Related papers: Frameworks for prior-free posterior probabilistic …
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
Reinforcement Learning is divided in two main paradigms: model-free and model-based. Each of these two paradigms has strengths and limitations, and has been successfully applied to real world domains that are appropriate to its…
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there…
Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to…
We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence…
Without assuming any pdf for some measured parameter, we derive a predictive pdf for the outcome of a second measurement, given the outcome of the first measurement and two common assumptions about the noise. These are that (1) it is…
Many areas of science rely on simulators that implicitly encode intractable likelihood functions of complex systems. Classical statistical methods are poorly suited for these so-called likelihood-free inference (LFI) settings, especially…
Inferring the means in the multivariate normal model $X \sim N_n(\theta, I)$ with unknown mean vector $\theta=(\theta_1,...,\theta_n)' \in \mathbb{R}^n$ and observed data $X=(X_1,...,X_n)'\in {\mathbb R}^n$ is a challenging task, known as…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…