An Overview of MCMC Methods: From Theory to Applications

Karras, Christos; Karras, Aristeidis; Avlonitis, Markos; Sioutas, Spyros

doi:10.1007/978-3-031-08341-9_26

Cited by 18 publications

(9 citation statements)

References 17 publications

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“…(1995) . MCMC methods generate random samples from a target distribution by simulating a Markov chain, a sequence of random variables where each variable depends solely on its immediate predecessor Karras et al. (2022) .…”

Section: Methodsmentioning

confidence: 99%

“…We also utilized Markov Chain Monte Carlo (MCMC) techniques, a class of algorithms designed to approximate complex probability distributions often encountered in Bayesian analysis Besag et al (1995). MCMC methods generate random samples from a target distribution by simulating a Markov chain, a sequence of random variables where each variable depends solely on its immediate predecessor Karras et al (2022). Over time, the chain converges to the desired distribution, enabling the estimation of various quantities of interest Robert (1995).…”

Section: Theoretical Framework 231 Bayesian Analysis and Markov Chain...mentioning

confidence: 99%

See 1 more Smart Citation

Assessing green manure impact on wheat productivity through Bayesian analysis of yield monitor data

Gamulin,

Zorić,

Karagić

et al. 2024

Front. Plant Sci.

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Agronomy research traditionally relies on small, controlled trial plots, which may not accurately represent the complexities and variabilities found in larger, real-world settings. To address this gap, we introduce a Bayesian methodology for the analysis of yield monitor data, systematically collected across extensive agricultural landscapes during the 2020/21 and 2021/22 growing seasons. Utilizing advanced yield monitoring equipment, our method provides a detailed examination of the effects of green manure on wheat yields in a real-world context. The results from this comprehensive analysis reveal significant insights into the impact of green manure application on wheat production, demonstrating enhanced yield outcomes across varied landscapes. This evidence suggests that the Bayesian approach to analyzing yield monitor data can offer more precise and contextually relevant information than traditional experimental designs. This research underscores the value of integrating large-scale data analysis techniques in agronomy, moving beyond small-scale trials to offer a broader, more accurate perspective on agricultural practices. The adoption of such methodologies promises to refine farming strategies and policies, ultimately leading to more effective and sustainable agricultural outcomes. The inclusion of a Python script in the appendix illustrates our analytical process, providing a tangible resource for replicating and extending this research within the agronomic community.

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Section: Methodsmentioning

confidence: 99%

Section: Theoretical Framework 231 Bayesian Analysis and Markov Chain...mentioning

confidence: 99%

Assessing green manure impact on wheat productivity through Bayesian analysis of yield monitor data

Gamulin,

Zorić,

Karagić

et al. 2024

Front. Plant Sci.

View full text Add to dashboard Cite

show abstract

“…This study uses a symmetrical Gaussian proposal distribution to simplify computing the acceptance ratio (Jones and Qin, 2022;Karras et al, 2022;South et al, 2022;Agrawal et al, 2023). We implemented the entire BLR process using the PyMC3 library within the Python computing environment (Salvatier et al, 2016).…”

Section: Methodsmentioning

confidence: 99%

imc-precip-iso: Open monthly stable isotope data of precipitation over the Indonesian Maritime Continent

Suwarman,

Herho,

Belgaman

et al. 2023

Preprint

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Stable isotopes, $\delta^2$H, $\delta^{18}$O, and d-excess, are valuable tools as natural tracers of diffusion processes and phase changes in the global hydroclimatological cycle. The Indonesian Maritime Continent (IMC) is an archipelago area surrounded by very warm waters which induce convective activities as the primary heat source driving global atmospheric circulation. Given the central role of IMC in this hydroclimatological cycle, comprehensive study and data collection on the stable isotopes of precipitation in this region is crucial.In this study, we collected monthly stable isotope data from 62 stations spread throughout the Indonesian archipelago from September 2010 to September 2017. We cleaned the data and conducted quality control activities by comparing the Local Meteoric Water Line (LMWL) to previous studies in a similar climatic region. We shared these data openly on our GitHub repository, making them easier to update and interact with users in the future.

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“…But, with a large number of parameters, it's posterior probability of Bayesian networks is intractable. Therefore, several Bayesian approximation methods have been proposed, such as Markov Chain Monte Carlo (MCMC) (Karras et al 2022) and Stochastic Gradient MCMC (SG-MCMC) (Welling and Teh 2011). But those methods heavily rely on sampling from the posterior distribution, which leads to increased computational costs.…”

Section: Related Wokmentioning

confidence: 99%

The Evidence Contraction Issue in Deep Evidential Regression: Discussion and Solution

Wu,

Shi,

Dong

et al. 2024

AAAI

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Deep Evidential Regression (DER) places a prior on the original Gaussian likelihood and treats learning as an evidence acquisition process to quantify uncertainty. For the validity of the evidence theory, DER requires specialized activation functions to ensure that the prior parameters remain non-negative. However, such constraints will trigger evidence contraction, causing sub-optimal performance. In this paper, we analyse DER theoretically, revealing the intrinsic limitations for sub-optimal performance: the non-negativity constraints on the Normal Inverse-Gamma (NIG) prior parameter trigger the evidence contraction under the specialized activation function, which hinders the optimization of DER performance. On this basis, we design a Non-saturating Uncertainty Regularization term, which effectively ensures that the performance is further optimized in the right direction. Experiments on real-world datasets show that our proposed approach improves the performance of DER while maintaining the ability to quantify uncertainty.

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An Overview of MCMC Methods: From Theory to Applications

Cited by 18 publications

References 17 publications

Assessing green manure impact on wheat productivity through Bayesian analysis of yield monitor data

Assessing green manure impact on wheat productivity through Bayesian analysis of yield monitor data

imc-precip-iso: Open monthly stable isotope data of precipitation over the Indonesian Maritime Continent

The Evidence Contraction Issue in Deep Evidential Regression: Discussion and Solution

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