# Bayesian Characterizations of Properties of Stochastic Processes with Applications

@article{Roy2020BayesianCO, title={Bayesian Characterizations of Properties of Stochastic Processes with Applications}, author={Sucharita Roy and Sourabh Bhattacharya}, journal={arXiv: Statistics Theory}, year={2020} }

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric and nonparametric stochastic processes. Interestingly, our theory builds on our previous work on Bayesian characterization of infinite series, which was applied to verification of the (in)famous Riemann Hypothesis. Thus, there seems to be interesting and…

## Figures from this paper

figure 10.1 figure 10.2 figure 10.3 figure 11.1 figure 11.2 figure 11.3 figure 11.4 figure 11.5 figure 11.6 figure 12.1 figure 12.2 figure 12.3 figure 13.1 figure 13.2 figure 13.3 figure 13.4 figure 13.5 figure 13.6 figure 14.1 figure 14.10 figure 14.11 figure 14.12 figure 14.2 figure 14.3 figure 14.4 figure 14.5 figure 14.6 figure 14.7 figure 14.8 figure 14.9 figure 15.1 figure 15.2 figure 15.3 figure 15.4 figure 15.5 figure 15.6 figure 15.7 figure 16.1 figure 16.10 figure 16.11 figure 16.12 figure 16.13 figure 16.14 figure 16.15 figure 16.16 figure 16.17 figure 16.18 figure 16.19 figure 16.2 figure 16.20 figure 16.21 figure 16.22 figure 16.23 figure 16.24 figure 16.25 figure 16.26 figure 16.27 figure 16.28 figure 16.29 figure 16.3 figure 16.30 figure 16.31 figure 16.32 figure 16.33 figure 16.34 figure 16.35 figure 16.36 figure 16.37 figure 16.38 figure 16.39 figure 16.4 figure 16.40 figure 16.41 figure 16.42 figure 16.43 figure 16.44 figure 16.45 figure 16.46 figure 16.47 figure 16.48 figure 16.49 figure 16.5 figure 16.50 figure 16.51 figure 16.52 figure 16.6 figure 16.7 figure 16.8 figure 16.9 figure 17.1 figure 17.10 figure 17.11 figure 17.12 figure 17.13 figure 17.14 figure 17.15 figure 17.16 figure 17.17 figure 17.18 figure 17.19 figure 17.2 figure 17.20 figure 17.21 figure 17.3 figure 17.4 figure 17.5 figure 17.6 figure 17.7 figure 17.8 figure 17.9

## 2 Citations

Bayesian Appraisal of Random Series Convergence with Application to Climate Change

- Mathematics
- 2020

Roy and Bhattacharya (2020) provided Bayesian characterization of infinite series, and their most important application, namely, to the Dirichlet series characterizing the (in)famous Riemann…

Bayesian Levy-Dynamic Spatio-Temporal Process: Towards Big Data Analysis

- Computer Science
- 2021

A new nonparametric, nonstationary and nonseparable dynamic spatio-temporal process is constructed with the additional realistic property that the lagged spatio -temporal correlations converge to zero as the lag tends to infinity.

## References

SHOWING 1-10 OF 74 REFERENCES

Nonstationary, Nonparametric, Nonseparable Bayesian Spatio-Temporal Modeling using Kernel Convolution of Order Based Dependent Dirichlet Process

- Mathematics
- 2014

In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as…

Convergence Control Methods for Markov Chain Monte Carlo Algorithms

- Mathematics
- 1995

Markov chain Monte Carlo methods have been increasingly popular since their introduction by Gelfand and Smith. However, while the breadth and variety of Markov chain Monte Carlo applications are…

Bayes meet Riemann- Bayesian Characterization of Infinite Series with Application to Riemann Hypothesis

- Mathematics
- 2016

In the classical literature on infinite series there are various tests to determine if a given infinite series converges, diverges, or oscillates. But unfortunately, for very many infinite series all…

A nonparametric test for stationarity based on local Fourier analysis

- Mathematics, Computer Science2009 IEEE International Conference on Acoustics, Speech and Signal Processing
- 2009

A test statistic is employed that measures the variation of time-localized estimates of the power spectral density of an observed random process under the null hypothesis of stationarity and is used to directly set test thresholds corresponding to constant false alarm rates.

A nonparametric test for stationarity in functional time series

- Mathematics
- 2021

We propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the $L^2$-distance between the spectral density operator of a non-stationary…

Inference from Iterative Simulation Using Multiple Sequences

- Computer Science
- 1992

The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.

A brief review of optimal scaling of the main MCMC approaches and optimal scaling of additive TMCMC under non-regular cases

- Computer ScienceBrazilian Journal of Probability and Statistics
- 2019

This paper discusses diffusion-based optimal scaling behavior for non-Gaussian proposal densities - in particular, uniform, Student's t and Cauchy proposals and compares the diffusion based TMCMC approach with that of ESJD based RWM approach for the very challenging CAUchy proposal case, showing that the former approach clearly outperforms the latter.

Testing the covariance structure of multivariate random fields

- Mathematics
- 2008

There is an increasing wealth of multivariate spatial and multivariate spatio-temporal data appearing. For such data, an important part of model building is an assessment of the properties of the…