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Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…

Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

Sequential recommendation as an emerging topic has attracted increasing attention due to its important practical significance. Models based on deep learning and attention mechanism have achieved good performance in sequential…

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…

In linear regression problems with related predictors, it is desirable to do variable selection and estimation by maintaining the hierarchical or structural relationships among predictors. In this paper we propose non-negative garrote…

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…

A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including…

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…

In recent years, great emphasis has been placed on the prediction of association football. Due to this, several studies have proposed different types of statistical models to predict the outcome of a football match. However, most existing…

In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…

A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…

We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

In official statistics, dual system estimation (DSE) is a well-known tool to estimate the size of a population. Two sources are linked, and the number of units that are missed by both sources is estimated. Often dual system estimation is…

Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring…

In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…

It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time.…