A Metropolis-class sampler for targets with non-convex support

We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support $$A\subset {\mathbb {R}}^d$$ A ⊂ R d , by reusing proposals in $$A^c$$ A c which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.

Generalized parallel tempering on Bayesian inverse problems

In the current work we present two generalizations of the Parallel Tempering algorithm in the context of discrete-time Markov chain Monte Carlo methods for Bayesian inverse problems. These generalizations use state-dependent swapping rates, inspired by the so-called continuous time Infinite Swapping algorithm presented in Plattner et al. (J Chem Phys 135(13):134111, 2011). We analyze the reversibility and ergodicity properties of our generalized PT algorithms. Numerical results on sampling from different target distributions, show that the proposed methods significantly improve sampling efficiency over more traditional sampling algorithms such as Random Walk Metropolis, preconditioned Crank–Nicolson, and (standard) Parallel Tempering.

GARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices

This study evaluates the empirical performance of four power transformation families: extended Tukey, Modulus, Exponential, and Yeo--Johnson, in modeling the return in the context of GARCH(1,1) models with two error distributions: Gaussian (normal) and Student-t. We employ an Adaptive Random Walk Metropolis method in Markov Chain Monte Carlo scheme to draw parameters. Using 19 international stock indices from the Oxford-Man Institute and basing on the log likelihood, Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion, the use of power transformation families to the return series clearly improves the fit of the normal GARCH(1,1) model. In particular, the Modulus transformation family provides the best fit. Under Student's t-error distribution assumption, the GARCH(1,1) models under power transformed returns perform better in few cases.

BAYESIAN ESTIMATION AND AN APPLICATION OF GIBBS SAMPLING TECHNIQUE AND RANDOM WALK METROPOLIS - HASTING ALGORITHM IN TWO PHASE LINEAR REGRESSION MODEL

Here, in this research paper, we have applied the Gibbs Sampling Technique and RWM-H (Random Walk Metropolis - Hasting) Algorithm for the Bayesian Estimation of m, β1, β2 and 1/2. Also we have assumed that at some point of time say 'm', the co-efficient of regression changes from β1 to β2. Further, we have discussed about the effects of prior information on the Bayes estimates on the basis of the TPLR (Two Phase Linear Regression) Model with a Bayesian approach.

Geometric Ergodicity of the Random Walk Metropolis with Position-Dependent Proposal Covariance

We consider a Metropolis–Hastings method with proposal N(x,hG(x)−1), where x is the current state, and study its ergodicity properties. We show that suitable choices of G(x) can change these ergodicity properties compared to the Random Walk Metropolis case N(x,hΣ), either for better or worse. We find that if the proposal variance is allowed to grow unboundedly in the tails of the distribution then geometric ergodicity can be established when the target distribution for the algorithm has tails that are heavier than exponential, in contrast to the Random Walk Metropolis case, but that the growth rate must be carefully controlled to prevent the rejection rate approaching unity. We also illustrate that a judicious choice of G(x) can result in a geometrically ergodic chain when probability concentrates on an ever narrower ridge in the tails, something that is again not true for the Random Walk Metropolis.

Volatilitas Kurs dan Saham Mengikuti Model EGARCH(1,1) Berdistribusi Versi Skew Normal dan Student-t

Studi ini membandingkan kinerja pencocokan model volatilitas GARCH(1,1) dan EGARCH(1,1) pada return kurs dan saham. Model mengasumsikan empat distribusi berbeda untuk error dari return: Normal, Skew-Normal (SN), Alpha-Skew Normal (ASN), dan Student-t. Data aset keuangan yang digunakan sebagai analisis perbandingan yaitu data kurs beli US Dollar (USD) dalam periode harian dari Januari 2010 sampai Desember 2017 dan data indeks saham FTSE100 dalam periode harian dari Januari 2000 sampai Desember 2013. Studi ini membandingkan metode Generalized Reduced Gradient (GRG) Non-Linier di Solver Excel dan metode Adaptive Random Walk Metropolis (ARWM) untuk mengestimasi model. Hasil menunjukkan bahwa metode GRG Non Linear Solver Excel memberikan estimasi yang serupa dengan metode ARWM dan tidak melanggar kendala model. Lebih lanjut, berdasarkan nilai Akaike Information Criterion (AIC), kedua data pengamatan menyediakan bukti bahwa model dengan distribusi Student-t adalah yang terbaik, diikuti oleh distribusi SN yang lebih baik daripada model dengan distribusi ASN dan Normal. Nilai AIC telah menyarankan model EGARCH(1,1) berdistribusi Student-t sebagai model pencocokan terbaik untuk kedua data pengamatan.

Bayesian estimation of generalized partition of unity copulas

This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.

A neural network assisted Metropolis adjusted Langevin algorithm

In this paper, we derive a Markov chain Monte Carlo (MCMC) algorithm supported by a neural network. In particular, we use the neural network to substitute derivative calculations made during a Metropolis adjusted Langevin algorithm (MALA) step with inexpensive neural network evaluations. Using a complex, high-dimensional blood coagulation model and a set of measurements, we define a likelihood function on which we evaluate the new MCMC algorithm. The blood coagulation model is a dynamic model, where derivative calculations are expensive and hence limit the efficiency of derivative-based MCMC algorithms. The MALA adaptation greatly reduces the time per iteration, while only slightly affecting the sample quality. We also test the new algorithm on a 2-dimensional example with a non-convex shape, a case where the MALA algorithm has a clear advantage over other state of the art MCMC algorithms. To assess the impact of the new algorithm, we compare the results to previously generated results of the MALA and the random walk Metropolis Hastings (RWMH).