Abstract Decision trees (DT) are highly famous in machine learning and usually acquire state-of-the-art performance. Despite that, well-known variants like CART, ID3, random forest, boosted miss a probabilistic version that encodes prior assumptions about tree structures shares statistical strength between node parameters. Existing work on Bayesian DT depends Markov Chain Monte Carlo (MCMC), wh...

In this paper we propose a Bayesian method for estimating hyperbolic diffusion models. The approach is based on the Markov Chain Monte Carlo (MCMC) method after discretization via the Milstein scheme. Our simulation study shows that the hyperbolic diffusion exhibits many of the stylized facts about asset returns documented in the financial econometrics literature, such as a slowly declining aut...

We have developed a Bayesian model to invert spectral induced-polarization SIP data for Cole-Cole parameters using Markov-chain Monte Carlo MCMC sampling methods. We compared the performance of the MCMC-based stochastic method with an iterative Gauss-Newton-based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton-base...

The goal of this Random Walks project is to code and experiment the Markov Chain Monte Carlo (MCMC) method for the problem of graph coloring. In this report, we present the plots of cost function H by varying the parameters like q (Number of colors that can be used in coloring) and c (Average node degree). The results are obtained by using simulated annealing scheme, where the temperature (inve...

One of the main shortcomings of Markov chain Monte Carlo samplers is their inability to mix between modes of the target distribution. In this paper we show that advance knowledge of the location of these modes can be incorporated into the MCMC sampler by introducing mode-hopping moves that satisfy detailed balance. The proposed sampling algorithm explores local mode structure through local MCMC...

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SGMCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SGMCMC in this setting: The latent discrete states, and needing to break dependencies when co...

Recently, Markov chain Monte Carlo (MCMC) methods have been applied to the design of blind Bayesian receivers in a number of digital communications applications. The salient features of these MCMC receivers include the following: a) They are optimal in the sense of achieving minimum symbol error rate; b) they do not require the knowledge of the channel states, nor do they explicitly estimate th...

Bayesian approaches to statistical inference and system identification became practical with the development of effective sampling methods like Markov Chain Monte Carlo (MCMC). However, because the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. Dynamical systems based samplers are an effective extension of traditional MCMC methods. Thes...

In the thesis, we study ergodicity of adaptive Markov Chain Monte Carlo methods (MCMC) based on two conditions (Diminishing Adaptation and Containment which together imply ergodicity), explain the advantages of adaptive MCMC, and apply the theoretical result for some applications. First we show several facts: 1. Diminishing Adaptation alone may not guarantee ergodicity; 2. Containment is not ne...