Variational Bayes approximation of factor stochastic volatility models

In this paper, efficient importance sampling (EIS) is used to perform a classical and Bayesian analysis of univariate and multivariate stochastic volatility (SV) models for financial return series. EIS provides a highly generic and very accurate procedure for the Monte Carlo (MC) evaluation of high-dimensional interdependent integrals. It can be used to carry out ML-estimation of SV models as well as simulation smoothing where the latent volatilities are sampled at once. Based on this EIS simulation smoother, a Bayesian Markov chain Monte Carlo (MCMC) posterior analysis of the parameters of SV models can be performed.

Approximate Bayesian computation (ABC) techniques permit inferences in complex demographic models, but are computationally inefficient. A Markov chain Monte Carlo (MCMC) approach has been proposed (Marjoram et al. 2003), but it suffers from computational problems and poor mixing. We propose several methodological developments to overcome the shortcomings of this MCMC approach and hence realize substantial computational advances over standard ABC. The principal idea is to relax the tolerance within MCMC to permit good mixing, but retain a good approximation to the posterior by a combination of subsampling the output and regression adjustment. We also propose to use a partial least-squares (PLS) transformation to choose informative statistics. The accuracy of our approach is examined in the case of the divergence of two populations with and without migration. In that case, our ABC-MCMC approach needs considerably lower computation time to reach the same accuracy than conventional ABC. We then apply our method to a more complex case with the estimation of divergence times and migration rates between three African populations.

Vector autoregressive (VAR) models are used to capture the dynamic relationships among multivariate time series. On the other hand, multivariate stochastic volatility (MSV) models allow modeling the variance as it changes over time. Student’s t-distribution is used to model extreme values in time series. Therefore, this article proposes the integration of a VAR model, an MSV model, and a Student’s t-distribution (VAR-MSV-t). The selection of the most appropriate VAR-MSV-t order is carried out using the Deviance Information Criterion (DIC). Formulas are presented to estimate the Mardia skewness and the Koziol kurtosis of the model. The model is applied to three key macroeconomic variables for the United States. The S&P 500 stock market index is added, and the results are interpreted. Parameter estimation is carried out using Markov chain Monte Carlo (MCMC) methods. The results indicate that the model effectively captures the dynamic relationships, time-varying variance, and extreme magnitude values.

Sampling technique is one of the asymptotically unbiased estimation approaches for inference in Bayesian probabilistic models. Markov chain Monte Carlo (MCMC) is a kind of sampling methods, which is widely used in the inference of complex probabilistic models. However, current MCMC methods can incur high autocorrelation of samples, which means that the samples generated by MCMC samplers are far from independent. In this paper, we propose the neural networks Langevin Monte Carlo (NNLMC) which makes full use of the flexibility of neural networks and the high efficiency of the Langevin dynamics sampling to construct a new MCMC sampling method. We propose the new update function to generate samples and employ appropriate loss functions to improve the performance of NNLMC during the process of sampling. We evaluate our method on a large diversity of challenging distributions and real datasets. Our results show that NNLMC is able to sample from the target distribution with low autocorrelation and rapid convergence, and outperforms the state-of-the-art MCMC samplers.

In order to gain an understanding of the effectiveness of phylogenetic Markov chain Monte Carlo (MCMC), it is important to understand how quickly the empirical distribution of the MCMC converges to the posterior distribution. In this article, we investigate this problem on phylogenetic tree topologies with a metric that is especially well suited to the task: the subtree prune-and-regraft (SPR) metric. This metric directly corresponds to the minimum number of MCMC rearrangements required to move between trees in common phylogenetic MCMC implementations. We develop a novel graph-based approach to analyze tree posteriors and find that the SPR metric is much more informative than simpler metrics that are unrelated to MCMC moves. In doing so, we show conclusively that topological peaks do occur in Bayesian phylogenetic posteriors from real data sets as sampled with standard MCMC approaches, investigate the efficiency of Metropolis-coupled MCMC (MCMCMC) in traversing the valleys between peaks, and show that conditional clade distribution (CCD) can have systematic problems when there are multiple peaks.

