adsabs/AstroCLIMB huggingface dataset:
Paper: Statistical Analysis of Circular-ribbon Flares
Authors: Yanjie Zhang, Qingmin Zhang, Dechao Song, Shuting Li, Jun Dai, Zhe Xu, Haisheng Ji
Figure caption: Left panels: three CFs observed by AIA in 131 Å. Middle panels: associated CMEs and shock waves observed by LASCO/C2. The apparent speeds of the CMEs are labeled. Right panels: radio dynamic spectra of the three events recorded by the e-Callisto stations, showing the corresponding type II radio bursts with drifting frequency.
Paper: Statistical Analysis of Circular-ribbon Flares
Authors: Yanjie Zhang, Qingmin Zhang, Dechao Song, Shuting Li, Jun Dai, Zhe Xu, Haisheng Ji
Figure caption: Scatterplot between the peak SXR flux in 1–8 Å of CFs related to CMEs and the CME angular widths (W CME). The correlation coefficient is ∼0.54.
Paper: Statistical Analysis of Circular-ribbon Flares
Authors: Yanjie Zhang, Qingmin Zhang, Dechao Song, Shuting Li, Jun Dai, Zhe Xu, Haisheng Ji
Figure caption: Scatterplot between V CME and W CME, indicating faster CMEs tend to be wider. The correlation coefficient is ∼0.56.
Paper: Statistical Analysis of Circular-ribbon Flares
Authors: Yanjie Zhang, Qingmin Zhang, Dechao Song, Shuting Li, Jun Dai, Zhe Xu, Haisheng Ji
Figure caption: Scatterplot between the peak SXR flux in 1–8 Å of CFs related to CMEs and V CME. The correlation coefficient is ∼0.37.
Paper: Statistical Analysis of Circular-ribbon Flares
Authors: Yanjie Zhang, Qingmin Zhang, Dechao Song, Shuting Li, Jun Dai, Zhe Xu, Haisheng Ji
Figure caption: (a) Percentages of M- and X-class flares for the three groups of CMEs. (b) Percentages of minifilament eruptions for the three groups of CMEs.
Paper: Statistical Analysis of Circular-ribbon Flares
Authors: Yanjie Zhang, Qingmin Zhang, Dechao Song, Shuting Li, Jun Dai, Zhe Xu, Haisheng Ji
Figure caption: Distribution of the CME speed (V CME) related to CFs.
Paper: Predicting Solar Energetic Particles Using SDO/HMI Vector Magnetic Data Products and a Bidirectional LSTM Network
Authors: Yasser Abduallah, Vania K. Jordanova, Hao Liu, Qin Li, Jason T. L. Wang, Haimin Wang
Figure caption: Architecture of the proposed biLSTM network. Yellow boxes represent biLSTM cells. These cells are connected to an attention layer (A) that contains m neurons, which are connected to a fully connected layer (FCL). (In the study presented here, m is set to 10.) During testing/prediction, the input to the network is a test data sequence with m consecutive data samples x  t−m+1, x  t−m+2 ...x  t−1, x  t  where x  t  is the test data sample at time point t. The trained biLSTM network predicts the label (color) of the test data sequence, more precisely the label (color) of x  t . The output layer of the biLSTM network calculates a probability (﹩\hat{y}﹩) between 0 and 1. If ﹩\hat{y}﹩ is greater than or equal to a threshold, which is set to 0.5, the biLSTM network outputs 1 and predicts x  t  to be positive, i.e., predicts the label (color) of x  t  to be blue; see Figure 1. Otherwise, the biLSTM network outputs 0 and predicts x  t  to be negative, i.e., predicts the label (color) of x  t  to be green; see Figure 1.
Paper: Predicting Solar Energetic Particles Using SDO/HMI Vector Magnetic Data Products and a Bidirectional LSTM Network
Authors: Yasser Abduallah, Vania K. Jordanova, Hao Liu, Qin Li, Jason T. L. Wang, Haimin Wang
Figure caption: Example data sequences used to train and test our biLSTM network where each data sequence contains 10 consecutive data samples. (a) Three positive training data sequences taken from a flaring AR. (b) Three negative training data sequences taken from a flaring AR. In (a) and (b), the label (color) of a training data sequence is defined to be the label (color) of the last data sample in the training data sequence while the labels (colors) of the other nine data samples in the training data sequence are ignored. (c) A test data sequence formed for predicting the label (color) of the last data sample x  t  in a flaring AR.
