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Accurately predicting future behaviors of surrounding vehicles is an essential capability for autonomous vehicles in order to plan safe and feasible trajectories. The behaviors of others, however, are full of uncertainties. Both rational…
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
Motivated by recent development of mean-field systems with common noise, this paper establishes Ito's formula for flows of conditional probability measures under a common filtration associated with general semimartingales. This generalizes…
Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to obtain several counterparts to well…
Borrowing ideas from open quantum systems, we describe a formalism to encode ensembles of trajectories of classical stochastic dynamics in terms of continuous matrix product states (cMPSs). We show how to define in this approach "biased" or…
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…
We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
A known property of conditional expectation is extended to the framework of Markov kernels. Its meaning in terms of densities is provided. Some examples located in the field of clinical diagnosis are presented to delimit the main result of…
This article is a lecture note on the potential theory of (possibly non-reversible) Markov processes and on the connection of this theory with quantitative analysis of the metastability of stochastic processes.
Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…
Given a normalized state-vector $\psi $, we define the conditional expectation $\mathbb{E }_{\psi } (A | B ) $ of a Hermitian operator $A $ with respect to a strongly commuting family of self-adjoint operators $B $ as the best…
Modeling worlds and actions under uncertainty is one of the central problems in the framework of decision-theoretic planning. The representation must be general enough to capture real-world problems but at the same time it must provide a…