Search results for "Statistics - Methodology"
showing 10 items of 82 documents
Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests
2021
We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The par…
L1-Penalized Censored Gaussian Graphical Model
2018
Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this article, we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithm…
On the stability of some controlled Markov chains and its applications to stochastic approximation with Markovian dynamic
2015
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading to the proof of the desired stability property. Of particular interest is the fact that the approach applies even in situations where the two components of the process present a time-scale separation, w…
Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses
2016
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over 50 years. We propose, as an alternative, the use of the odds of a correct rejection of the null hypothesis to incorrect rejection. Both pre-experimental versions (involving the power and Type I error) and post-experimental versions (depending on the actual data) are considered. Implementations are provided that range from depending only on the p-value to consideration of full Bayesian analysis. A surprise is that all implementations -- even the full Baye…
Multiscale Information Storage of Linear Long-Range Correlated Stochastic Processes
2019
Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then …
On the interpretability and computational reliability of frequency-domain Granger causality
2017
This Correspondence article is a comment which directly relates to the paper “A study of problems encountered in Granger causality analysis from a neuroscience perspective” (Stokes and Purdon, 2017). We agree that interpretation issues of Granger causality (GC) in neuroscience exist, partially due to the historically unfortunate use of the name “causality”, as described in previous literature. On the other hand, we think that Stokes and Purdon use a formulation of GC which is outdated (albeit still used) and do not fully account for the potential of the different frequency-domain versions of GC; in doing so, their paper dismisses GC measures based on a suboptimal use of them. Furthermore, s…
Group Importance Sampling for particle filtering and MCMC
2018
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discus…
Unsupervised Anomaly and Change Detection With Multivariate Gaussianization
2022
Anomaly detection (AD) is a field of intense research in remote sensing (RS) image processing. Identifying low probability events in RS images is a challenging problem given the high dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While a plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary, especially now with the data deluge problem. In this article, we propose an unsupervised method for detecting anomalies and changes …
Analyzing multidimensional movement interaction with generalized cross-wavelet transform
2021
Humans are able to synchronize with musical events whilst coordinating their movements with others. Interpersonal entrainment phenomena, such as dance, involve multiple body parts and movement directions. Along with being multidimensional, dance movement interaction is plurifrequential, since it can occur at different frequencies simultaneously. Moreover, it is prone to nonstationarity, due to, for instance, displacements around the dance floor. Various methodological approaches have been adopted for the study of human entrainment, but only spectrogram-based techniques allow for an integral analysis thereof. This article proposes an alternative approach based upon the cross-wavelet transfor…
Do-search -- a tool for causal inference and study design with multiple data sources
2020
Epidemiologic evidence is based on multiple data sources including clinical trials, cohort studies, surveys, registries, and expert opinions. Merging information from different sources opens up new possibilities for the estimation of causal effects. We show how causal effects can be identified and estimated by combining experiments and observations in real and realistic scenarios. As a new tool, we present do-search, a recently developed algorithmic approach that can determine the identifiability of a causal effect. The approach is based on do-calculus, and it can utilize data with nontrivial missing data and selection bias mechanisms. When the effect is identifiable, do-search outputs an i…