Related papers: Anytime-valid t-tests and confidence sequences for…
This paper considers the problem of constructing a confidence sequence, which is a sequence of confidence intervals that hold uniformly over time, for estimating the mean of bounded real-valued random processes. This paper revisits the…
Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-dependent rather than predetermined. The aforementioned methods…
Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…
A confidence sequence (CS) is an anytime-valid sequential inference primitive which produces an adapted sequence of sets for a predictable parameter sequence with a time-uniform coverage guarantee. This work constructs a non-parametric…
Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
We propose a new fiducial Markov Chain Monte Carlo (MCMC) method for fitting parametric Gaussian models. We utilize the Cayley transform to decompose the parametric covariance matrix, which in turn allows us to formulate a general data…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…
Suppose we observe an infinite series of coin flips $X_1,X_2,\ldots$, and wish to sequentially test the null that these binary random variables are exchangeable. Nonnegative supermartingales (NSMs) are a workhorse of sequential inference,…
A/B tests are the gold standard for evaluating digital experiences on the web. However, traditional "fixed-horizon" statistical methods are often incompatible with the needs of modern industry practitioners as they do not permit continuous…
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…
Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
We study the following fundamental hypothesis testing problem, which we term Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on $\mathbb{R}^d$, the task is to distinguish, with high probability, between the following…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…
Gaussian process (GP) models have become a well-established frameworkfor the adaptive design of costly experiments, and notably of computerexperiments. GP-based sequential designs have been found practicallyefficient for various objectives,…
We study sequential mean estimation in $\mathbb{R}^d$. In particular, we derive time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of random vectors with high probability simultaneously across…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…