We present a new technique for statistical static timing analysis (SSTA) based on Markov chain Monte Carlo (MCMC), that allows fast and accurate estimation of the right-hand tail of the delay distribution. A ¿naive¿ MCMC approach is inadequate for SSTA. Several modifications and enhancements, presented in this paper, enable application of MCMC to SSTA. Moreover, such an approach overcomes inherent limitations of techniques such as importance sampling and Quasi-Monte Carlo. Our results on open source designs, with an independent delay variation model, demonstrate that our technique can obtain more than an order of magnitude improvement in computation time over simple Monte Carlo, given an estimation accuracy target at a point in the tail. Our approach works by providing a large number of samples in the region of interest. Open problems include extension of algorithm applicability to a broader class of synthesis conditions, and handling of correlated delay variations. In a broader context, this work aims to show that MCMC and associated techniques can be useful in rare event analyses related to circuits, particularly for high-dimensional problems.

This study primarily aimed to apply a novel, advanced stochastic volatility model incorporating leverage and an asymmetrically heavy-tailed distribution (ASV-GHskw) to 18 financial asset returns, including 10 Asia-Pacific and six European stock market returns and two crude oil market returns. The study employed a generalized hyperbolic skew student's t-distribution using the Bayesian approach. The study's secondary aim was to concentrate on one-day-ahead downside market risk measurement of the related financial asset returns under Basel Ⅳ regulations based on the ASV-GHskw model. For comparison, an asymmetric stochastic volatility model with a symmetric student's t-distribution (ASV-st) was also considered. The findings indicated that the proposed Bayesian Markov chain Monte Carlo (MCMC) approach was sufficiently efficient, especially when estimating the ASV-GHskw model parameters. Further, the ASV-GHskw model provided a better fit for all financial asset returns examined than its competing ASV-st model. Moreover, the results revealed that the financial institutions taking positions in the examined financial markets will be required to hold additional regulatory capital for market risk exposures under the latest Basel capital regulations. Lastly, the findings give valuable information for risk-averse investors interested in the examined financial markets, as they expect to receive higher-than-average returns by holding less-risky assets.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods

Identification of contaminant sources in rivers is crucial for river protection and emergency response. This study presents an innovative approach for identifying river pollution sources by using Bayesian inference and cellular automata (CA) modeling. A general Bayesian framework is proposed that combines the CA model with observed data to identify unknown sources of river pollution. To reduce the computational burden of the Bayesian inference, a CA contaminant transport model is developed to efficiently simulate pollutant concentration values in the river. These simulated concentration values are then used to calculate the likelihood function of available measurements. The Markov chain Monte Carlo (MCMC) method is used to produce the posterior distribution of contaminant source parameters, which is a sampling-based method that enables the estimation of complex posterior distributions. The suggested methodology is applied to a real case study of the Fen River in Yuncheng City, Shanxi Province, Northern China, and it estimates the release time, release mass, and source location with relative errors below 19%. The research indicates that the proposed methodology is an effective and flexible way to identify the location and concentrations of river contaminant sources.

The recent proliferation of Markov Chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields, including reliability engineering. With the current (and future) proliferation of new products, old problems continue to hamper us, while new challenges keep appearing. In Bayesian reliability, these include but are not limited to: (1) achieving and making use of prior information; (2) applying small data sets or system operating/environmental (SOE) data with big and complex data; and (3) making posterior inferences from high-dimensional numerical integration. To deal with old problems while meeting new challenges, this paper proposes an improved procedure for Bayesian reliability inference with MCMC, discussing modern reliability data and noting some applications where the Bayesian reliability approach with MCMC can be used. It also explores opportunities to use Bayesian reliability models to create stronger statistical methods from prior to posterior. Finally, it outlines some practical concerns and remaining challenges for future research.

This paper deals with the pricing of derivatives written on several underlying assets or factors satisfying a multivariate model with Wishart stochastic volatility matrix. This multivariate stochastic volatility model leads to a closed-form solution for the conditional Laplace transform, and quasi-explicit solutions for derivative prices written on more than one asset or underlying factor. Two examples are presented: (i) a multiasset extension of the stochastic volatility model introduced by Heston (1993), and (ii) a model for credit risk analysis that extends the model of Merton (1974) to a framework with stochastic firm liability, stochastic volatility, and several firms. A bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional Laplace transform of the stock returns.