Paper: Predicting Solar Energetic Particles Using SDO/HMI Vector Magnetic Data Products and a Bidirectional LSTM Network
Authors: Yasser Abduallah, Vania K. Jordanova, Hao Liu, Qin Li, Jason T. L. Wang, Haimin Wang
Figure caption: Confusion matrices of RF, MLP, SVM, LSTM, and biLSTM for the FC_S problem. For each T, T = 12, 24, 36, 48, 60, 72, and each machine-learning method, the figure shows the minimum, average, maximum (displayed from top to bottom) TP, FN, TN, FP, respectively, from the six runs based on our cross-validation scheme.
Paper: Predicting Solar Energetic Particles Using SDO/HMI Vector Magnetic Data Products and a Bidirectional LSTM Network
Authors: Yasser Abduallah, Vania K. Jordanova, Hao Liu, Qin Li, Jason T. L. Wang, Haimin Wang
Figure caption: Confusion matrices of RF, MLP, SVM, LSTM, and biLSTM for the F_S problem. For each T, T = 12, 24, 36, 48, 60, 72, and each machine-learning method, the figure shows the minimum, average, maximum (displayed from top to bottom) TP, FN, TN, FP, respectively, from the six runs based on our cross-validation scheme.
Paper: Predicting Solar Energetic Particles Using SDO/HMI Vector Magnetic Data Products and a Bidirectional LSTM Network
Authors: Yasser Abduallah, Vania K. Jordanova, Hao Liu, Qin Li, Jason T. L. Wang, Haimin Wang
Figure caption: Parameter selection results for (a) the FC_S problem, and (b) the F_S problem.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Top: the microlensing formalism of Gould (2000) augmented by microlensing parallax relevant parameters. The bold line represents the path of light from the source (S) to the heliocentric observer (O ⊙), which is deflected by the lens (L). D L and D S are the assumed Euclidean distances to the lens and source from O ⊙, respectively. The deflection angle α is a function of the Einstein radius r E(α = 4GM/r E c 2), while θ E is the Einstein angular radius on the sky. The Einstein radius projected onto the S–O normal plane is defined as ﹩{\tilde{r}}_{{\rm{E}}}﹩. In this projection, Earth’s orbit (green dashed line) is angled by the ecliptic latitude of the source star β. Bottom: the orbit of Earth (dashed green ellipse) projected onto the S-O ⊙ normal plane. Note that the ellipticity and corresponding semimajor and semiminor axes a and b, respectively, are representative of a nearly circular orbit projected on the plane. The frame is oriented such that the time, t  c , at which the Earth is closest to the O ⊙–S line is at the top. Within the orbital plane of Earth, λ is the angle of t  c  from the vernal equinox. Note that t  c  can be determined by the time of vernal equinox, t VE and the ecliptic longitude of S, ﹩\lambda \,({t}_{c}=\tfrac{\lambda }{2\pi }T\,+{t}_{\mathrm{VE}})﹩, where T is the Earth’s orbital period in days. The angle β in the left figure is simply the ecliptic latitude of S, and ξ  n  is in the plane of the page and corresponds to the northern celestial coordinate unit vector. The phase angle of Earth at time t is given by λ + Ω0 ∗ (t − t  c ), where Ω0 = 2π/T is the conversion factor for the orbital time to radians.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Example OGLE-III light curve (OGLE BLG 156.7.141434) with results from our MCMC analysis. First panel: raw data published by Wyrzykowski et al. (2015); second panel: GP component of the PSPL+parallax+GP model with the MAP in thick black and 50 random draws from our posteriors in orange. The data has the MAP PSPL+parallax subtracted from the raw data in the first panel and rescaled uncertainty on each measurement by the MAP value of K in our model. Third panel: 200 microlensing posterior samples (orange) and MAP parallax model (solid blue) subtracting away the MAP GP from the panel above. The MAP PSPL+GP model is also plotted for comparison. The data is detrended, meaning the MAP GP model realization (black curve in the second panel) is subtracted away. Fourth panel: residual flux after subtracting the PSPL+GP model. The blue curve shows the difference between PSPL+parallax+GP and PSPL+GP models. In this case, the two are similar (PSPL+parallax+GP to PSPL+GP likelihood-ratio = 1.6).
