Bayesian Correction Research Articles

Characterizing the Value of Actuarial Violence Risk Assessments

Using the Violence Risk Appraisal Guide, relative operating characteristic (ROC) statistics are exemplified. Criticisms of actuarials and ROCs as measures of accuracy are discussed—ROC statistics are independent of base rates, but optimal decisions are not. Using sex offenders, the importance of accurate base rate information in the relevant population is examined. Although Bayes affords estimates of posterior probabilities for any base rate, Bayesian corrections can be too extreme in practice. This article illustrates that undesirable posterior probabilities are improved by superior selection ratios and refutes the criticism that “confidence intervals around individual scores” are so large as to make actuarial assessment meaningless. Personal values play a role in forensic decision making, and actuarial methods sharpen the focus on such values.

FORECASTING THE SOUTH AFRICAN ECONOMY WITH GIBBS SAMPLED BVECMs

AbstractThe paper uses the Gibbs sampling technique to estimate a heteroscedastic Bayesian Vector Error Correction Model (BVECM) of the South African economy for the period 1970:1‐2000:4, and then forecasts GDP, consumption, investment, short and long term interest rates, and the CPI over the period of 2001:1 to 2005:4. We find that a tight prior produces relatively more accurate forecasts than a loose one. The out‐of‐sample‐forecast accuracy resulting from the Gibbs sampled BVECM is compared with those generated from a Classical VECM and a homoscedastic BVECM. The homoscedastic BVECM is found to produce the most accurate out of sample forecasts.

The Bayesian Bias Correction Method of the First-Order Approximation of Nonlinear Mixed-Effects Models for Population Pharmacokinetics

Population pharmacokinetic analysis usually employs nonlinear mixed-effects models. To estimate the parameters, Beal and Sheiner (1982) proposed the first-order method that employs a first-order Taylor series expansion around the means of random individual parameters. Because of the small computational burden and the high convergence proportion of maximization of the log likelihood function, this method is often used in practice. However, it is known that the estimates are biased. This paper proposes a simple procedure to reduce the bias. The proposed method maximizes the nonapproximated log likelihood functions of each individual given estimates of the population parameters derived from the first-order method, and the derived Bayes estimates of the random individual parameters are utilized to improve the estimates of the population mean parameters. We confirmed that the proposed method reduced the bias using simulated data and actual erythropoietin concentration data.

FORECASTING THE SOUTH AFRICAN ECONOMY WITH VARs AND VECMs

AbstractThe paper develops a Bayesian Vector Error Correction Model (BVECM) of the South African economy for the period 1970:1‐2000:4 and forecasts GDP, consumption, investment, short and long term interest rates, and the CPI. We find that a tight prior produces relatively more accurate forecasts than a loose one. The out‐of‐sample‐forecast accuracy resulting from the BVECM is compared with those generated from the Classical variant of the VAR and VECM and the Bayesian VAR. The BVECM is found to produce the most accurate out of sample forecasts. It also correctly predicts the direction of change in the chosen macroeconomic indicators.

A Bayesian nonlinear support vector machine error correction model

The use of linear error correction models based on stationarity and cointegration analysis, typically estimated with least squares regression, is a common technique for financial time series prediction. In this paper, the same formulation is extended to a nonlinear error correction model using the idea of a kernel-based implicit nonlinear mapping to a high-dimensional feature space in which linear model formulations are specified. Practical expressions for the nonlinear regression are obtained in terms of the positive definite kernel function by solving a linear system. The nonlinear least squares support vector machine model is designed within the Bayesian evidence framework that allows us to find appropriate trade-offs between model complexity and in-sample model accuracy. From straightforward primal–dual reasoning, the Bayesian framework allows us to derive error bars on the prediction in a similar way as for linear models and to perform hyperparameter and input selection. Starting from the results of the linear modelling analysis, the Bayesian kernel-based prediction is successfully applied to out-of-sample prediction of an aggregated equity price index for the European chemical sector. Copyright © 2006 John Wiley & Sons, Ltd.

Taxon sampling effects in molecular clock dating: An example from the African Restionaceae

Three commonly used molecular dating methods for correction of variable rates (non-parametric rate smoothing, penalized likelihood, and Bayesian rate correction) as well as the assumption of a global molecular clock were tested for sensitivity to taxon sampling. The test dataset of 6854 basepairs for 300 terminals includes a nearly complete sample of the Restio-clade of the African Restionaceae (272 of the 288 species), as well as 26 outgroup species. Of this, nested subsets of 35, 51, 80, 120, 150, and the full 300 species were used. Molecular dating experiments with these datasets showed that all methods are sensitive to undersampling, but that this effect is more severe in analyses that use more extreme rate smoothing. Additionally, the undersampling effect is positively related to distance from the calibration node. The combined effect of undersampling and distance from the calibration node resulted in up to threefold differences in the age estimation of nodes from the same dataset with the same calibration point. We suggest that the most suitable methods are penalized likelihood and Bayesian when a global clock assumption has been rejected, as these methods are more successful at finding optimal levels of smoothing to correct for rate heterogeneity, and are less sensitive to undersampling.

