Optimal Statistical Model Research Articles

Untangling the complex inter-relationships between horse managers’ perceptions of effectiveness of biosecurity practices using Bayesian graphical modelling

On-farm biosecurity practices have been promoted in many animal industries to protect animal populations from infections. Current approaches based on regression modelling techniques for assessing biosecurity perceptions and practices are limited for analysis of the interrelationships between multivariate data. A suitable approach, which does not require background knowledge of relationships, is provided by Bayesian network modelling. Here we apply such an approach to explore the complex interrelationships between the variables representing horse managers’ perceptions of effectiveness of on-farm biosecurity practices.The dataset was derived from interviews conducted with 200 horse managers in Australia after the 2007 equine influenza outbreak. Using established computationally intensive techniques, an optimal graphical statistical model was identified whose structure was objectively determined, directly from the observed data. This methodology is directly analogous to multivariate regression (i.e. multiple response variables). First, an optimal model structure was identified using an exact (exhaustive) search algorithm, followed by pruning the selected model for over-fitting by the parametric bootstrapping approach.Perceptions about effectiveness of movement restrictions and access control were linked but were generally segregated from the perceptions about effectiveness of personal and equipment hygiene. Horse managers believing in the effectiveness of complying with movement restrictions in stopping equine influenza spread onto their premises were also more likely to believe in the effectiveness of reducing their own contact with other horses and curtailing professional visits. Similarly, the variables representing the effectiveness of disinfecting vehicles, using a disinfectant footbath, changing into clean clothes on arrival at the premises and washing hands before contact with managed horses were clustered together. In contrast, horse managers believing in the effectiveness of disinfecting vehicles (hygiene measure) were less likely to believe in the effectiveness of controlling who has access to managed horses (access control).The findings of this analysis provide new insights into the relationships between perceptions of effectiveness of different biosecurity measures. Different extension education strategies might be required for horse managers believing more strongly in the effectiveness of access control or hygiene measures.

Finding the optimal statistical model to describe target motion during radiotherapy delivery—a Bayesian approach

Early approaches to characterizing errors in target displacement during a fractionated course of radiotherapy assumed that the underlying fraction-to-fraction variability in target displacement, known as the ‘treatment error’ or ‘random error’, could be regarded as constant across patients. More recent approaches have modelled target displacement allowing for differences in random error between patients. However, until recently it has not been feasible to compare the goodness of fit of alternate models of random error rigorously. This is because the large volumes of real patient data necessary to distinguish between alternative models have only very recently become available. This work uses real-world displacement data collected from 365 patients undergoing radical radiotherapy for prostate cancer to compare five candidate models for target displacement. The simplest model assumes constant random errors across patients, while other models allow for random errors that vary according to one of several candidate distributions. Bayesian statistics and Markov Chain Monte Carlo simulation of the model parameters are used to compare model goodness of fit. We conclude that modelling the random error as inverse gamma distributed provides a clearly superior fit over all alternatives considered. This finding can facilitate more accurate margin recipes and correction strategies.

Modelling the distribution of cortical lesions in multiple sclerosis

Recent studies have shown the relevance of the cerebral grey matter involvement in multiple sclerosis (MS). Cortical lesions (CLs), detected by specific MRI sequences, are likely to become a new research outcome in MS studies. The aim of this study was to infer the optimal statistical model describing the distribution of CLs in patients with relapsing–remitting (RR)MS. The negative binomial model gave the best fit to the observed distribution of CLs in a group of 44 RRMS patients with one MRI scan of the brain. This observation has important implications for the statistical analysis of CLs in MS studies.

Dynamic Model Selection With its Applications to Novelty Detection

We are concerned with the issue of dynamically selecting optimal statistical models from time series. The goal is not to select a single optimal model over the data as in conventional model selection, but to select a time series of optimal models under the assumption that the data source may be nonstationary. We call this issue dynamic model selection (DMS). From the standpoint of minimum description length principle, we first propose coding-theoretic criteria for DMS. Next, we propose efficient DMS algorithms on the basis of the criteria and analyze their performance in terms of their total code lengths and computation time. Finally, we apply DMS to novelty detection and demonstrate its effectiveness through empirical results on masquerade detection using UNIX command sequences.

Optimal statistical model for forecasting ozone

The objective of this paper is to apply time series analysis and multiple regression method to ozone data in order to obtain the optimal statistical model for forecasting next day ozone level. The best estimated model is then used to produce one-step ahead point and interval estimates of future values of the ozone series. Ozone data is analyzed using time series analysis, which resulted in an Auto Regressive Moving Average, ARMA (20, 2) with Mean Absolute Percentage Error (MAPE)=42%. Applying multiple regression method and examination of several possible contributing factors, showed that Wind speed, Mixing height where the complex chemical reactions that produce ozone take place, current and predicted next day temperatures and current ozone concentration are influential on the next day ozone concentration levels. Diagnostics tests and statistics including R-square, residual analysis and Durbin-Watson Statistic (DW) were applied in order to select the best fitted model and finally the best prediction model was found using MAPE and Mean Absolute Deviation (MAD) as predictive criteria. Regression analysis of this data, using tomorrow's and today's maximum temperature, today's wind speed and tomorrow's maximum height at 10 am, as explanatory variables results in R-square of 50.7% with MAD=12.423, MAPE=30% and DW=1.66