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: The geometry in the plane of the sky normal to the heliocentric observer-source axis. The lens (black circle) passes to the north and west of the source with a relative proper-motion direction characterized by the angle ϕ with a minimum angular separation of u 0. These are each model parameters in our analysis. The unit vectors ﹩{\hat{\xi }}_{n}﹩ and ﹩{\hat{\xi }}_{e}﹩ are aligned with the ecliptic coordinate latitude and longitude, respectively. The unit vector ﹩{\hat{\mu }}_{\mathrm{rel}}﹩ is in the direction of the relative motion of the lens with respect to the O ⊙–S coordinate.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Graphical representation for the prior probability density function for the population modeling of the Einstein crossing time distribution for OGLE-III (left panel) and OGLE-IV (right panel). The blue histogram in each panel shows the normalized bin heights for the MAP t E values for our individual fits. The orange bars show the 68% confidence interval, about the mean (solid orange curve), for random samples from the Dirichlet-prior distribution (shown in gray ticks). The Dirichlet priors are for b = 20 and c = 0.02.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Example OGLE-III light curve (OGLE BLG 156.7.141434) showing the baseline of the light curve. The baseline is clearly rising over the course of several years in addition to a quasiperiodic oscillatory behavior. We have designed our GP kernel to handle these systematics specifically since these are frequent in OGLE data.
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Petersen diagram: P long/P short vs. P long. Black dots denote classical RRd stars based on OGLE and K2 observations, red circles show the anomalous RRd (aRRd) stars, blue triangles show the peculiar RRd stars (pRRd) stars. Green triangles show our two new RRd stars, while the yellow triangles show KPP#25, a nonmodulated RRab star with an additional frequency that places it among the classical RRd stars, and KPP#16, a modulated star with frequency content similar to RR Lyrae, the eponym of its class. The figure is adapted from Figure 1 of Nemec & Moskalik (2021).
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Comparison of Fourier parameters with OGLE-IV LMC field RR Lyrae stars from Soszyński et al. (2016b) and other known non-Blazhko Kepler RRab stars from Nemec et al. (2011). The red points are RRab, blue squares are RRc, and light green triangles are RRd stars from OGLE. Downward orange triangles are known Kepler non-Blazhko RRab stars. Green squares, circles, and triangles are the new RRab, RRc, and RRd stars, respectively, identified in this project. Both RRd stars are shown by two green triangles in each panel. For better visibility, we circled the markers representing the RRd stars.
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Petersen diagram focusing on the 0.61 period ratio characteristic of RR Lyrae stars pulsating in the first radial overtone mode (RRc and RRd stars). Gray dots show the OGLE stars, light blue dots denote K2 objects, while colored triangles correspond to our newly found RRc (downward triangles) and RRd (upward triangles) stars. The figure is adapted from Figure 3 of Netzel & Smolec (2019) and unpublished K2 RR Lyrae data (H. Netzel et al. 2022, in preparation).
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Gaia vs. Kepler magnitudes of previously known (red dots) and newly discovered (black triangles) RR Lyrae stars. The plot nicely demonstrates the amount of lost flux in the Kepler apertures because our targets in the new sample were not the main targets of the Kepler mission. Thus, orange points deviating downward significantly from the 1:1 line are faint background objects, where some part of the flux was lost, while stars contaminated by nearby bright stars are outliers above the 1:1 line.
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Fourier spectrum of the newly found RRd star KPP#8. The upper panel shows the original Fourier spectrum. Then, in each subsequent panel, we subtracted the frequencies and their harmonics as shown by vertical green dashed lines. In the bottom panel, we show in the insert the close-up of the f  X  (f 0.61) frequency structure.
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Light curve (left) and pixel selection (right) of a newly found RRd star on the Target Pixel File (TPF). The main target is centered on pixel (274,473), while the new variable star is at the lower-left corner (three pixels outlined with white borders: (271,471), (271,472), and (271,473)). The plot was made by the Lightkurve package (Lightkurve Collaboration et al. 2018).
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Five-day sections and phase-folded light curves of each candidate RR Lyrae.
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Known and new RR Lyrae stars in the original Kepler field. Red dots show the already known RR Lyrae stars selected by the KASC, and black triangles denote 26 new RR Lyrae stars found and confirmed by this project.
