Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite sample properties of the ML estimator in relation to the widely used conditional least
squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

Corrigendum Vol. 30, Issue 2, 259, Article first published online: 15 MAR 2009 to correct the order of authors names: Bu R., K. Hadri, and B. McCabe.

Transform both sides model: A parametric approach

A parametric regression model for right-censored data with a log-linear median regression function and a transformation in both response and regression parts, named parametric Transform-Both-Sides (TBS) model, is presented. The TBS model has a parameter that handles data asymmetry while allowing various different distributions for the error, as long as they are unimodal symmetric distributions centered at zero. The discussion is focused on the estimation procedure with five important error distributions (normal, double-exponential, Student's t, Cauchy and logistic) and presents properties, associated functions (that is, survival and hazard functions) and estimation methods based on maximum likelihood and on the Bayesian paradigm. These procedures are implemented in TBSSurvival, an open-source fully documented R package. The use of the package is illustrated and the performance of the model is analyzed using both simulated and real data sets.

Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

Improving parameter learning of Bayesian nets from incomplete data

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the maximum penalized log-likelihood and the maximum a posteriori estimate) has severe drawbacks, being affected both by overfitting and model uncertainty. Two ideas are discussed to overcome these issues: a maximum entropy approach and a Bayesian model averaging approach. Both ideas can be easily applied on top of EM, while the entropy idea can be also implemented in a more sophisticated way, through a dedicated non-linear solver. A vast set of experiments shows that these ideas produce significantly better estimates and inferences than the traditional and widely used maximum (penalized) log-likelihood and maximum a posteriori estimates. In particular, if EM is adopted as optimization engine, the model averaging approach is the best performing one; its performance is matched by the entropy approach when implemented using the non-linear solver. The results suggest that the applicability of these ideas is immediate (they are easy to implement and to integrate in currently available inference engines) and that they constitute a better way to learn Bayesian network parameters.

Posterior Probability Modeling and Image Classification for Archaeological Site Prospection: Building a Survey Efficacy Model for Identifying Neolithic Felsite Workshops in the Shetland Islands

The application of custom classification techniques and posterior probability modeling (PPM) using Worldview-2 multispectral imagery to archaeological field survey is presented in this paper. Research is focused on the identification of Neolithic felsite stone tool workshops in the North Mavine region of the Shetland Islands in Northern Scotland. Sample data from known workshops surveyed using differential GPS are used alongside known non-sites to train a linear discriminant analysis (LDA) classifier based on a combination of datasets including Worldview-2 bands, band difference ratios (BDR) and topographical derivatives. Principal components analysis is further used to test and reduce dimensionality caused by redundant datasets. Probability models were generated by LDA using principal components and tested with sites identified through geological field survey. Testing shows the prospective ability of this technique and significance between 0.05 and 0.01, and gain statistics between 0.90 and 0.94, higher than those obtained using maximum likelihood and random forest classifiers. Results suggest that this approach is best suited to relatively homogenous site types, and performs better with correlated data sources. Finally, by combining posterior probability models and least-cost analysis, a survey least-cost efficacy model is generated showing the utility of such approaches to archaeological field survey.

Directional genetic differentiation and relative migration

Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly used to gather this information. One potential caveat is that these measures assume gene flow to be symmetric. However, asymmetric gene flow is common in nature, especially in systems driven by physical processes such as wind or water currents. As information about levels of asymmetric gene flow among populations is essential for the correct interpretation of the distribution of contemporary genetic diversity within species, this should not be overlooked. To obtain information on asymmetric migration patterns from genetic data, complex models based on maximum-likelihood or Bayesian approaches generally need to be employed, often at great computational cost. Here, a new simpler and more efficient approach for understanding gene flow patterns is presented. This approach allows the estimation of directional components of genetic divergence between pairs of populations at low computational effort, using any of the classical or modern measures of genetic differentiation. These directional measures of genetic differentiation can further be used to calculate directional relative migration and to detect asymmetries in gene flow patterns. This can be done in a user-friendly web application called divMigrate-online introduced in this study. Using simulated data sets with known gene flow regimes, we demonstrate that the method is capable of resolving complex migration patterns under a range of study designs.

Genetic maternity and paternity in a local population of armadillos assessed by microsatellite DNA markers and field data.

