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

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 341
Author(s):  
Samuel Livingstone
Keyword(s):  
Growth Rate ◽  
Random Walk ◽  
Rejection Rate ◽  
Geometric Ergodicity ◽  
Target Distribution ◽  
Current State ◽  
Random Walk Metropolis ◽  
Judicious Choice

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.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (1) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝd. This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (01) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝ d . This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

scholarly journals Ergodicity of Markov chain Monte Carlo with reversible proposal

2017 ◽  
Vol 54 (2) ◽  
pp. 638-654 ◽  
Author(s):  
K. Kamatani
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Random Walk ◽  
Markov Chain Monte Carlo ◽  
Geometric Ergodicity ◽  
Suitable Transformation ◽  
Ergodic Properties ◽  
Random Walk Metropolis ◽  
Heavy Tailed ◽  
Random Walk Metropolis Algorithm

Abstract We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.

scholarly journals Diffusion limits of the random walk Metropolis algorithm in high dimensions

2012 ◽  
Vol 22 (3) ◽  
pp. 881-930 ◽  
Author(s):  
Jonathan C. Mattingly ◽  
Natesh S. Pillai ◽  
Andrew M. Stuart
Keyword(s):  
Random Walk ◽  
Metropolis Algorithm ◽  
High Dimensions ◽  
Random Walk Metropolis ◽  
Diffusion Limits ◽  
Random Walk Metropolis Algorithm

scholarly journals Asymptotic analysis of the random walk Metropolis algorithm on ridged densities

2018 ◽  
Vol 28 (5) ◽  
pp. 2966-3001 ◽  
Author(s):  
Alexandros Beskos ◽  
Gareth Roberts ◽  
Alexandre Thiery ◽  
Natesh Pillai
Keyword(s):  
Random Walk ◽  
Asymptotic Analysis ◽  
Metropolis Algorithm ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

scholarly journals Optimal Scaling of Random Walk Metropolis Algorithms with Non-Gaussian Proposals

2010 ◽  
Vol 13 (3) ◽  
pp. 583-601 ◽  
Author(s):  
Peter Neal ◽  
Gareth Roberts
Keyword(s):  
Random Walk ◽  
Optimal Scaling ◽  
Random Walk Metropolis ◽  
Non Gaussian

scholarly journals Optimal Strategies for Prudent Investors

1998 ◽  
Vol 01 (04) ◽  
pp. 473-486 ◽  
Author(s):  
Roberto Baviera ◽  
Michele Pasquini ◽  
Maurizio Serva ◽  
Angelo Vulpiani
Keyword(s):  
Growth Rate ◽  
Random Walk ◽  
Exponential Growth ◽  
Optimal Strategies ◽  
Maximum Amount ◽  
Exponential Growth Rate ◽  
One Dimensional ◽  
Economic Level ◽  
Random Walk With Drift ◽  
Analytical Expressions

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

scholarly journals The Evolution of Economic Activity in the Rural Area of Region 2 South - East

2021 ◽  
Vol 95 ◽  
pp. 01007
Author(s):  
Daniela – Lavinia Balasan ◽  
Dragoş Horia Buhociu
Keyword(s):  
Economic Growth ◽  
Growth Rate ◽  
Economic Development ◽  
Economic Activity ◽  
Labour Force ◽  
Standard Of Living ◽  
Economic Growth Rate ◽  
Current State ◽  
Per Capita ◽  
The Impact

When we talk about economic development, we can refer to improve the standard of living and the prosperity of the population. This is due by increasing per capita income. In order to analyze economic activity, severe indicators must be studied, namely productivity, economic growth rate, labour force share, gross domestic product. In order to carry out as accurate an analysis as possible, it is required to discover the bottlenecks and problems that Region 2 South East makes and to develop a set of reservations and indications leading to the reduction and, why not, the removal of negative aspects. The main purpose of this work is to achieve a strategic plan by studying the current state and the impact of the economic system in recent times in all its forms, with a view to the development of the countryside of Region 2 South – East. I set out to create a website based on the advice of small rural entrepreneurs that evolves gathering information in realistically identifying all the strengths and concentrating them in the region’s potential innovation.

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