Building Optimal Statistical Models with the Parabolic Equation Method

In this paper, we present a new application of electromagnetic propagation model- ing methods like Parabolic Equation (PE) algorithms: these tools can be used to obtain optimal statistical propagation models i.e., best-fltted statistical model for a given propagation envi- ronment. Statistical propagation models are widely used because of their convenience to make predictions that are valid for difierent types of propagation environments and operation condi- tions. However their accuracy is often questionable because they are obtained either empirically with a limited amount of experimental data collected in few propagation environments or de- duced using rough and general theory. As a result the model doesn't square satisfactorily with real operation. Our goal is to improve the preceding process by designing a method that would give an optimized statistical model (OSM) for a given environment. The process that leads to the OSM for a particular application involves several steps that are described in detail in the paper. Sample results are also given and comparisons between OSM and standard statistical models are discussed.

Optimal statistical model for forecasting ozone

The objective of this paper is to apply time series analysis and multiple regression method to ozone data in order to obtain the optimal statistical model for forecasting next day ozone level. The ...

Building optimal 2D statistical shape models

Statistical shape models are used widely as a basis for segmenting and interpreting images. A major drawback of the approach is the need, during training, to establish a dense correspondence across a training set of segmented shapes. We show that model construction can be treated as an optimisation problem, automating the process and guaranteeing the effectiveness of the resulting models. This is achieved by optimising an objective function with respect to the correspondence. We use an information theoretic objective function that directly promotes desirable features of the model. This is coupled with an effective method of manipulating correspondence, based on re-parameterising each training shape, to build optimal statistical shape models. The method is evaluated on several training sets of shapes, showing that it constructs better models than alternative approaches.

Optimized statistical deformable surface models with manifold embedding

A key challenge for statistical shape modeling is the definition of a set of dense correspondence points across a group of segmented shapes. This paper describes a novel method for building an optimal statistical deformable model from a set of surfaces whose topological realization is homeomorphic to a compact 2D manifold with boundary. The optimal parameterization of each shape is recursively refined by using hierarchical piecewise bilinear maps (PBMs) and tensor product B-spline representation of the surface. A criterion based on minimum description length (MDL) is used to define the internal correspondence of the training data. The strength of the proposed technique is demonstrated by deriving a concise statistical model of the human left ventricle which has principal modes of variation that correspond to intrinsic cardiac motions. The extension of the technique to shapes with complex topology is also discussed.

Flexible Modelling in Survival Analysis. Structuring Biological Complexity from the Information Provided by Tumor Markers

The aim of the present article is to introduce and discuss the problem of optimal modelling of the prognostic information provided by putative prognostic variables, possibly measured on a quantitative scale. A number of methodological aspects will be treated, with particular reference to the role of spline functions and artificial neural networks, which will be discussed in the context of the analysis of survival data. The problem of the evaluation and the choice of the optimal statistical models will be examined, with particular attention to the critical aspects related to the definition of prognostic indexes on the basis of the results of the selected models. Clinical examples in breast cancer on the evaluation of the prognostic impact of several tumor markers are provided. This paper is addressed to all researchers who are interested in the evaluation of the prognostic role of tumor markers, therefore we will stress the necessity of integrating the methodologies of biological, clinical and statistical research in the assessment of prognosis.

An information criterion for optimal neural network selection

The choice of an optimal neural network design for a given problem is addressed. A relationship between optimal network design and statistical model identification is described. A derivative of Akaike's information criterion (AIC) is given. This modification yields an information statistic which can be used to objectively select a ;best' network for binary classification problems. The technique can be extended to problems with an arbitrary number of classes.

Model Analysis of the Efficacy of Advanced Flight Deck Display Concepts

The application of mathematical models of the functioning of pilots with respect to cockpit instrumentation is briefly discussed, in light of the progress which has been made towards the wedding of our existing knowledge about the control and decision-making capabilities of (well-trained) human operators with our ability conveniently to formulate and thus quantify, on the basis of perceptual cues and psychophysical limitations, the information content of various display concepts. This (relatively new) human engineering tool is expected to play a major role in the designing of future flight deck displays whose inevitable implementation will be made possible by the technical advances presently being made in digital avionics. One consequence of this technology is the tendency towards almost completely automated flight, whereby the role of the pilot is evolving from a system regulator to a system supervisor. It is therefore incumbent upon our modelling “technology” to be able to predict not only manual control performance and workload but the human operator's monitoring and failure detection behaviour as well. These considerations form the motivation in this presentation for a predictive analysis, using optimal control and statistical decision theoretic models, of pilot behaviour during both manual and monitored approach to landing scenarios, as a function of the information content of a sequence of perspective status display formats.