Simulated convergence rates with application to an intractable α-stable inference problem

© 2017 IEEE. We report the results of a series of numerical studies examining the convergence rate for some approximate representations of α-stable distributions, which are a highly intractable class of distributions for inference purposes. Our proposed representation turns the intractable inference for an infinite-dimensional series of parameters into an (approximately) conditionally Gaussian representation, to which standard inference procedures such as Expectation-Maximization (EM), Markov chain Monte Carlo (MCMC) and Particle Filtering can be readily applied. While we have previously proved the asymptotic convergence of this representation, here we study the rate of this convergence for finite values of a truncation parameter, c. This allows the selection of appropriate truncations for different parameter configurations and for the accuracy required for the model. The convergence is examined directly in terms of cumulative distribution functions and densities, through the application of the Berry theorems and Parseval theorems. Our results indicate that the behaviour of our representations is significantly superior to that of representations that simply truncate the series with no Gaussian residual term

Corporate governance performance ratings with machine learning

We use machine learning with a cross-sectional research design to predict governance controversies and to develop a measure of the governance component of the environmental, social, governance (ESG) metrics. Based on comprehensive governance data from 2,517 companies over a period of 10 years and investigating nine machine-learning algorithms, we find that governance controversies can be predicted with high predictive performance. Our proposed governance rating methodology has two unique advantages compared with traditional ESG ratings: it rates companies' compliance with governance responsibilities and it has predictive validity. Our study demonstrates a solution to what is likely the greatest challenge for the finance industry today: how to assess a company's sustainability with validity and accuracy. Prior to this study, the ESG rating industry and the literature have not provided evidence that widely adopted governance ratings are valid. This study describes the only methodology for developing governance performance ratings based on companies' compliance with governance responsibilities and for which there is evidence of predictive validity

Convergence results for tractable inference in α-stable stochastic processes

The α-stable distribution is highly intractable for inference because of the lack of a closed form density function in the general case. However, it is well-established that the α-stable distribution admits a Poisson series representation (PSR) in which the terms of the series are a function of the arrival times of a unit rate Poisson process. In our previous work, we have shown how to carry out inference for regression models using this series representation, which leads to a very convenient conditionally Gaussian framework, amenable to tractable Gaussian inference procedures. The PSR has to be truncated to a finite number of terms for practical purposes. The residual error terms have been approximated in our previous work by a Gaussian distribution, and we have recently shown that this approximation can be justified through a Central Limit Theorem (CLT). In this paper we present a new and exact characterisation of the first and second moments of the residual series over finite time intervals for the unit rate Poisson process, correcting a previous version that was only true in the infinite time limit. This enables us to test through simulation the rapid convergence of the residual terms to a Gaussian distribution of the Poisson series residual. We test this convergence using both Q-Q plots and the classical Kolmogorov-Smirnov test of Gaussianity

Efficient bridging-based destination inference in object tracking

© 2017 IEEE. This paper proposes a probabilistic intent inference approach that is significantly more computationally efficient than other existing bridging-distributions-based predictors. It sequentially determines the probabilities of all possible destinations of a tracked object, whose motion is modelled by a Markov chain with the distribution of its terminal state equal to that of a nominal endpoint. This encapsulates the long term dependencies in the object trajectory as dictated by intent. Simulations using real data show that the notable reductions in computations achieved by the introduced bridging-based predictor does not impact the quality of the overall inference results

Nonasymptotic Gaussian Approximation for Inference with Stable Noise

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of alpha -stable distributions. Although they play a key role in modelling random processes with jumps and discontinuities, the use of alpha -stable distributions in inference often leads to analytically intractable problems. The LePage series, which is a probabilistic representation employed in this work, is used to transform an intractable, infinite-dimensional inference problem into a finite-dimensional (conditionally Gaussian) parametric problem. A major component of our approach is the approximation of the tail of this series by a Gaussian random variable. Standard statistical techniques, such as Expectation-Maximization (EM), Markov chain Monte Carlo, and Particle Filtering, can then be readily applied. In addition to the asymptotic normality of the tail of this series, we establish explicit, nonasymptotic bounds on the approximation error. Their proofs follow classical Fourier-analytic arguments, using Esséen's smoothing lemma. Specifically, we consider the distance between the distributions of: (i) the tail of the series and an appropriate Gaussian; (ii) the full series and the truncated series; and (iii) the full series and the truncated series with an added Gaussian term. In all three cases, sharp bounds are established, and the theoretical results are compared with the actual distances (computed numerically) in specific examples of symmetric alpha -stable distributions. This analysis facilitates the selection of appropriate truncations in practice and offers theoretical guarantees for the accuracy of resulting estimates. One of the main conclusions obtained is that, for the purposes of inference, the use of a truncated series together with an approximately Gaussian error term has superior statistical properties and is likely a preferable choice in practice

Modelling received signal strength from on-vehicle BLE beacons using skewed distributions: A preliminary study

© 2017 International Society of Information Fusion (ISIF). This paper describes a study on modelling the Received Signal Strength Indicator (RSSI) measured by the smartphone of a vehicle user. The present transmissions are emitted by dedicated radio frequency sources, such as Bluetooth Low Energy (BLE) beacons, mounted to the vehicle to determine the driver/passenger(s) proximity or relative position(s). Based on empirical data, a model of the measurements noise, which utilises skewed distributions, is proposed to capture inconsistencies in reception and the impact of occlusions on the RSSI profile in an automotive setting, for example occlusions in car parks. Experimental data is used to demonstrate the suitability of the introduced model

