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Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques…
Full likelihood has been widely used in loss tomography because most believe it can produce accurate estimates although the full likelihood estimators proposed so far are complex in structure and expensive in execution. We in this paper…
The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…
We estimate the expected value of certain function $f:\{-1,1\}^{n}\to\mathbb{R}$. For example, with computer assistance, we show that if $\Delta$ is the Laplacian of the Cayley graph of…
One can consider $\mu$-Martin-L\"of randomness for a probability measure $\mu$ on $2^{\omega}$, such as the Bernoulli measure $\mu_p$ given $p \in (0, 1)$. We study Bernoulli randomness of sequences in $n^{\omega}$ with parameters $p_0,…
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
In this paper we consider a group sequentially monitored trial on a survival endpoint, monitored using a weighted log-rank (WLR) statistic with deterministic weight function. We introduce a summary statistic in the form of a weighted…
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter…
We determine the probability, structure dependent, that the block Wiedemann algorithm correctly computes leading invariant factors. This leads to a tight lower bound for the probability, structure independent. We show, using block size…
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess…
Let $b(x)$ be the probability that a sum of independent Bernoulli random variables with parameters $p_1, p_2, p_3, \ldots \in [0,1)$ equals $x$, where $\lambda := p_1 + p_2 + p_3 + \cdots$ is finite. We prove two inequalities for the…
Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function.…
We outline a general procedure on how to apply random positive linear operators in nonparametric estimation. As a consequence, we give explicit confidence bands and intervals for a distribution function $F$ concentrated on $[0,1]$ by means…