Nalan Basturk

A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood

Strategic choices for efficient and accurate evaluation of marginal likelihoods by means of Monte Carlo simulation methods are studied for the case of highly non-elliptical posterior distributions. A comparative analysis is presented of possible advantages and limitations of different simulation techniques; of possible choices of candidate distributions and choices of target or warped target distributions; and finally of numerical standard errors. The importance of a robust and flexible estimation strategy is demonstrated where the complete posterior distribution is explored. Given an appropriately yet quickly tuned adaptive candidate, straightforward importance sampling provides a computationally efficient estimator of the marginal likelihood (and a reliable and easily computed corresponding numerical standard error) in the cases investigated, which include a non-linear regression model and a mixture GARCH model. Warping the posterior density can lead to a further gain in efficiency, but it is more important that the posterior kernel be appropriately wrapped by the candidate distribution than that it is warped.

Genome-wide analysis of macrosatellite repeat copy number variation in worldwide populations: evidence for differences and commonalities in size distributions and size restrictions

BackgroundMacrosatellite repeats (MSRs), usually spanning hundreds of kilobases of genomic DNA, comprise a significant proportion of the human genome. Because of their highly polymorphic nature, MSRs represent an extreme example of copy number variation, but their structure and function is largely understudied. Here, we describe a detailed study of six autosomal and two X chromosomal MSRs among 270 HapMap individuals from Central Europe, Asia and Africa. Copy number variation, stability and genetic heterogeneity of the autosomal macrosatellite repeats RS447 (chromosome 4p), MSR5p (5p), FLJ40296 (13q), RNU2 (17q) and D4Z4 (4q and 10q) and X chromosomal DXZ4 and CT47 were investigated.ResultsRepeat array size distribution analysis shows that all of these MSRs are highly polymorphic with the most genetic variation among Africans and the least among Asians. A mitotic mutation rate of 0.4-2.2% was observed, exceeding meiotic mutation rates and possibly explaining the large size variability found for these MSRs. By means of a novel Bayesian approach, statistical support for a distinct multimodal rather than a uniform allele size distribution was detected in seven out of eight MSRs, with evidence for equidistant intervals between the modes.ConclusionsThe multimodal distributions with evidence for equidistant intervals, in combination with the observation of MSR-specific constraints on minimum array size, suggest that MSRs are limited in their configurations and that deviations thereof may cause disease, as is the case for facioscapulohumeral muscular dystrophy. However, at present we cannot exclude that there are mechanistic constraints for MSRs that are not directly disease-related. This study represents the first comprehensive study of MSRs in different human populations by applying novel statistical methods and identifies commonalities and differences in their organization and function in the human genome.

A multi-covariate semi-parametric conditional volatility model using probabilistic fuzzy systems

Value at Risk (VaR) has been successfully estimated using single covariate probabilistic fuzzy systems (PFS), a method which combines a linguistic description of the system behaviour with statistical properties of data. In this paper, we consider VaR estimation based on a PFS model for density forecast of a continuous response variable conditional on a high-dimensional set of covariates. The PFS model parameters are estimated by a novel two-step process. The performance of the proposed model is compared to the performance of a GARCH model for VaR estimation of the S&P 500 index. Furthermore, the additional information and process understanding provided by the different interpretations of the PFS models are illustrated. Our findings show that the validity of GARCH models are sometimes rejected, while those of PFS models of VaR are never rejected. Additionally, the PFS model captures both instant and periods of high volatility, and leads to less conservative models.

Structural differences in economic growth: an endogenous clustering approach

This article addresses heterogeneity in determinants of economic growth in a data-driven way. Instead of defining groups of countries with different growth characteristics a priori, based on, for example, geographical location, we use a finite mixture panel model and endogenous clustering to examine cross-country differences and similarities in the effects of growth determinants. Applying this approach to an annual unbalanced panel of 59 countries in Asia, Latin and Middle America and Africa for the period 1971–2000, we can identify two groups of countries in terms of distinct growth structures. The structural differences between the country groups mainly stem from different effects of investment, openness measures and government share in the economy. Furthermore, the detected segmentation of countries does not match with conventional classifications in the literature.

