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On Lq convergence of the Hamiltonian Monte Carlo

Ghosh Soumyadip, Lu Yingdong, Nowicki Tomasz

Journal of Applied Analysis

2023

Vol. 29, nr 1

161--169

We establish Lq convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly for 1 < q < 2) to the desired target distribution. In addition, we establish a general convergence rate for an Lq convergence given a convergence rate at a specific q∗, and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions.We also present the results of experiments to illustrate convergence in Lq.

Predicting IoT failures with Bayesian workflow

Baranowski Jerzy

Eksploatacja i Niezawodność

2022

Vol. 24, no. 2

248--259

IoT networks are so voluminous that they cannot be treated as individual devices, but as populations. Main aim of the paper is to create a comprehensive method for predicting failures taking device variance into consideration. We propose using data fusion of happenstance observations (resets and failures) to better estimate device parameters. We propose using methods of population analysis in Bayesian statistics to estimate failure times investigating only a part of the population. For this purpose, we use multilevel hierarchical Bayesian model and provide it with post stratification. We propose model assumptions, construct the model and evaluate it, and perform computations using Hamiltonian Monte Carlo. This method is known as the Bayesian workflow. We have analyzed three different models showing that, in case of small device variance, it can be ignored, or at least compensated, while significant differences require hierarchical modeling. We also show that hierarchical model shows significant robustness to a small amount of data. We have shown attractiveness of Bayesian approach to modeling failures of IoT devices. Ability to diagnose and tune models, and assure their computational fidelity is a great advantage of Bayesian workflow.