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Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
The thresholding of time series of activity or intensity is frequently used to define and differentiate events. This is either implicit, for example due to resolution limits, or explicit, in order to filter certain small scale physics from…
We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time…
The identification of causal effects in observational studies typically relies on two standard assumptions: unconfoundedness and overlap. However, both assumptions are often questionable in practice: unconfoundedness is inherently…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…
Recurrent events often serve as key endpoints in clinical studies but may be prematurely truncated by terminal events such as death, creating selection bias and complicating causal inference. To address this challenge, we develop a Bayesian…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the…
Suppose a process yields independent observations whose distributions belong to a family parameterized by \theta\in\Theta. When the process is in control, the observations are i.i.d. with a known parameter value \theta_0. When the process…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
We develop an asymptotic statistical theory for parameter estimation from a class of non-i.i.d. periodic binary event-detection processes subject to nonparalyzable dead time and gating, which we call "dead-time event detection" (DED)…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
Diffusion-based generative models demonstrate state-of-the-art performance across various image synthesis tasks, yet their tendency to replicate and amplify dataset biases remains poorly understood. Although previous research has viewed…
We consider continuous-time models with a large panel of moment conditions, where the structural parameter depends on a set of characteristics, whose effects are of interest. The leading example is the linear factor model in financial…