Search results for "uncertainty."
showing 10 items of 972 documents
Fourth Moments and Independent Component Analysis
2015
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting wi…
Bayesian Modeling of Sequential Discoveries
2022
We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects. We propose a novel Bayesian method for species sampling modelling by directly specifying the probability of a new discovery, therefore allowing for flexible specifications. The asymptotic behavior and finite sample properties of such an approach are extensively studied. Interestingly, our enlarged class of sequential processes includes highly tr…
Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the…
Networks as mediating variables: a Bayesian latent space approach
2022
AbstractThe use of network analysis to investigate social structures has recently seen a rise due to the high availability of data and the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different perspective by considering the whole network as a random variable conveying the effect of an exposure on a response. This point of view represents a classical mediation setting, where the interest lies in estimating the indirect effect, that is, the effect propagated through the mediating variable. We introduce a latent space model mapping the network into a …
bssm: Bayesian Inference of Non-linear and Non-Gaussian State Space Models in R
2021
We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and the extended Kalman filter. The package accommodates also discretely observed latent diffusion processes. The inference is based on fully automatic, adaptive Markov chain Monte Carlo (MCMC) on the hyperparameters, with optional importance sampling post-correction to eliminate any approximation bias. The package implements also a direct pseudo-marginal MCMC and a delayed acceptance pseudo-marginal MCMC using intermediate approximations. The package offers …
Pricing of Asian exchange rate options under stochastic interest rates as a sum of options
2002
The aim of the paper is to develop pricing formulas for long term European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. The emphasis is devoted to the discretely sampled Asian option. It is shown how the value of this option can be approximated as the sum of Black-Scholes options. The formula is obtained under the extension of results developed by Rogers and Shi (1995) and Jamshidian (1991). In addition bounds for the pricing error are determined. Comparing with Monte Carlo simulation the pricing is found to be very precise.
Bayesian longitudinal models for paediatric kidney transplant recipients
2015
Chronic kidney disease is a progressive loss of renal function which results in the inability of the kidneys to properly filter waste from the blood. Renal function is usually estimated by the glomerular filtration rate (eGFR), which decreases with the worsening of the disease. Bayesian longitudinal models with covariates, random effects, serial correlation and measurement error are discussed to analyse the progression of eGFR in first transplanted children taken from a study in Valencia, Spain.
Two hundred and fifty-four metagenome-assembled bacterial genomes from the bank vole gut microbiota.
2020
Abstract Vertebrate gut microbiota provide many essential services to their host. To better understand the diversity of such services provided by gut microbiota in wild rodents, we assembled metagenome shotgun sequence data from a small mammal, the bank vole Myodes glareolus (Rodentia, Cricetidae). We were able to identify 254 metagenome assembled genomes (MAGs) that were at least 50% ( n = 133 MAGs), 80% ( n = 77 MAGs) or 95% ( n = 44 MAGs) complete. As typical for a rodent gut microbiota, these MAGs are dominated by taxa assigned to the phyla Bacteroidetes ( n = 132 MAGs) and Firmicutes ( n = 80), with some Spirochaetes ( n = 15) and Proteobacteria ( n = 11). Based on coverage over…
Test of the Latent Dimension of a Spatial Blind Source Separation Model
2024
We assume a spatial blind source separation model in which the observed multivariate spatial data is a linear mixture of latent spatially uncorrelated random fields containing a number of pure white noise components. We propose a test on the number of white noise components and obtain the asymptotic distribution of its statistic for a general domain. We also demonstrate how computations can be facilitated in the case of gridded observation locations. Based on this test, we obtain a consistent estimator of the true dimension. Simulation studies and an environmental application in the Supplemental Material demonstrate that our test is at least comparable to and often outperforms bootstrap-bas…
Systematic handling of missing data in complex study designs : experiences from the Health 2000 and 2011 Surveys
2016
We present a systematic approach to the practical and comprehensive handling of missing data motivated by our experiences of analyzing longitudinal survey data. We consider the Health 2000 and 2011 Surveys (BRIF8901) where increased non-response and non-participation from 2000 to 2011 was a major issue. The model assumptions involved in the complex sampling design, repeated measurements design, non-participation mechanisms and associations are presented graphically using methodology previously defined as a causal model with design, i.e. a functional causal model extended with the study design. This tool forces the statistician to make the study design and the missing-data mechanism explicit…