相关论文: On asymptotic validity of naive inference with an …

We investigate the high-probability estimation of discrete distributions from an \iid sample under $\chi^2$-divergence loss. Although the minimax risk in expectation is well understood, its high-probability counterpart remains largely…

Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the…

The problem of assigning probabilities when little is known is analized in the case where the quanities of interest are physical observables, i.e. can be measured and their values expressed by numbers. It is pointed out that the assignment…

This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…

Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…

Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Levy probability metric, given any number of atoms,…

We consider the problem of estimating states and parameters in a model based on a system of coupled stochastic differential equations, based on noisy discrete-time data. Special attention is given to nonlinear dynamics and state-dependent…

When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new asymptotic theory about inference with missing data that is more general than…

Sometimes, we do not use a maximum likelihood estimator of a probability but it's a smoothed estimator in order to cope with the zero frequency problem. This is often the case when we use the Naive Bayes classifier. Laplace smoothing is a…

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…