Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

Abstract

We derive general bounds on the probability that the empirical first-passage time ${\overline{\tau }}_n\equiv {\sum }_{i=1}^n{\tau }_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct non-asymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

arXiv commentRevised version, contains new bounds on extreme first-passage time and additional illustrative examples

References in corpus (87)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Forecast and Control of Epidemics in a Globalized World
• Diffusion with Stochastic Resetting
• Intermittent search strategies
• First-passage times in complex scale-invariant media
• Stochastic Resetting and Applications
• Persistence and First-Passage Properties in Non-equilibrium Systems
• First Passage Under Restart
• Geometry-controlled kinetics
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Stability of adhesion clusters under constant force
• Stochastic resetting in backtrack recovery by RNA polymerases
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• First-passage times for random walks in bounded domains
• First passages in bounded domains: When is the mean first passage time meaningful?
• Mean first-passage times of non-Markovian random walkers in confinement
• Direct Measurement of Kramers Turnover with a Levitated Nanoparticle
• First passages for a search by a swarm of independent random searchers
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• The dissipation-time uncertainty relation
• Activated escape of a self-propelled particle from a metastable state
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• From the area under the Bessel excursion to anomalous diffusion of cold atoms
• Decision Making in the Arrow of Time
• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Mortality, Redundancy, and Diversity in Stochastic Search
• Optimization in First-Passage Resetting
• First passage under restart with branching
• Quantum walks: the first detected passage time problem
• In vivo facilitated diffusion model
• Universal formula for the mean first passage time in planar domains
• Facilitated diffusion of proteins on chromatin
• First detected arrival of a quantum walker on an infinite line
• Record statistics and persistence for a random walk with a drift
• Towards a full quantitative description of single-molecule reaction kinetics in biological cells
• On the area under a continuous time Brownian motion till its first-passage time
• Experimental Persistence Probability for Fluctuating Steps
• The semiparametric Bernstein-von Mises theorem
• Optimizing Brownian escape rates by potential shaping
• Temporal and spatial persistence of combustion fronts
• Plasticity of hydrogen bond networks regulates mechanochemistry of cell adhesion complexes
• From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers
• Simulating rare events using a Weighted Ensemble-based string method
• Efficient Stochastic Simulation of Chemical Kinetics Networks using a Weighted Ensemble of Trajectories
• Interlacing Relaxation and First-Passage Phenomena in Reversible Discrete and Continuous Space Markovian Dynamics
• First passage time statistics for two-channel diffusion
• Persistence in nonequilibrium surface growth
• Stochastic Dynamics of Nanoparticle and Virus Uptake
• The first-passage area for drifted Brownian motion and the moments of the Airy distribution
• The longest excursion of stochastic processes in nonequilibrium systems
• Duality Between Relaxation and First Passage in Reversible Markov Dynamics: Rugged Energy Landscapes Disentangled
• A probabilistic approach to extreme statistics of Brownian escape times in dimensions 1, 2, and 3
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• A Bernstein-Von Mises Theorem for discrete probability distributions
• First-passage Brownian functionals with stochastic resetting
• Kinetic uncertainty relation on first passage time for accumulated current
• Optimal non-Markovian search strategies with n-step memory
• Extreme first passage times for random walks on networks
• Universal First-Passage-Time Distribution of Non-Gaussian Currents
• Estimating Entropy Production Rates with First-Passage Processes
• Infinite family of persistence exponents for interface fluctuations
• First hitting times to intermittent targets
• Efficient estimation of rare-event kinetics
• A Bernstein-von Mises theorem in the nonparametric right-censoring model
• Transient hydrophobic exposure in the molecular dynamics of Abeta peptide at low water concentration
• Criticality in Cell Adhesion
• A Unified Approach to Gated Reactions on Networks
• Statistics of the first passage time of Brownian motion conditioned by maximum value or area
• Sampling Time Effects for Persistence and Survival in Step Structural Fluctuations
• Freezing transition in the barrier crossing rate of a diffusing particle
• Active Brownian Particles in a Circular Disk with an Absorbing Boundary
• Protein recruitment through indirect mechanochemical interactions
• Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
• First-passage Fingerprints of Water Diffusion near Glutamine Surfaces
• First-passage time to clear the way for receptor-ligand binding in a crowded environment
• Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble
• First Invader Dynamics in Diffusion-Controlled Absorption
• Concentration Inequalities for Output Statistics of Quantum Markov Processes
• First detection of threshold crossing events under intermittent sensing
• On the Bernstein-von Mises theorem for the Dirichlet process
• First-passage times in complex energy landscapes: a case study with nonmuscle myosin II assembly

Cited by in corpus (7)

• Restart uncertainty relation for monitored quantum dynamics
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Inferring intermediate states by leveraging the many-body Arrhenius law
• Mutual Linearity is a Generic Property of Steady-State Markov Networks
• Concentration of Empirical First-Passage Times
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems
• Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors