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Statistical Methods in Medical Research 2007年第3期16卷 300 - 301页

作者： Dawn E. Holmes Department of Statistics and Applied Probability South Hall University of California Santa Barbara CA 93106 USA

On inference for fractional differential equations

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Statistical Inference for Stochastic Processes 2013年第1期16卷 29-61页

作者： Chronopoulou, Alexandra Tindel, Samy Institut Élie Cartan Nancy 54506 Vandoeuvre-lès-Nancy Cedex B.P. 239 France Department of Statistics and Applied Probability University of California Santa Barbara CA 93106-3110 United States

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. Rates of convergence for the approximation task are provided, and numerical experiments show that our procedure leads to good results in terms of estimation. © 2013 Springer Science+Business Media Dordrecht.

关键词： Fractional brownian motion Inference for stochastic processes Malliavin calculus Stochastic differential equations

Generalized probabilistic bisection for stochastic root-finding

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arXiv 2017年

作者： Rodriguez, Sergio Ludkovski, Mike University of California Department of Statistics and Applied Probability Santa Barbara United States

We consider numerical schemes for root finding of noisy responses through generalizing the Probabilistic Bisection Algorithm (PBA) to the more practical context where the sampling distribution is unknown and location-dependent. As in standard PBA, we rely on a knowledge state for the approximate posterior of the root location. To implement the corresponding Bayesian updating, we also carry out inference of oracle accuracy, namely learning the probability of correct response. To this end we utilize batched querying in combination with a variety of frequentist and Bayesian estimators based on majority vote, as well as the underlying functional responses, if available. For guiding sampling selection we investigate both Information Directed sampling, as well as Quantile sampling. Our numerical experiments show that these strategies perform quite differently;in particular we demonstrate the efficiency of randomized quantile sampling which is reminiscent of Thompson sampling. Our work is motivated by the root-finding sub-routine in pricing of Bermudan financial derivatives, illustrated in the last section of the paper. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

Reluctant Interaction Modeling in Generalized Linear Models

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arXiv 2024年

作者： Lu, Hai Yu, Guo Department of Statistics and Applied Probability University of California Santa Barbara United States

While including pairwise interactions in a regression model can better approximate response surface, fitting such an interaction model is a well-known difficult problem. In particular, analyzing contemporary high-dimensional datasets often leads to extremely large-scale interaction modeling problem, where the challenge is posed to identify important interactions among millions or even billions of candidate interactions. While several methods have recently been proposed to tackle this challenge, they are mostly designed by (1) assuming the hierarchy assumption among the important interactions and (or) (2) focusing on the case in linear models with interactions and (sub)Gaussian errors. In practice, however, neither of these two building blocks has to hold. In this paper, we propose an interaction modeling framework in generalized linear models (GLMs) which is free of any assumptions on hierarchy. We develop a non-trivial extension of the reluctance interaction selection principle to the GLMs setting, where a main effect is preferred over an interaction if all else is equal. Our proposed method is easy to implement, and is highly scalable to large-scale datasets. Theoretically, we demonstrate that it possesses screening consistency under high-dimensional setting. Numerical studies on simulated datasets and a real dataset show that the proposed method does not sacrifice statistical performance in the presence of significant computational gain. Copyright © 2024, The Authors. All rights reserved.

关键词： Numerical methods

Exponential convergence rate of ruin probabilities for level-dependent Lévy-driven risk processes

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arXiv 2017年

作者： Goffard, Pierre-Olivier Sarantsev, Andrey Department of Statistics and Applied Probability University of California Santa Barbara United States

We explicitly find the rate of exponential long-term convergence for the ruin probabil- ity in a level-dependent Lévy-driven risk model, as time goes to infinity. Siegmund duality allows to reduce the problem to long-term convergence of a reected jump-diffusion to its stationary distribution, which is handled via Lyapunov *** Codes 60H10, 60J60, 60J75, 91B30 Copyright © 2017, The Authors. All rights reserved.

关键词： Lyapunov functions

Book Review: Discovering knowledge in data: an introduction to data mining

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Statistical Methods in Medical Research 2005年第5期14卷 530 - 531页

作者： Dawn E Holmes Department of Statistics and Applied Probability South Hall University of California Santa Barbara CA 93106 USA

Optimal disease outbreak decisions using stochastic simulation 11

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Optimal disease outbreak decisions using stochastic simulati...

Simulation Winter Conference

作者： Mike Ludkovski Jarad Niemi Department of Statistics and Applied Probability University of California Santa Barbara CA USA

Management policies for disease outbreaks balance the expected morbidity and mortality costs versus the cost of intervention policies. We present a methodology for dynamic determination of optimal policies in a stochastic compartmental model with parameter uncertainty. Our approach is to first carry out sequential Bayesian estimation of outbreak parameters and then solve the dynamic programming equations. The latter step is simulation-based and relies on regression Monte Carlo techniques. To improve performance we investigate lasso regression and global policy iteration. Comparisons demonstrate the realized cost savings of choosing interventions based on the computed dynamic policy over simpler decision rules.

关键词： Stochastic processes Monte Carlo methods Dynamic programming Diseases Mathematical model Approximation methods Uncertainty

Learning Gaussian graphical models with latent confounders

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arXiv 2021年

作者： Wang, Ke Franks, Alexander Oh, Sang-Yun Department of Statistics and Applied Probability University of California Santa Barbara United States

Gaussian Graphical models (GGM) are widely used to estimate network structure in domains ranging from biology to finance. In practice, data is often corrupted by latent confounders which biases inference of the underlying true graphical structure. In this paper, we compare and contrast two strategies for inference in graphical models with latent confounders: Gaussian graphical models with latent variables (LVGGM) and PCA-based removal of confounding (PCA+GGM). While these two approaches have similar goals, they are motivated by different assumptions about confounding. In this paper, we explore the connection between these two approaches and propose a new method, which combines the strengths of these two approaches. We prove the consistency and convergence rate for the PCA-based method and use these results to provide guidance about when to use each method. We demonstrate the effectiveness of our methodology using both simulations and two real-world applications. © 2021, CC BY.

关键词： Gaussian distribution

Sequential Kalman filter for fast online changepoint detection in longitudinal health records

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arXiv 2023年

作者： Li, Hanmo Wang, Yuedong Gu, Mengyang Department of Statistics and Applied Probability University of California Santa Barbara United States

This article introduces the sequential Kalman filter, a computationally scalable approach for online changepoint detection with temporally correlated data. The temporal correlation was not considered in the Bayesian online changepoint detection approach due to the large computational cost. Motivated by detecting COVID-19 infections for dialysis patients from massive longitudinal health records with a large number of covariates, we develop a scalable approach to detect multiple changepoints from correlated data by sequentially stitching Kalman filters of subsequences to compute the joint distribution of the observations, which has linear computational complexity with respect to the number of observations between the last detected changepoint and the current observation at each time point, without approximating the likelihood function. Compared to other online changepoint detection methods, simulated experiments show that our approach is more precise in detecting single or multiple changes in mean, variance, or correlation for temporally correlated data. Furthermore, we propose a new way to integrate classification and changepoint detection approaches that improve the detection delay and accuracy for detecting COVID-19 infection compared to other alternatives. © 2023, CC BY.

关键词： Computational complexity

Stochastic models of tumor latency and their biostatistical applications

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Bulletin of Mathematical Biology 1997年第2期59卷 404-406页

作者： Svetlozar T. Rachev Department of Statistics and Applied Probability University of California Santa Barbara CA 93106-3110 U.S.A.