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In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute.…
Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
In this paper, we are concerned with estimating the joint probability of random variables $X$ and $Y$, given $N$ independent observation blocks $(\boldsymbol{x}^i,\boldsymbol{y}^i)$, $i=1,\ldots,N$, each of $M$ samples…
We consider data fusion for the purpose of smoothing and interpolation based on observation records with missing data. Stochastic processes are generated by linear stochastic models. The paper begins by drawing a connection between time…
In this paper we consider the linear regression model $Y =S X+\varepsilon $ with functional regressors and responses. We develop new inference tools to quantify deviations of the true slope $S$ from a hypothesized operator $S_0$ with…
We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted…
We consider the problem of efficiently inferring interventional distributions in a causal Bayesian network from a finite number of observations. Let $\mathcal{P}$ be a causal model on a set $\mathbf{V}$ of observable variables on a given…
Big data analytics has opened new avenues in economic research, but the challenge of analyzing datasets with tens of millions of observations is substantial. Conventional econometric methods based on extreme estimators require large amounts…
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
Probabilistic inference problems arise naturally in distributed systems such as sensor networks and teams of mobile robots. Inference algorithms that use message passing are a natural fit for distributed systems, but they must be robust to…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…