The bias in reversing the Box-Cox transformation in time series forecasting: An empirical study based on neural networks

The Box-Cox transformation is a technique mostly utilized to turn the probabilistic distribution of a time series data into approximately normal. And this helps statistical and neural models to perform more accurate forecastings. However, it introduces a bias when the reversion of the transformation is conducted with the predicted data. The statistical methods to perform a bias-free reversion require, necessarily, the assumption of Gaussianity of the transformed data distribution, which is a rare event in real-world time series. So, the aim of this study was to provide an effective method of removing the bias when the reversion of the Box-Cox transformation is executed. Thus, the developed method is based on a focused time lagged feedforward neural network, which does not require any assumption about the transformed data distribution. Therefore, to evaluate the performance of the proposed method, numerical simulations were conducted and the Mean Absolute Percentage Error, the Theil Inequality Index and the Signal-to-Noise ratio of 20-step-ahead forecasts of 40 time series were compared, and the results obtained indicate that the proposed reversion method is valid and justifies new studies. (C) 2014 Elsevier B.V. All rights reserved.

Earthquake forecasting and seismic hazard analysis: some insights on the testing phase and the modeling

This thesis is divided in three chapters. In the first chapter we analyse the results of the world forecasting experiment run by the Collaboratory for the Study of Earthquake Predictability (CSEP). We take the opportunity of this experiment to contribute to the definition of a more robust and reliable statistical procedure to evaluate earthquake forecasting models. We first present the models and the target earthquakes to be forecast. Then we explain the consistency and comparison tests that are used in CSEP experiments to evaluate the performance of the models. Introducing a methodology to create ensemble forecasting models, we show that models, when properly combined, are almost always better performing that any single model. In the second chapter we discuss in depth one of the basic features of PSHA: the declustering of the seismicity rates. We first introduce the Cornell-McGuire method for PSHA and we present the different motivations that stand behind the need of declustering seismic catalogs. Using a theorem of the modern probability (Le Cam's theorem) we show that the declustering is not necessary to obtain a Poissonian behaviour of the exceedances that is usually considered fundamental to transform exceedance rates in exceedance probabilities in the PSHA framework. We present a method to correct PSHA for declustering, building a more realistic PSHA. In the last chapter we explore the methods that are commonly used to take into account the epistemic uncertainty in PSHA. The most widely used method is the logic tree that stands at the basis of the most advanced seismic hazard maps. We illustrate the probabilistic structure of the logic tree, and then we show that this structure is not adequate to describe the epistemic uncertainty. We then propose a new probabilistic framework based on the ensemble modelling that properly accounts for epistemic uncertainties in PSHA.

Dynamics of coastal aquifers: data-driven forecasting and risk analysis

This work is focused on the study of saltwater intrusion in coastal aquifers, and in particular on the realization of conceptual schemes to evaluate the risk associated with it. Saltwater intrusion depends on different natural and anthropic factors, both presenting a strong aleatory behaviour, that should be considered for an optimal management of the territory and water resources. Given the uncertainty of problem parameters, the risk associated with salinization needs to be cast in a probabilistic framework. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters are modeled as random variables, and global sensitivity analysis is used to determine their influence on the position of saltwater interface. The analyses presented in this work rely on an efficient model reduction technique, based on Polynomial Chaos Expansion, able to combine the best description of the model without great computational burden. When the assumptions of classical analytical models are not respected, and this occurs several times in the applications to real cases of study, as in the area analyzed in the present work, one can adopt data-driven techniques, based on the analysis of the data characterizing the system under study. It follows that a model can be defined on the basis of connections between the system state variables, with only a limited number of assumptions about the "physical" behaviour of the system.

Short-term wind power forecasting using Gaussian processes

Since wind has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safety and economics of wind energy utilization. In this paper, we investigate a combination of numeric and probabilistic models: one-day-ahead wind power forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical Weather Prediction (NWP) model. Firstly the wind speed data from NWP was corrected by a GP. Then, as there is always a defined limit on power generated in a wind turbine due the turbine controlling strategy, a Censored GP was used to model the relationship between the corrected wind speed and power output. To validate the proposed approach, two real world datasets were used for model construction and testing. The simulation results were compared with the persistence method and Artificial Neural Networks (ANNs); the proposed model achieves about 11% improvement in forecasting accuracy (Mean Absolute Error) compared to the ANN model on one dataset, and nearly 5% improvement on another.

Forecasting trends in the Brisbane central business district office market

The Queensland Department of Public Works (DPW) holds a significant interest in the Brisbane Central Business District (CBD) in controlling approximately 20 percent of the office space within its confines. This comprises a total of 333,903 square metres of space, of which 170,111 square metres is owned and 163,792 square metres is leased from the private sector. The department’s nominal ownership extends to several enduring, landmark buildings as well as several modern office towers. The portfolio includes the oldest building in the CBD, being the former Commissariat Stores building and one of the newest, a 15,000 square metre office tower under construction at 33 Charlotte Street.

