Related papers: Logistic-beta processes for dependent random proba…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
We present a functional data analysis approach for studying time-dependent, continuous glucose monitoring data with repeated measures for each individual in an experiment. After scaling the glucose concentration curves to the interval [0,…
Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…
We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the…
In this paper, we are concerned with the stochastic process \begin{equation} \beta_{n}(q_{t},t)=\beta_{n}(t)=\frac{1}{\sqrt{n}}\sum_{j=1}^{n}\left\{G_{t,n}(Y(t))-G_{t}(Y_{j}(t))\right\} q_{t}(Y_{j}(t)), \tag{A} \end{equation} where for…
Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
Compositional Data Analysis (CoDa) has gained popularity in recent years. This type of data consists of values from disjoint categories that sum up to a constant. Both Dirichlet regression and logistic-normal regression have become popular…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
We introduce a unified probabilistic framework for solving sequential decision making problems ranging from Bayesian optimisation to contextual bandits and reinforcement learning. This is accomplished by a probabilistic model-based approach…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
The literature has covered the features and uses of the traditional univariate and bivariate logistic distributions in great detail. It is reasonable to wonder, though, if logistic marginals and conditionals could exhibit a similar…