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The Barker proposal: Combining robustness and efficiency in gradient-based MCMC.

ABSTRACT: There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be more sensitive to the choice of step-size parameter and less robust to heterogeneity of the distribution of interest. We characterise this phenomenon by studying the behaviour of spectral gaps as an increasingly poor step-size is chosen for the algorithm. Motivated by these considerations, we propose a novel and simple gradient-based MCMC algorithm, inspired by the classical Barker accept-reject rule, with improved robustness properties. Extensive theoretical results, dealing with robustness to tuning, geometric ergodicity and scaling with dimension, suggest that the novel scheme combines the robustness of simple schemes with the efficiency of gradient-based ones. We show numerically that this type of robustness is particularly beneficial in the context of adaptive MCMC, giving examples where our proposed scheme significantly outperforms state-of-the-art alternatives.

SUBMITTER: Livingstone S

PROVIDER: S-EPMC9303935 | biostudies-literature | 2022 Apr

REPOSITORIES: biostudies-literature

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The Barker proposal: Combining robustness and efficiency in gradient-based MCMC.

Livingstone Samuel S Zanella Giacomo G

Journal of the Royal Statistical Society. Series B, Statistical methodology 20220111 2

There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be more sensitive to the choice of step-size parameter and less robust to heterogeneity of the distribution of interest. We characterise this phenomenon by studying the behaviour of spectral gaps as an increasingly poor step-size is chosen for the algorithm. Motiva ...[more]

PMID: 35910401

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Project description:BackgroundThe clonogenic assay is a versatile and frequently used tool to quantify reproductive cell survival in vitro. Current state-of-the-art analysis relies on plating efficiency-based calculations which assume a linear correlation between the number of cells seeded and the number of colonies counted. The present study was designed to test the validity of this assumption and to evaluate the robustness of clonogenic survival results obtained.MethodsA panel of 50 established cancer cell lines was used for comprehensive evaluation of the clonogenic assay procedure and data analysis. We assessed the performance of plating efficiency-based calculations and examined the influence of critical experimental parameters, such as cell density seeded, assay volume, incubation time, as well as the cell line-intrinsic factor of cellular cooperation by auto-/paracrine stimulation. Our findings were integrated into a novel mathematical approach for the analysis of clonogenic survival data.ResultsFor various cell lines, clonogenic growth behavior failed to be adequately described by a constant plating efficiency, since the density of cells seeded severely influenced the extent and the dynamics of clonogenic growth. This strongly impaired the robustness of survival calculations obtained by the current state-of-the-art method using plating efficiency-based normalization. A novel mathematical approach utilizing power regression and interpolation of matched colony numbers at different irradiation doses applied to the same dataset substantially reduced the impact of cell density on survival results. Cellular cooperation was observed to be responsible for the non-linear clonogenic growth behavior of a relevant number of cell lines and the impairment of survival calculations. With 28/50 cell lines of different tumor entities showing moderate to high degrees of cellular cooperation, this phenomenon was found to be unexpectedly common.ConclusionsOur study reveals that plating efficiency-based analysis of clonogenic survival data is profoundly compromised by cellular cooperation resulting in strongly underestimated assay-intrinsic errors in a relevant proportion of established cancer cell lines. This severely questions the use of plating efficiency-based calculations in studies aiming to achieve more than semiquantitative results. The novel approach presented here accounts for the phenomenon of cellular cooperation and allows the extraction of clonogenic survival results with clearly improved robustness.

Project description:In multicellular organisms, the timing and placement of gene expression in a developing tissue assigns the fate of each cell in the embryo in order for a uniform field of cells to differentiate into a reproducible pattern of organs and tissues. This positional information is often achieved through the action of spatial gradients of morphogens. Spatial patterns of gene expression are paradoxically robust to variations in morphogen dosage, given that, by definition, gene expression must be sensitive to morphogen concentration. In this work we investigate the robustness of the Dorsal/NF-κB signaling module with respect to perturbations to the dosage of maternally-expressed dorsal mRNA. The Dorsal morphogen gradient patterns the dorsal-ventral axis of the early Drosophila embryo, and we found that an empirical description of the Dorsal gradient is highly sensitive to maternal dorsal dosage. In contrast, we found experimentally that gene expression patterns are highly robust. Although the components of this signaling module have been characterized in detail, how their function is integrated to produce robust gene expression patterns to variations in the dorsal maternal dosage is still unclear. Therefore, we analyzed a mechanistic model of the Dorsal signaling module and found that Cactus, a cytoplasmic inhibitor for Dorsal, must be present in the nucleus for the system to be robust. Furthermore, active Toll, the receptor that dissociates Cactus from Dorsal, must be saturated. Finally, the vast majority of robust descriptions of the system require facilitated diffusion of Dorsal by Cactus. Each of these three recently-discovered mechanisms of the Dorsal module are critical for robustness. These mechanisms synergistically contribute to changing the amplitude and shape of the active Dorsal gradient, which is required for robust gene expression. Our work highlights the need for quantitative understanding of biophysical mechanisms of morphogen gradients in order to understand emergent phenotypes, such as robustness.

Dataset Information

The Barker proposal: Combining robustness and efficiency in gradient-based MCMC.

Publications

The Barker proposal: Combining robustness and efficiency in gradient-based MCMC.

Similar Datasets

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