Related papers: Estimating Real Log Canonical Thresholds
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
Maximum likelihood estimates (MLEs) are asymptotically normally distributed, and this property is used in meta-analyses to test the heterogeneity of estimates, either for a single cluster or for several sub-groups. More recently, MLEs for…
Akaike's Bayesian information criterion (ABIC) has been widely used in geophysical inversion and beyond. However, little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution…
In this article, we investigate the properties of the EBIC in variable selection for generalized linear models with non-canonical links and diverging number of parameters in ultra-high dimensional feature space. The selection consistency of…
The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…
BIC criterion is widely used by the neural-network community for model selection tasks, although its convergence properties are not always theoretically established. In this paper we will focus on estimating the number of components in a…
In the field of spatial data analysis, spatially varying coefficients (SVC) models, which allow regression coefficients to vary by region and flexibly capture spatial heterogeneity, have continued to be developed in various directions.…
Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data…
Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the…
A growing family of approaches to causal inference rely on Bayesian formulations of assumptions that go beyond causal graph structure. For example, Bayesian approaches have been developed for analyzing instrumental variable designs,…
By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…
Methods for combining predictions from different models in a supervised learning setting must somehow estimate/predict the quality of a model's predictions at unknown future inputs. Many of these methods (often implicitly) make the…
Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…
We study the \L ojasiewicz exponent and the log canonical threshold of ideals of $\mathcal O_n$ when restricted to generic subspaces of $\mathbb C^n$ of different dimensions. We obtain effective formulas of the resulting numbers for ideals…
The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the…
In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…
Determining how to appropriately select the tuning parameter is essential in penalized likelihood methods for high-dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…