Related papers: Some Simple Formulas for Posterior Convergence Rat…
Let x and y be two length n DNA sequences, and suppose we would like to estimate the divergence time T. A well known simple but crude estimate of T is p := d(x,y)/n, the fraction of mutated sites (the p-distance). We establish a posterior…
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
The autoregressive process of order $p$ (AR($p$)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR($p$) model. Although it is easy to write down…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…
Bounds on Bayesian posterior convergence rates, assuming the prior satisfies both local and global support conditions, are now readily available. In this paper we explore, in the context of density estimation, Bayesian convergence rates…
Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
Many descent algorithms for multiobjective optimization have been developed in the last two decades. Tanabe et al. (Comput Optim Appl 72(2):339--361, 2019) proposed a proximal gradient method for multiobjective optimization, which can solve…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Theoretical guarantees for causal inference using propensity scores are partly based on the scores behaving like conditional probabilities. However, scores between zero and one, especially when outputted by flexible statistical estimators,…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…
We derive functional a posteriori error equalities and constant free two sided estimates for certain types of partial differential equations. The error is measured in a combined norm which takes into account both the primal and dual…
Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…
We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…