Related papers: Low-parameter phylogenetic estimation under the ge…
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…
Phylogenetic varieties related to equivariant substitution models have been studied largely in the last years. One of the main objectives has been finding a set of generators of the ideal of these varieties, but this has not yet been…
We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
Instrumental-variable (IV) regression enables causal estimation under endogeneity, but modern IV problems often involve nonlinear structural effects and high-dimensional covariates. Existing nonlinear IV methods directly learn the causal…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
Modelling exchangeable relational data can be described by \textit{graphon theory}. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the…
Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…
In this paper, we propose a class of low-rank panel quantile regression models which allow for unobserved slope heterogeneity over both individuals and time. We estimate the heterogeneous intercept and slope matrices via nuclear norm…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…
This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this…
Skewness is a common occurrence in statistical applications. In recent years, various distribution families have been proposed to model skewed data by introducing unequal scales based on the median or mode. However, we argue that the point…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
Hidden Markov models (HMMs) are powerful tools for analysing time series data that depend on discrete underlying but unobserved states. As such, they have gained prominence across numerous empirical disciplines, in particular ecology,…
Several statistical models used in genome-wide prediction assume independence of marker allele substitution effects, but it is known that these effects might be correlated. In statistics, graphical models have been identified as a useful…