Genetic data from polymorphic microsatellite loci were employed to estimate paternity and maternity in a local population of nine-banded armadillos (Dasypus novemcinctus) in northern Florida. The parentage assessments took advantage of maximum likelihood procedures developed expressly for situations when individuals of neither gender can be excluded a priori as candidate parents. The molecular data for 290 individuals, interpreted alone and in conjunction with detailed biological and spatial information for the population, demonstrate high exclusion probabilities and reasonably strong likelihoods of genetic parentage assignment in many cases; low mean probabilities of successful reproductive contribution to the local population by individual armadillo adults in a given year; and statistically significant microspatial associations of parents and their offspring. Results suggest that molecular assays of highly polymorphic genetic systems can add considerable power to assessments of biological parentage in natural populations even when neither parent is otherwise known.

Object tracking using SIFT features and mean shift

A scale invariant feature transform (SIFT) based mean shift algorithm is presented for object tracking in real scenarios. SIFT features are used to correspond the region of interests across frames. Meanwhile, mean shift is applied to conduct similarity search via color histograms. The probability distributions from these two measurements are evaluated in an expectation–maximization scheme so as to achieve maximum likelihood estimation of similar regions. This mutual support mechanism can lead to consistent tracking performance if one of the two measurements becomes unstable. Experimental work demonstrates that the proposed mean shift/SIFT strategy improves the tracking performance of the classical mean shift and SIFT tracking algorithms in complicated real scenarios.

Measurements, modeling and simulation of the off-body radio channel for the implementation of bodyworn antenna diversity at 868 MHz

This paper presents a systematic measurement campaign of diversity reception techniques for use in multiple-antenna wearable systems operating at 868 MHz. The experiments were performed using six time-synchronized bodyworn receivers and considered mobile off-body communications in an anechoic chamber, open office area and a hallway. The cross-correlation coefficient between the signal fading measured by bodyworn receivers was dependent upon the local environment and typically below 0.7. All received signal envelopes were combined in post-processing to study the potential benefits of implementing receiver diversity based upon selection combination, equal-gain and maximal-ratio combining. It is shown that, in an open office area, the 5.7 dB diversity gain obtained using a dual-branch bodyworn maximal-ratio diversity system may be further improved to 11.1 dB if a six-branch system was used. First-and second-order theoretical equations for diversity reception techniques operating in Nakagami fading conditions were used to model the postdetection combined envelopes. Maximum likelihood estimates of the Nakagami-parameter suggest that the fading conditions encountered in this study were generally less severe than Rayleigh. The paper also describes an algorithm that may be used to simulate the measured output of an M-branch diversity combiner operating in independent and identically-distributed Nakagami fading environments.

Channel characterization for single- and multiple-antenna wearable systems used for indoor body-to-body communications

In this paper, an analysis of radio channel characteristics for single- and multiple-antenna bodyworn systems for use in body-to-body communications is presented. The work was based on an extensive measurement campaign conducted at 2.45 GHz representative of an indoor sweep and search scenario for fire and rescue personnel. Using maximum-likelihood estimation in conjunction with the Akaike information criterion (AIC), five candidate probability distributions were investigated and from these the kappa - mu distribution was found to best describe small-scale fading observed in the body-to-body channels. Additional channel parameters such as autocorrelation and the cross-correlation coefficient between fading signal envelopes were also analyzed. Low cross correlation and small differences in mean signal levels between potential dual-branch diversity receivers suggested that the prospect of successfully implementing diversity in this type application is extremely good. Moreover, using selection combination, maximal ratio, and equal gain combining, up to 8.69-dB diversity gain can be made available when four spatially separated antennas are used at the receiver. Additional improvements in the combined envelopes through lower level crossing rates and fade durations at low signal levels were also observed.

An experimental investigation into the influence of user state and environment on fading characteristics in wireless body area networks at 2.45 GHz

Using seven strategically placed, time-synchronized bodyworn receivers covering the head, upper front and back torso, and the limbs, we have investigated the effect of user state: stationary or mobile and local environment: anechoic chamber, open office area and hallway upon first and second order statistics for on-body fading channels. Three candidate models were considered: Nakagami, Rice and lognormal. Using maximum likelihood estimation and the Akaike information criterion it was established that the Nakagami-m distribution best described small-scale fading for the majority of on-body channels over all the measurement scenarios. When the user was stationary, Nakagami-m parameters were found to be much greater than 1, irrespective of local surroundings. For mobile channels, Nakagami-m parameters significantly decreased, with channels in the open office area and hallway experiencing the worst fading conditions.

Achieving Space and Time Diversity by Using Lattice Constellation Based Joint Alamouti Coding

In this letter, we propose a simple space-time code to simultaneously achieve both the space and time diversities over time dispersive channels by using two-dimensional lattice constellations and Alamouti codes. The proposed scheme still reserves full space diversity and double-real-symbols joint maximum likelihood decoding which has the similar computation complexity as the Alamouti code.