Beating the random walk in Central and Eastern Europe

We compare the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian error correction (BVEC) models in forecasting the exchange rates of five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Slovak Koruna, Slovenian Tolar and Polish Zloty) against the US Dollar and the Euro. Although these models tend to outperform the random walk model for long-term predictions (6 months ahead and beyond), even the best models in terms of average prediction error fail to reject the test of equality of forecasting accuracy against the random walk model in short-term predictions. Copyright © 2005 John Wiley & Sons, Ltd.

Forecasting exchange rates in transition economies: A comparison of multivariate time series models

This article compares the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian vector error correction (BVEC) models in forecasting the exchange rates for five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Polish Zloty, Slovak Koruna and Slovenian Tolar) against the Euro and the US dollar. Among the specifications composing this battery of multivariate time series models, those with the smallest prediction error still fail to reject the test of equality of forecasting accuracy against the random walk model in short-term predictions, with the exception of the Slovenian Tolar/Euro exchange rate.

Bayesian color correction method for non-colorimetric digital image sensors

Bayesian color correction method for non-colorimetric digital image sensors

Parallel Particle Filtering

In recent years, there has been exciting advances in estimation methods based on Monte Carlo techniques. The particle filtering technique may cope with non-linear models as well as non-Gaussian dynamic and observation noises. It recursively constructs the conditional probability density of the state variables, with respect to all available measurements, through a random exploration of the state space by entities called particles. A weight is assigned to each particle by a Bayesian correction term based on measurements. The main drawback of this procedure is due to the large number of particles needed which limits its application to on-line filtering. A data parallel algorithm is proposed to achieve real-time particle filtering. Extensive results are presented. They show that the accuracy of the method is preserved and that the computing times of the parallel algorithm are compatible with the real-time constraints of the most challenging applications.

A Bayesian vector error correction model for forecasting exchange rates

This paper develops a new method called Bayesian Vector Error Correction Model (BVECM), which is applied to forecast 1 month ahead changes of currency exchange rates for three major Asia Pacific economies. The study also compares out-of-sample forecasting performance with those of the random walk model and the Bayesian Vector Autoregression (BVAR), which has been shown in recent studies to outperform a variety competing of econometric techniques in exchange rate forecasting. Our experimental results indicate that both BVECM and BVAR are able to forecast the changes in exchange rates better than the random walk model. In terms of conventional forecast evaluation statistics, BVECM outperforms BVAR for all three currencies examined. In addition, the bias tests find that BVECM produces systematically less biased and more efficient out-of-sample forecasts than BVAR. Although the results of market timing tests indicate that both BVAR and BVECM have an economically significant value in predicting the directional change in two of the three exchange rates, BVECM is shown to produce equally or more economically significant directional change forecasts than BVAR.

Improvement of brain perfusion SPET using iterative reconstruction with scatter and non-uniform attenuation correction.

Filtered back-projection (FBP) is generally used as the reconstruction method for single-photon emission tomography although it produces noisy images with apparent streak artefacts. It is possible to improve the image quality by using an algorithm with iterative correction steps. The iterative reconstruction technique also has an additional benefit in that computation of attenuation correction can be included in the process. A commonly used iterative method, maximum-likelihood expectation maximisation (ML-EM), can be accelerated using ordered subsets (OS-EM). We have applied to the OS-EM algorithm a Bayesian one-step late correction method utilising median root prior (MRP). Methodological comparison was performed by means of measurements obtained with a brain perfusion phantom and using patient data. The aim of this work was to quantitate the accuracy of iterative reconstruction with scatter and non-uniform attenuation corrections and post-filtering in SPET brain perfusion imaging. SPET imaging was performed using a triple-head gamma camera with fan-beam collimators. Transmission and emission scans were acquired simultaneously. The brain phantom used was a high-resolution three-dimensional anthropomorphic JB003 phantom. Patient studies were performed in ten chronic pain syndrome patients. The images were reconstructed using conventional FBP and iterative OS-EM and MRP techniques including scatter and nonuniform attenuation corrections. Iterative reconstructions were individually post-filtered. The quantitative results obtained with the brain perfusion phantom were compared with the known actual contrast ratios. The calculated difference from the true values was largest with the FBP method; iteratively reconstructed images proved closer to the reality. Similar findings were obtained in the patient studies. The plain OS-EM method improved the contrast whereas in the case of the MRP technique the improvement in contrast was not so evident with post-filtering.

Does Current-Quarter Information Improve Quarterly Forecasts for the U.S. Economy?

This paper presents new evidence on the benefits of conditioning quarterly model forecasts on monthly current-quarter data. On the basis of a quarterly Bayesian vector error corrections model, the findings indicate that such conditioning produces economically relevant and statistically significant improvement. The improvement, which begins as early as the end of the first week of the second month of the quarter, is largest in the current quarter, but in some cases, extends beyond the current quarter. Forecast improvement is particularly large during periods of recessions but generally extends to other periods as well. Overall, the findings suggest that it is rational to update one's quarterly forecast in response to incoming monthly data.