Paper: Kepler Pixel Project: Background RR Lyrae Stars in the Primary Kepler Mission Field of View
Authors: Adrienn Forró, Róbert Szabó, Attila Bódi, Kornél Császár
Figure caption: Gaia G magnitude distribution of the previously known (gray) and our new RR Lyrae sample (blue) in the original Kepler field.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Top row: marginal t E–π E values for 3560 OGLE-III (left panel) and 5760 OGLE-IV (right panel) microlensing events. The points represent the median posterior values for the two parameters. The lines demarcate 50% purity of astrophysical black holes in the PopSyCLE OGLE-III and -IV simulations (Lam et al. 2020); i.e., a random event below the line is roughly 50% likely to be a black hole conditioned on the PopSyCLE simulations. There are 107 and 283 events below the lines for OGLE-III and -IV, respectively. The bulk of the short-timescale events lie along the median of the prior PDF for the timescale since there are few points to allow the likelihood to pull the posterior PDF away from the prior. The posterior PDF is wide for any given event here (see the lower panels for typical uncertainty in a given event). The dashed box is presented as an inset below. Bottom row: zoom into the likely black hole regime. We have presented the same data as the above panels and added 68% confidence intervals to a random selection of 50 points to show that the confidence in any one point is low; however, the bulk of the posterior is below the cut for many events. Furthermore, even events well above the line have tails that extend well into the region below the cut line. Thus, the numbers of point estimates below the line (107 and 283 for OGLE-III and -IV on the left and right, respectively) are likely conservative.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: An example t E distribution from the Mao & Paczynski (1996) formalism, modified for a mixture model composed of two separate power-law mass distributions (blue curve). Mixture component 1 has a min and max mass range of 0.1–3  M ⊙ and power-law slope of −1.5, while mixture component 2 has a min and max mass range of 1–100  M ⊙ and power-law slope of −1.5. The relative proportion of each mixture is 0.8 and 0.2, respectively. The black dashed lines plot ±3 power-law slopes. There is clearly deviation from the −3 slope due to the second mass component.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Posterior corner plot for OGLE-III BLG 102.7.44461 (see Figures 8 and 13) covering the microlensing model parameters with and without the GP component of the model.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Posterior corner plot for OGLE-III BLG 155.1.13052 (see Figure 6) covering the microlensing model parameters with and without the GP component of the model.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: The same as Figure 11 except that the hierarchical parallax t E distribution (black) in the top panel corresponds to events fit with a uniform prior in ﹩\mathrm{log}({t}_{{\rm{E}}})﹩ space from 1 day < t E < 1000 days (see bottom panel) instead of the prior noted in Table 1 and shown in Figure 11. We observe the same significant decrement of t E > 100 day events relative to the distribution from Wyrzykowski et al. (2015; orange), suggesting that the prior is not responsible for the observed decrement.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: The same as Figure 12 except that the hierarchical parallax t E distribution (black) in the top panel corresponds to events fit with a uniform prior in ﹩\mathrm{log}({t}_{{\rm{E}}})﹩ space from 1 day < t E < 1000 days (see bottom panel) instead of the prior noted in Table 1 and shown in Figure 11. We observe the same significant decrement of t E > 100 day events relative to the distribution from Mróz et al. (2019; orange), suggesting that the prior is not responsible for the observed decrement.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: OGLE-III population results for the global observed t E distribution (no survey efficiency corrections have been applied to any of the distributions). The black thin and thick bars show the 68% and 95% confidence intervals on the bin heights in our hierarchical model of the global distribution. The orange histogram shows the binned values presented in Wyrzykowski et al. (2015) for comparison, and the blue histogram shows the MAP-point estimates from our individual PSPL+parallax+GP model fits. In the lower panel, we show the prior PDF on t E given by Equation (32). Note that the effect of our broadening of the t E prior is apparent by the amplitude that varies from ∼0.1 to 0.5, whereas the actual distribution amplitudes vary by approximately 3 dex.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: OGLE-IV population results for the global observed t E distribution (no survey efficiency corrections have been applied to any of the distributions). The black thin and thick bars show the 68% and 95% confidence intervals on the bin heights in our hierarchical model of the global distribution. The orange histogram shows the binned values presented in Mróz et al. (2019) for comparison, and the blue histogram shows the MAP-point estimates from our individual PSPL+parallax+GP model fits. In the lower panel, we show the prior PDF on t E given by Equation (32). Note that the effect of our broadening of the t E prior is apparent by the amplitude that varies from ∼0.1 to 0.5, whereas the actual distribution amplitudes vary by approximately 3 dex.
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Example OGLE-III light curve (OGLE BLG 102.7.44461) with results from our MCMC analysis. This figure is analogous to Figure 5 but with a much simpler GP component and a clear parallax signal (PSPL+parallax+GP to PSPL+GP likelihood-ratio = 25).
Paper: A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV
Authors: Nathan Golovich, William Dawson, Fran Bartolić, Casey Y. Lam, Jessica R. Lu, Michael S. Medford, Michael D. Schneider, George Chapline, Edward F. Schlafly, Alex Drlica-Wagner, Kerianne Pruett
Figure caption: Example OGLE-III light curve (OGLE BLG 155.1.13052) with results from our MCMC analysis. This figure is analogous to Figure 5 but with a much simpler GP component. Again there is little parallax signal (PSPL+parallax+GP to PSPL+GP likelihood-ratio = 1.1).