract: We present the first version of the Automatic Learning for the Rapid Classification of Events (ALeRCE) broker light curve classifier. ALeRCE is currently processing the Zwicky Transient Facility (ZTF) alert stream, in preparation for the Vera C. Rubin Observatory. The ALeRCE light curve classifier uses variability features computed from the ZTF alert stream and colors obtained from AllWISE and ZTF photometry. We apply a balanced random forest algorithm with a twolevel scheme where the top level classifies each source as periodic, stochastic, or transient, and the bottom level further resolves each of these hierarchical classes among 15 total classes. This classifier corresponds to the first attempt to classify multiple classes of stochastic variables (including core and hostdominated active galactic nuclei, blazars, young stellar objects, and cataclysmic variables) in addition to different classes of periodic and transient sources, using real data. We created a labeled set using various public catalogs (such as the Catalina Surveys and Gaia DR2 variable stars catalogs, and the Million Quasars catalog), and we classify all objects with >= 6 gband or >= 6 rband detections in ZTF (868,371 sources as of 2020 June 9), providing updated classifications for sources with new alerts every day. For the top level we obtain macroaveraged precision and recall scores of 0.96 and 0.99, respectively, and for the bottom level we obtain macroaveraged precision and recall scores of 0.57 and 0.76, respectively. Updated classifications from the light curve classifier can be found at the ALeRCE Explorer website (http://alerce.online)..
Keywords: Active galaxies; Astronomy data analysis; Variable stars; Supernovae; Surveys

Sandford, E., Espinoza, N., Brahm, R., & Jordan, A. (2019). Estimation of singly transiting K2 planet periods with Gaia parallaxes. Mon. Not. Roy. Astron. Soc., 489(3), 3149–3161.
Abstract: When a planet is only observed to transit once, direct measurement of its period is impossible. It is possible, however, to constrain the periods of single transiters, and this is desirable as they are likely to represent the cold and far extremes of the planet population observed by any particular survey. Improving the accuracy with which the period of single transiters can be constrained is therefore critical to enhance the longperiod planet yield of surveys. Here, we combine Gaia parallaxes with stellar models and broadband photometry to estimate the stellar densities of K2 planet host stars, then use that stellar density information to model individual planet transits and infer the posterior period distribution. We show that the densities we infer are reliable by comparing with densities derived through asteroseismology, and apply our method to 27 validation planets of known (directly measured) period, treating each transit as if it were the only one, as well as to 12 true single transiters. When we treat eccentricity as a free parameter, we achieve a fractional period uncertainty over the true single transits of 94(58)(+87) per cent, and when we fix e = 0, we achieve fractional period uncertainty 15(6)(+30) per cent, a roughly threefold improvement over typical period uncertainties of previous studies.

SantosNeto, M., Cysneiros, F. J. A., Leiva, V., & Barros, M. (2014). A Reparameterized BirnbaumSaunders Distribution And Its Moments, Estimation And Applications. REVSTATStat. J., 12(3), 247–272.
Abstract: The BirnbaumSaunders (BS) distribution is a model that is receiving considerable attention due to its good properties. We provide some results on moments of a reparameterized version of the BS distribution and a generation method of random numbers from this distribution. In addition, we propose estimation and inference for the mentioned parameterization based on maximum likelihood, moment, modified moment and generalized moment methods. By means of a Monte Carlo simulation study, we evaluate the performance of the proposed estimators. We discuss applications of the reparameterized BS distribution from different scientific fields and analyze two realworld data sets to illustrate our results. The simulated and real data are analyzed by using the R software.

