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A common complication that can arise with analyses of high-dimensional data is the repeated use of hypothesis tests. A second complication, especially with small samples, is the reliance on asymptoticp-values. Our proposed approach for addressing both complications uses a scientifically motivated scalar summary statistic, and although not entirely novel, seems rarely used. The method is illustrated using a crossover study of seventeen participants examining the effect of exposure to ozone versus clean air on the DNA methylome, where the multivariate outcome involved 484,531 genomic locations. Our proposed test yields a single null randomization distribution, and thus a single Fisher-exactp-value that is statistically valid whatever the structure of the data. However, the relevance and power of the resultant test requires the careful a priori selection of a single test statistic. The common practice using asymptoticp-values or meaningless thresholds for “significance” is inapposite in general.

 

We apply the color–magnitude intercept calibration method (CMAGIC) to the Nearby Supernova Factory SNe Ia spectrophotometric data set. The currently existing CMAGIC parameters are the slope and intercept of a straight line fit to the linear region in the color–magnitude diagram, which occurs over a span of approximately 30 days after maximum brightness. We define a new parameter,ω_XY, the size of the “bump” feature near maximum brightness for arbitrary filtersXandY. We find a significant correlation between the slope of the linear region,β_XY, in the CMAGIC diagram andω_XY. These results may be used to our advantage, as they are less affected by extinction than parameters defined as a function of time. Additionally,ω_XYis computed independently of templates. We find that current empirical templates are successful at reproducing the features described in this work, particularly SALT3, which correctly exhibits the negative correlation between slope and “bump” size seen in our data. In 1D simulations, we show that the correlation between the size of the “bump” feature andβ_XYcan be understood as a result of chemical mixing due to large-scale Rayleigh–Taylor instabilities.

 

Abstract We construct a physically parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of Type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an autoencoder that is interpreted probabilistically after training using a normalizing flow. We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times directly from the data. By introducing a correlation penalty term and multistage training setup alongside our physically parameterized network, we show that intrinsic and extrinsic modes of variability can be separated during training, removing the need for the additional models to perform magnitude standardization. We then use our PAE in a number of downstream tasks on SNe Ia for increasingly precise cosmological analyses, including the automatic detection of SN outliers, the generation of samples consistent with the data distribution, and solving the inverse problem in the presence of noisy and incomplete data to constrain cosmological distance measurements. We find that the optimal number of intrinsic model parameters appears to be three, in line with previous studies, and show that we can standardize our test sample of SNe Ia with an rms of 0.091 ± 0.010 mag, which corresponds to 0.074 ± 0.010 mag if peculiar velocity contributions are removed. Trained models and codes are released at https://github.com/georgestein/suPAErnova. 

A large fraction of Type Ia supernova (SN Ia) observations over the next decade will be in the near-infrared (NIR), at wavelengths beyond the reach of the current standard light-curve model for SN Ia cosmology, SALT3 (∼2800–8700 Å central filter wavelength). To harness this new SN Ia sample and reduce future light-curve standardization systematic uncertainties, we train SALT3 at NIR wavelengths (SALT3-NIR) up to 2μm with the open-source model-training softwareSALTshaker, which can easily accommodate future observations. Using simulated data, we show that the training process constrains the NIR model to ∼2%–3% across the phase range (−20 to 50 days). We find that Hubble residual (HR) scatter is smaller using the NIR alone or optical+NIR compared to optical alone, by up to ∼30% depending on filter choice (95% confidence). There is significant correlation between NIR light-curve stretch measurements and luminosity, with stretch and color corrections often improving HR scatter by up to ∼20%. For SN Ia observations expected from the Roman Space Telescope, SALT3-NIR increases the amount of usable data in the SALT framework by ∼20% at redshiftz≲ 0.4 and by ∼50% atz≲ 0.15. The SALT3-NIR model is part of the open-sourceSNCosmoandSNANASN Ia cosmology packages.

 

A public deep and wide science enabling survey will be needed to discover these black holes and supernovae, and to cover the area large enough for cosmic infrared background to be reliably studied. This enabling survey will find a large number of other transients and enable supernova cosmology up to z 5.