Related papers: Applications of Bayesian model selection to cosmol…
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…
We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive…
A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a…
We explore the theoretical and numerical property of a fully Bayesian model selection method in sparse ultrahigh-dimensional settings, i.e., $p\gg n$, where $p$ is the number of covariates and $n$ is the sample size. Our method consists of…
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
I revisit the question of the adiabaticity of initial conditions for cosmological perturbations in view of the 3-year WMAP data. I focus on the simplest alternative to pure adiabatic conditions, namely a superposition of the adiabatic mode…
The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…
Double descent is a phenomenon of over-parameterized statistical models such as deep neural networks which have a re-descending property in their risk function. As the complexity of the model increases, risk exhibits a U-shaped region due…
We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to…
Bayesian nonparametric regression with dependent wavelets has dual shrinkage properties: there is shrinkage through a dependent prior put on functional differences, and shrinkage through the setting of most of the wavelet coefficients to…
Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…
We present posterior likelihoods and Bayesian model selection analysis for generalized cosmological models where the primordial perturbations include correlated adiabatic and cold dark matter isocurvature components. We perform nested…
Bayes factors have become a popular tool in exoplanet spectroscopy for testing atmosphere models against one another. We show that the commonly used method for converting these values into significance "sigmas" is invalid. The formula is…
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In…