In genetic counseling for cancer risk, the probability of carrying a mutation of a cancer-causing gene plays an important role. Family history of various cancers is important in calculating this probability. BRCAPRO is a widely used software for calculating the probability of carrying mutations in BRCA1 and BRCA2 genes given the family history of breast and ovarian cancer in first- and second-degree relatives. BRCAPRO uses an analytical (exact) calculational procedure. Using Markov chain Monte Carlo (MCMC) methods, we extend BRCAPRO to handle, in principle, any type of cancer, family history, any number of genes and alleles that each gene may have. When the information used in this MCMC approach is the same as for BRCAPRO (two genes: BRCA1 and BRCA2; two cancers: breast and ovarian; first- and second-degree relatives only), the two approaches give essentially the same answer. Extending the model to include (1) prostate cancer, (2) two mutated alleles of BRCA2, namely, mutations in Ovarian Cancer Cluster Region (OCCR) and non-OCCR region, and (3) relatives of degree greater than second-degree, leads to different carrier probabilities. The MCMC approach is a useful tool in building a comprehensive model to give accurate estimates of carrier probabilities. Such an approach will be even more important as additional information about the genetics of various cancers becomes available.

Density-estimation likelihood-free inference (DELFI) has recently been\nproposed as an efficient method for simulation-based cosmological parameter\ninference. Compared to the standard likelihood-based Markov Chain Monte Carlo\n(MCMC) approach, DELFI has several advantages: it is highly parallelizable,\nthere is no need to assume a possibly incorrect functional form for the\nlikelihood and complicated effects (e.g the mask and detector systematics) are\neasier to handle with forward models. In light of this, we present two DELFI\npipelines to perform weak lensing parameter inference with lognormal\nrealizations of the tomographic shear field -- using the C_l summary statistic.\nThe first pipeline accounts for the non-Gaussianities of the shear field,\nintrinsic alignments and photometric-redshift error. We validate that it is\naccurate enough for Stage III experiments and estimate that O(1000) simulations\nare needed to perform inference on Stage IV data. By comparing the second DELFI\npipeline, which makes no assumption about the functional form of the\nlikelihood, with the standard MCMC approach, which assumes a Gaussian\nlikelihood, we test the impact of the Gaussian likelihood approximation in the\nMCMC analysis. We find it has a negligible impact on Stage IV parameter\nconstraints. Our pipeline is a step towards seamlessly propagating all\ndata-processing, instrumental, theoretical and astrophysical systematics\nthrough to the final parameter constraints.\n

We propose a new method in which a generative network (GN) set within a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. We train the GN using only unconditional simulations of the discretized PDE model. A GN is used here to exploit the ability of these methods to generate realistic outputs from complex probability distributions, such as the ones that represent the possible states and parameters of a physical problem. We compare the proposed method with the gold standard Markov chain Monte Carlo (MCMC). Additionally, we suggest the use of a novel type of time-stepping regularization to improve the representativeness of the physical solution, and we present a new way of evaluating the GN training, taking advantage of the real/generated sample structure. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the gold standard. This is achieved using only a limited number of unconditional simulations from the full-order numerical PDE model (40 simulations). The GN-based ROM operates 60 times faster than the gold standard (MCMC), while producing uncertainties that closely match those generated by the MCMC approach. The proposed method is a general framework for quantifying uncertainties in numerical physical simulations and is not restricted to the specific physics of this application.

This chapter describes how Markov chain Monte Carlo methods can be used to analyze data from outbreaks of infectious disease. Specifically, methods are described for Bayesian estimation of the parameters of stochastic disease transmission models. The methods are highly flexible in nature, being applicable to a wide range of models and types of data. The methods also can cater for missing data, particularly in the sense that the actual process of infection need not be observed, as is typical in practice. As well as providing details of the Markov chain Monte Carlo methods, practical guidelines are given in the chapter. The methods are illustrated in detail for a simple example featuring a simple susceptible-infective-removed model, and also a more complex example of a real-life data set on a measles outbreak.