Modeling multivariate co integrated systems: Insights from non‐linear dynamics

AbstractJohansen's test for co integration is applied to Litterman's original six‐variable Bayesian vector auto regression (BVAR) model to obtain vector error correction mechanism (VECM) and Bayesian error correction (BECM) versions of the model. The Brock, Dechert, and Scheinkman (BDS) test for independence from the non‐linear dynamics literature is then applied to the error structures of each estimated equation of the BECM and VECM models, plus two BVAR versions of the model. The results show that none of the models produce independent and identically distributed (IID) errors for all six equations. However, the BDS results suggest the elimination of the Bayesian prior from the BECM model, given that the univariate VECM errors are IID in five equations, compared to only two or three equations under the three Bayesian restricted models. These results combined with previous evidence regarding the superior forecasting performance of BECM over ECM models suggest future experimentation with less restrictive BVAR priors, BECM models corrected for heteroscedasticity, or hybrid specifications based on the nonlinear dynamics literature.

Using Spatial Contiguity as Bayesian Prior Information in Regional Forecasting Models

Spatial contiguity relationships represent a frequently ignored source of information that is available to economists modeling cross-sections of metropolitan areas, counties, states, regions, and countries. Shown here is how contiguity relationships can be incorporated as prior information in Bayesian vector autoregressive and error correction models with little or no effort, using existing software, to produce improvements in forecasting performance. A comparison of alternative forecasting methods is undertaken using annual postwar time series of agricultural output for a sample of 15 corn-producing states. The models that incorporate prior information regarding spatial contiguity are found to dominate those that ignore this information, producing much better forecasts.

An Improved Method for Detection of Words with Unusual Occurrence Frequency in Nucleotidic Sequences

A statistical analysis designed to deal with the problem of identifying rare or abundant "words" of arbitrary length in genomic fragments is presented. Our approach has the novelty of taking into account the statistical role of the presence of shorter words nested into longer ones and of introducing a Bayesian correction to minimize the effects of statistical fluctuations and of possible mistakes in genomic data. The method is successfully used in a thorough analysis of the abundance of short nucleotide sequences in the Escherichia coli genome.

Bayesian and Frequentist Bartlett Corrections for Likelihood Ratio and Conditional Likelihood Ratio Tests

SUMMARY This paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio and the conditional likelihood ratio (CLR) statistics differ by o(1). It is seen that, except for sample points with negligible probability, the CLR statistic has a posterior distribution for which a posterior Bartlett correction exists. This observation leads to an alternative proof of the existence of a frequentist Bartlett correction for the CLR statistic.

Characterization of priors under which Bayesian and frequentist Bartlett corrections are equivalent in the multiparameter case

In a multiparameter situation, this paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio statistic differ by o(1). The role of Jeffreys' prior in this regard has also been investigated.

A method to estimate intensity occurrence probabilities in low seismic activity regions

AbstractThe estimation of site intensity occurrence probabilities in low seismic activity regions has been studied from different points of view. However, no method has been definitively established because several problems arise when macroseismic historical data are incomplete and the active zones are not well determined. The purpose of this paper is to present a method that estimates site occurrence probabilities and at the same time measures the uncertainties inherent in these probabilities in low activity regions. The region to be studied is divided into very broad seismic zones. An exponential intensity probability law is adjusted for each zone and the degree of uncertainty in the assumed incompleteness of the catalogue is evaluated for each intensity. These probabilities are used to establish what may be termed ‘prior site occurrence models’. A Bayesian method is used to improve ‘prior models’ and to obtain the ‘posterior site occurrence models’. Epicentre locations are used to recover spatial information lost in the prior broad zoning. This Bayesian correction permits the use of specific attenuation for different events and may take into account, by means of conservative criteria, epicentre location errors. Following Bayesian methods, probabilities are assumed to be random variables and their distribution may be used to estimate the degree of uncertainty arising from (a) the statistical variance of estimators, (b) catalogue incompleteness and (c) mismatch of data to prior assumptions such as Poisson distribution for events and exponential distribution for intensities. The results are maps of probability and uncertainty for each intensity. These maps exhibit better spatial definition than those obtained by means of simple, broad zones. Some results for Catalonia (NE of Iberian Peninsula) are shown.

A Comparison of the Forecasting Ability of ECM and VAR Models

The results of forecasting experiments based on an error correction mechanism (ECM) model and various types of vector autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models are presented. A Bayesian error correction mechanism (BECM) model is also tested. This model represents a hybrid of the BVAR and ECM models. The results from experiments using fifty industries and monthly Ohio labor market data demonstrate that the ECM model produces forecasts with much lower errors than any of the alternative VAR or BVAR models when the variables used in the model pass the statistical tests for cointegration. The findings confirm many of the beliefs expressed by Granger (1986) and Engle and Yoo (1987) based on theoretical consideration of the ECM model versus the VAR model. A result contradictory to the contentions of Engle and Yoo is that the BECM model performs well at the longer forecast horizons for both cointegrated and non-cointegrated industries.