Statistical model

About: Statistical model is a research topic. Over the lifetime, 19987 publications have been published within this topic receiving 904164 citations. The topic is also known as: Models, Statistical & statistical model.

Bayesian perspectives on statistical modelling

Abstract: This thesis explores the representation of probability measures in a coherent Bayesian modelling framework, together with the ensuing characterisation properties of posterior functionals First, a decision theoretic approach is adopted to provide a unified modelling criterion applicable to assessing prior-likelihood combinations, design matrices, model dimensionality and choice of sample size The utility structure and associated Bayes risk induces a distance measure, introducing concepts from differential geometry to aid in the interpretation of modelling characteristics Secondly, analytical and approximate computations for the implementation of the Bayesian paradigm, based on the properties of the class of transformation models, are discussed Finally, relationships between distance measures (in the form of either a derivative of a Bayes mapping or an induced distance) are explored, with particular reference to the construction of sensitivity measures

Application of statistical parameter estimation methods to physical measurements

Abstract: Statistical methods for estimation of physical parameters from observations are discussed. Different from conventional deterministic methods, statistical methods for measurement of parameters use a mathematical model of the observations that includes statistical errors. Advantages of statistically modelling the observations are discussed. In the first place statistical models of the observations offer the possibility to analyse statistically the precision and systematic error of parameter measurement methods. Furthermore, parameter measurement problems can be reformulated as statistical parameter estimation problems.

Uncertainty decomposition in environmental modelling and mapping

Abstract: In recent years computational models and statistical modelling have been increasingly coupled together. On the one side, statistics is a useful tool for computer simulation design and output analysis, namely importance, uncertainty and sensistivity analysis. On the other side simulation is becoming an important part of statistical modelling. Moreover, data assimilation based on statistical modelling allows us to manage both empirical data and computer outputs on a common ground.In this paper, we consider some techniques for decomposing and analysing the output uncertainty for environmental models with spatio-temporal components. This extends standard sensitivity analysis variance decompositions to the case of correlated inputs which is useful for assessing the adjusted anthropic impact on the environment through appropriate models. The model setup used is based on the hierarchical spatio-temporal approach, which allows to define various model components in a relatively easy way and to introduce both spatial and temporal correlation. Moreover, this gives a natural frame for discussing uncertainty decomposition in terms of model components and mapping capability.Two motivating applications are given. The first one involves daily data on particulate matters related to both a monitoring network and an emission inventory model coupled with a meteorological and chemical computer model. The second one is related to impact assessment of vehicle traffic on hourly carbon oxides in Turin, Italy.

Fast derivatives of likelihood functionals for ODE based models using adjoint-state method

Abstract: We consider time series data modeled by ordinary differential equations (ODEs), widespread models in physics, chemistry, biology and science in general. The sensitivity analysis of such dynamical systems usually requires calculation of various derivatives with respect to the model parameters. We employ the adjoint state method (ASM) for efficient computation of the first and the second derivatives of likelihood functionals constrained by ODEs with respect to the parameters of the underlying ODE model. Essentially, the gradient can be computed with a cost (measured by model evaluations) that is independent of the number of the ODE model parameters and the Hessian with a linear cost in the number of the parameters instead of the quadratic one. The sensitivity analysis becomes feasible even if the parametric space is high-dimensional. The main contributions are derivation and rigorous analysis of the ASM in the statistical context, when the discrete data are coupled with the continuous ODE model. Further, we present a highly optimized implementation of the results and its benchmarks on a number of problems. The results are directly applicable in (e.g.) maximum-likelihood estimation or Bayesian sampling of ODE based statistical models, allowing for faster, more stable estimation of parameters of the underlying ODE model.

Non-Bayesian Social Learning with Uncertain Models over Time-Varying Directed Graphs

Abstract: We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing literature, we focus our attention on the scenario where the statistical models held by the agents about possible states of the world are built from finite observations. We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions. Therefore, we propose a new algorithm to iteratively construct a set of beliefs that indicate whether a certain hypothesis is supported by the empirical evidence. This new algorithm can be implemented over time-varying directed graphs, with non{-}doubly stochastic weights.