Structural Differences in Economic Growth

This paper addresses heterogeneity in determinants of economic growth in a data-driven way. Instead of defining groups of countries with different growth characteristics a priori, based on, for example, geographical location, we use a finite mixture panel model and endogenous clustering to examine cross-country differences and similarities in the effects of growth determinants. Applying this approach to an annual unbalanced panel of 59 countries in Asia, Latin and Middle America and Africa for the period 1971-2000, we can identify two groups of countries in terms of distinct growth structures. The structural differences between the country groups mainly stem from different effects of investment, openness measures and government share in the economy. Furthermore, the detected segmentation of countries does not match with conventional classifications in the literature.

Probabilistic fuzzy systems for seasonality analysis and multiple horizon forecasts

Probabilistic fuzzy systems (PFS), a model which combines a linguistic description of the system behaviour with statistical properties of data, have been successfully applied to one day ahead Value at Risk (VaR) estimation for the stock market returns data. In this work, we propose a multi-covariate multi-output PFS model which provides the conditional density forecasts of returns for one day ahead and one month ahead periods. Such a multi-output PFS model was not considered in the literature. Furthermore, this model allows to analyze seasonal patterns in returns. The proposed model is applied to daily S&P500 stock returns. It is found that the proposed model indicates seasonal patterns in short and longer horizons as well as conservative VaR in long term forecasts. The model is shown to perform well in VaR estimation according to the unconditional coverage and independence tests.

Posterior-Predictive Evidence on US Inflation using Phillips Curve Models with Non-Filtered Time Series

Changing time series properties of US inflation and economic activity are analyzed within a class of extended Phillips Curve (PC) models. First, the misspecification effects of mechanical removal of low frequency movements of these series on posterior inference of a basic PC model are analyzed using a Bayesian simulation based approach. Next, structural time series models that describe changing patterns in low and high frequencies and backward as well as forward inflation expectation mechanisms are incorporated in the class of extended PC models. Empirical results indicate that the proposed models compare favorably with existing Bayesian Vector Autoregressive and Stochastic Volatility models in terms of fit and predictive performance. Weak identification and dynamic persistence appear less important when time varying dynamics of high and low frequencies are carefully modeled. Modeling inflation expectations using survey data and adding level shifts and stochastic volatility improves substantially in sample fit and out of sample predictions. No evidence is found of a long run stable cointegration relation between US inflation and marginal costs. Tails of the complete predictive distributions indicate an increase in the probability of disinflation in recent years.

Conditional density estimation using fuzzy GARCH models

Time series data exhibits complex behavior including non-linearity and path-dependency. This paper proposes a flexible fuzzy GARCH model that can capture different properties of data, such as skewness, fat tails and multimodality in one single model. Furthermore, additional information and simple understanding of the underlying process can be provided by the linguistic interpretation of the proposed model. The model performance is illustrated using two simulated data examples.

The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation

This paper presents the R package MitISEM, which provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. The package provides also an extended MitISEM algorithm, ‘sequential MitISEM’, which substantially decreases the computational time when the target density has to be approximated for increasing data samples. This occurs when the posterior distribution is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that the candidate distribution obtained by MitISEM outperforms those obtained by ‘naive’ approximations in terms of numerical efficiency. Further, the MitISEM approach can be used for Bayesian model comparison, using the predictive likelihoods.

Time varying correlation estimation using probabilistic fuzzy systems

Accurate financial risk analysis has drawn considerable attention after the recent financial crisis. Several regulatory agencies recently documented the need for proper assessment and reporting of financial risk for banks and other financial institutions. It is stressed that risk analysis should take into account changing risk properties over time. For a set of financial assets, risk analysis relies on the correlation and covariance structure among these returns from these assets. Therefore analyzing changes in the correlations and covariances of assets is essential to document changing risk properties. In this paper we show that a PFS can be used to model unobserved time-varying correlation between financial returns. The method is applied to simulated data and real data of daily NASDAQ and HSI stock returns. We show that the PFS application improves over the conventional moving window approximation of time-varying correlation by decreasing the sensitivity of the results to the selection of the window length.