High-level concept annotation using ontology and probabilistic inference

Image annotation is a significant step towards semantic based image retrieval. Ontology is a popular approach for semantic representation and has been intensively studied for multimedia analysis. However, relations among concepts are seldom used to extract higher-level semantics. Moreover, the ontology inference is often crisp. This paper aims to enable sophisticated semantic querying of images, and thus contributes to 1) an ontology framework to contain both visual and contextual knowledge, and 2) a probabilistic inference approach to reason the high-level concepts based on different sources of information. The experiment on a natural scene database from LabelMe database shows encouraging results.

Mid-level concept learning with visual contextual ontologies and probabilistic inference for image annotation

To date, automatic recognition of semantic information such as salient objects and mid-level concepts from images is a challenging task. Since real-world objects tend to exist in a context within their environment, the computer vision researchers have increasingly incorporated contextual information for improving object recognition. In this paper, we present a method to build a visual contextual ontology from salient objects descriptions for image annotation. The ontologies include not only partOf/kindOf relations, but also spatial and co-occurrence relations. A two-step image annotation algorithm is also proposed based on ontology relations and probabilistic inference. Different from most of the existing work, we specially exploit how to combine representation of ontology, contextual knowledge and probabilistic inference. The experiments show that image annotation results are improved in the LabelMe dataset.

Intelligent prognostics of machinery health utilising suspended condition monitoring data

The ability to forecast machinery failure is vital to reducing maintenance costs, operation downtime and safety hazards. Recent advances in condition monitoring technologies have given rise to a number of prognostic models for forecasting machinery health based on condition data. Although these models have aided the advancement of the discipline, they have made only a limited contribution to developing an effective machinery health prognostic system. The literature review indicates that there is not yet a prognostic model that directly models and fully utilises suspended condition histories (which are very common in practice since organisations rarely allow their assets to run to failure); that effectively integrates population characteristics into prognostics for longer-range prediction in a probabilistic sense; which deduces the non-linear relationship between measured condition data and actual asset health; and which involves minimal assumptions and requirements. This work presents a novel approach to addressing the above-mentioned challenges. The proposed model consists of a feed-forward neural network, the training targets of which are asset survival probabilities estimated using a variation of the Kaplan-Meier estimator and a degradation-based failure probability density estimator. The adapted Kaplan-Meier estimator is able to model the actual survival status of individual failed units and estimate the survival probability of individual suspended units. The degradation-based failure probability density estimator, on the other hand, extracts population characteristics and computes conditional reliability from available condition histories instead of from reliability data. The estimated survival probability and the relevant condition histories are respectively presented as “training target” and “training input” to the neural network. The trained network is capable of estimating the future survival curve of a unit when a series of condition indices are inputted. Although the concept proposed may be applied to the prognosis of various machine components, rolling element bearings were chosen as the research object because rolling element bearing failure is one of the foremost causes of machinery breakdowns. Computer simulated and industry case study data were used to compare the prognostic performance of the proposed model and four control models, namely: two feed-forward neural networks with the same training function and structure as the proposed model, but neglected suspended histories; a time series prediction recurrent neural network; and a traditional Weibull distribution model. The results support the assertion that the proposed model performs better than the other four models and that it produces adaptive prediction outputs with useful representation of survival probabilities. This work presents a compelling concept for non-parametric data-driven prognosis, and for utilising available asset condition information more fully and accurately. It demonstrates that machinery health can indeed be forecasted. The proposed prognostic technique, together with ongoing advances in sensors and data-fusion techniques, and increasingly comprehensive databases of asset condition data, holds the promise for increased asset availability, maintenance cost effectiveness, operational safety and – ultimately – organisation competitiveness.

Forecasting time-varying value-at-risk

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices —ASX 200, S&P 500 and FT 30—, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.

Probabilistic world modeling for distributed team planning

This paper describes an application of decoupled probabilistic world modeling to achieve team planning. The research is based on the principle that the action selection mechanism of a member in a robot team can select an effective action if a global world model is available to all team members. In the real world, the sensors are imprecise, and are individual to each robot, hence providing each robot a partial and unique view about the environment. We address this problem by creating a probabilistic global view on each agent by combining the perceptual information from each robot. This probabilistic view forms the basis for selecting actions to achieve the team goal in a dynamic environment. Experiments have been carried out to investigate the effectiveness of this principle using custom-built robots for real world performance, in addition, to extensive simulation results. The results show an improvement in team effectiveness when using probabilistic world modeling based on perception sharing for team planning.

Probabilistic visual recognition of artificial landmarks for simultaneous localization and mapping

Probabilistic robotics, most often applied to the problem of simultaneous localisation and mapping (SLAM), requires measures of uncertainly to accompany observations of the environment. This paper describes how uncertainly can be characterised for a vision system that locates coloured landmark in a typical laboratory environment. The paper describes a model of the uncertainly in segmentation, the internal camera model and the mounting of the camera on the robot. It =plains the implementation of the system on a laboratory robot, and provides experimental results that show the coherence of the uncertainly model,