Sedaghati, E., MacDonald, R. J., CasasayasBarris, N., Hoeijmakers, H. J., Boffin, H. M. J., Rodler, F., et al. (2021). A spectral survey of WASP19b with ESPRESSO. Mon. Not. Roy. Astron. Soc., 505(1), 435–458.
Abstract: Highresolution precision spectroscopy provides a multitude of robust techniques for probing exoplanetary atmospheres. We present multiple VLT/ESPRESSO transit observations of the hotJupiter exoplanet WASP19b with previously published but disputed atmospheric features from low resolution studies. Through spectral synthesis and modelling of the RossiterMcLaughlin (RM) effect we calculate stellar, orbital and physical parameters for the system. From narrowband spectroscopy we do not detect any of Hi, Fei, Mgi, Cai, Nai, and Ki neutral species, placing upper limits on their line contrasts. Through crosscorrelation analyses with atmospheric models, we do not detect Fei and place a 3 sigma upper limit of on its mass fraction, from injection and retrieval. We show the inability to detect the presence of H2O for known abundances, owing to lack of strong absorption bands, as well as relatively low S/N ratio. We detect a barely significant peak (3.02 +/ 0.15 sigma) in the crosscorrelation map for TiO, consistent with the subsolar abundance previously reported. This is merely a hint for the presence of TiO and does not constitute a confirmation. However, we do confirm the presence of previously observed enhanced scattering towards blue wavelengths, through chromatic RM measurements, pointing to a hazy atmosphere. We finally present a reanalysis of lowresolution transmission spectra of this exoplanet, concluding that unocculted starspots alone cannot explain previously detected features. Our reanalysis of the FORS2 spectra of WASP19b finds a similar to 100x subsolar TiO abundance, precisely constrained to , consistent with the TiO hint from ESPRESSO. We present plausible paths to reconciliation with other seemingly contradicting results.

UlmerMoll, S., Lendl, M., Gill, S., Villanueva, S., Hobson, M. J., Bouchy, F., et al. (2022). Two longperiod transiting exoplanets on eccentric orbits: NGTS20 b (TOI5152 b) and TOI5153 b. Astron. Astrophys., 666, A46.
Abstract: Context. Longperiod transiting planets provide the opportunity to better understand the formation and evolution of planetary systems. Their atmospheric properties remain largely unaltered by tidal or radiative effects of the host star, and their orbital arrangement reflects a different and less extreme migrational history compared to closein objects. The sample of longperiod exoplanets with welldetermined masses and radii is still limited, but a growing number of longperiod objects reveal themselves in the Transiting Exoplanet Survey Satellite (TESS) data.
Aims. Our goal is to vet and confirm singletransit planet candidates detected in the TESS spacebased photometric data through spectroscopic and photometric followup observations with groundbased instruments. Methods. We used highresolution spectrographs to confirm the planetary nature of the transiting candidates and measure their masses. We also used the Next Generation Transit Survey (NGTS) to photometrically monitor the candidates in order to observe additional transits. Using a joint modeling of the light curves and radial velocities, we computed the orbital parameters of the system and were able to precisely measure the mass and radius of the transiting planets. Results. We report the discovery of two massive, warm Jupitersize planets, one orbiting the F8type star TOI5153 and the other orbiting the G1type star NGTS20 (=TOI5152). From our spectroscopic analysis, both stars are metal rich with a metallicity of 0.12 and 0.15, respectively. Only TOI5153 presents a second transit in the TESS extended mission data, but NGTS observed NGTS20 as part of its monotransit followup program and detected two additional transits. Followup highresolution spectroscopic observations were carried out with CORALIE, CHIRON, FEROS, and HARPS. TOI5153 hosts a planet with a period of 20.33 days, a planetary mass of 3.26(0.17)(+0.18) Jupiter masses (Mj), a radius of 1.06(0.04)(+0.04)R(J), and an orbital eccentricity of 0.091(0.02)(6)(+0.024). NGTS20 b is a 2.98()(0.)(15)(+0.16) MJ planet with a radius of 1.07(0.0)(4)(+0.04) RJ on an eccentric (0.432(0.023)(+0.023)) orbit with an orbital period of 54.19 days. Both planets are metal enriched and their heavy element content is in line with the previously reported massmetallicity relation for gas giants. Conclusions. Both warm Jupiters orbit moderately bright host stars, making these objects valuable targets for followup studies of the planetary atmosphere and measurement of the spinorbit angle of the system. 