Sharp Gaussian Approximation Bounds for Linear Systems with α-stable Noise

We report the results of several theoretical studies into the convergence rate for certain random series representations of α-stable random variables, which are motivated by and find application in modelling heavy-tailed noise in time series analysis, inference, and stochastic processes. The use of α-stable noise distributions generally leads to analytically intractable inference problems. The particular version of the Poisson series representation invoked here implies that the resulting distributions are “conditionally Gaussian,” for which inference is relatively straightforward, although an infinite series is still involved. Our approach is to approximate the residual (or “tail”) part of the series from some point, c > 0, say, to ∞, as a Gaussian random variable. Empirically, this approximation has been found to be very accurate for large c. We study the rate of convergence, as c → ∞, of this Gaussian approximation. This allows the selection of appropriate truncation parameters, so that a desired level of accuracy for the approximate model can be achieved. Explicit, nonasymptotic bounds are obtained for the Kolmogorov distance between the relevant distribution functions, through the application of probability-theoretic tools. The theoretical results obtained are found to be in very close agreement with numerical results obtained in earlier work

Simulated convergence rates with application to an intractable α-stable inference problem

© 2017 IEEE. We report the results of a series of numerical studies examining the convergence rate for some approximate representations of α-stable distributions, which are a highly intractable class of distributions for inference purposes. Our proposed representation turns the intractable inference for an infinite-dimensional series of parameters into an (approximately) conditionally Gaussian representation, to which standard inference procedures such as Expectation-Maximization (EM), Markov chain Monte Carlo (MCMC) and Particle Filtering can be readily applied. While we have previously proved the asymptotic convergence of this representation, here we study the rate of this convergence for finite values of a truncation parameter, c. This allows the selection of appropriate truncations for different parameter configurations and for the accuracy required for the model. The convergence is examined directly in terms of cumulative distribution functions and densities, through the application of the Berry theorems and Parseval theorems. Our results indicate that the behaviour of our representations is significantly superior to that of representations that simply truncate the series with no Gaussian residual term

The first discrete choice experiment on usage of bypassing agents in hemophilic patients in Iran

Background: Bleeding events in hemophilic patients with inhibitors are managed by bypassing agents. Currently available agents in Iran are recombinant activated factor VII (rfVIIa; Aryogen, Aryoseven) and Feiba (factor eight inhibitor bypassing agent). No standardized and accurate assay is currently available for monitoring the effectiveness of bypassing agents. We suggested that history of the patients� response and also their preference could be a reliable method for assessing the efficacy of bypassing agents; therefore, we designed a multi-centric discrete choice experiment study to assess the factors that affect the efficacy of bypassing agents. Methods: Hemophilic patients older than 2 years with inhibitors who required bypassing agents for the treatment of bleeding episodes were eligible to participate in the study. Patients� preference toward treatment with either Feiba or Aryoseven was measured with a DCE (discrete choice experiment) design on a phone interview. Results: 80 patients were enrolled from 5 centers in Iran. At enrollment, the mean age was18.6 years (range, 2-50 years). 47 patients (58) preferred to receive FEIBA, 21 patients (21.2) favored Aryoseven and 12 (14.8) patients claimed no difference between the two products. Conclusion: Our results indicated that according to the DCE method, patients preferred Feiba to Aryoseven while the main reason was their higher efficacy. In addition, adverse reactions in both groups were almost equal. As a result, it seems that presence of both products in the market for hemophilic patients with inhibitors is absolutely essential. © 2016 Iranian Pediatric Hematology and Oncology Society. All rights reserved

The first discrete choice experiment on usage of bypassing agents in hemophilic patients in Iran

Background: Bleeding events in hemophilic patients with inhibitors are managed by bypassing agents. Currently available agents in Iran are recombinant activated factor VII (rfVIIa; Aryogen, Aryoseven) and Feiba (factor eight inhibitor bypassing agent). No standardized and accurate assay is currently available for monitoring the effectiveness of bypassing agents. We suggested that history of the patients� response and also their preference could be a reliable method for assessing the efficacy of bypassing agents; therefore, we designed a multi-centric discrete choice experiment study to assess the factors that affect the efficacy of bypassing agents. Methods: Hemophilic patients older than 2 years with inhibitors who required bypassing agents for the treatment of bleeding episodes were eligible to participate in the study. Patients� preference toward treatment with either Feiba or Aryoseven was measured with a DCE (discrete choice experiment) design on a phone interview. Results: 80 patients were enrolled from 5 centers in Iran. At enrollment, the mean age was18.6 years (range, 2-50 years). 47 patients (58) preferred to receive FEIBA, 21 patients (21.2) favored Aryoseven and 12 (14.8) patients claimed no difference between the two products. Conclusion: Our results indicated that according to the DCE method, patients preferred Feiba to Aryoseven while the main reason was their higher efficacy. In addition, adverse reactions in both groups were almost equal. As a result, it seems that presence of both products in the market for hemophilic patients with inhibitors is absolutely essential. © 2016 Iranian Pediatric Hematology and Oncology Society. All rights reserved