Summary. We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ‐dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments and rejuvenates the θ‐particles through a resampling step and a Markov chain Monte Carlo update step. In state space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x‐dimension, for any fixed θ. This motivates the SMC2 algorithm that is proposed in the paper: a sequential Monte Carlo algorithm, defined in the θ‐dimension, which propagates and resamples many particle filters in the x‐dimension. The filters in the x‐dimension are an example of the random weight particle filter. In contrast, the particle Markov chain Monte Carlo framework that has been developed by Andrieu and colleagues allows us to design appropriate Markov chain Monte Carlo rejuvenation steps. Thus, the θ‐particles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and non‐sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x‐particles. We contrast our approach with various competing methods, both conceptually and empirically through a detailed simulation study, and based on particularly challenging examples.

SummaryCrop yield has been greatly enhanced during the last century. However, most elite cultivars are adapted to temperate climates and are not well suited to more stressful conditions. In the context of climate change, stress resistance is a major concern. To overcome these difficulties, scientists may help breeders by providing genetic markers associated with stress resistance. However, multistress resistance cannot be obtained from the simple addition of single stress resistance traits. In the field, stresses are unpredictable and several may occur at once. Consequently, the use of single stress resistance traits is often inadequate. Although it has been historically linked with the heat stress response, the heat‐shock protein (HSP)/chaperone network is a major component of multiple stress responses. Among the HSP/chaperone ‘client proteins’, many are primary metabolism enzymes and signal transduction components with essential roles for the proper functioning of a cell. HSPs/chaperones are controlled by the action of diverse heat‐shock factors, which are recruited under stress conditions. In this review, we give an overview of the regulation of the HSP/chaperone network with a focus on Arabidopsis thaliana. We illustrate the role of HSPs/chaperones in regulating diverse signalling pathways and discuss several basic principles that should be considered for engineering multiple stress resistance in crops through the HSP/chaperone network.

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Plant nucleotide-binding leucine-rich repeat receptors (NLRs) regulate immunity and cell death. In Arabidopsis, a subfamily of “helper” NLRs are required by many “sensor” NLRs. Active NRG1.1 oligomerized, was enriched in plasma membrane puncta and conferred cytoplasmic Ca2+ influx in plant and human cells. NRG1.1-dependent Ca2+ influx and cell death were sensitive to Ca2+ channel blockers and were suppressed by mutations impacting oligomerization or plasma membrane enrichment. Ca2+ influx and cell death mediated by NRG1.1 and ACTIVATED DISEASE RESISTANCE 1 (ADR1), another “helper” NLR, required conserved negatively charged N-terminal residues. Whole-cell voltage-clamp recordings demonstrate that Arabidopsis “helper” NLRs form Ca2+-permeable cation channels to directly regulate cytoplasmic Ca2+ levels and consequent cell death. Thus, “helper” NLRs transduce cell death signals directly.

Plant nucleotide-binding (NB) leucine-rich repeat (LRR) receptor (NLR) proteins function as intracellular immune receptors that perceive the presence of pathogen-derived virulence proteins (effectors) to induce immune responses. The 2 major types of plant NLRs that "sense" pathogen effectors differ in their N-terminal domains: these are Toll/interleukin-1 receptor resistance (TIR) domain-containing NLRs (TNLs) and coiled-coil (CC) domain-containing NLRs (CNLs). In many angiosperms, the RESISTANCE TO POWDERY MILDEW 8 (RPW8)-CC domain containing NLR (RNL) subclass of CNLs is encoded by 2 gene families, ACTIVATED DISEASE RESISTANCE 1 (ADR1) and N REQUIREMENT GENE 1 (NRG1), that act as "helper" NLRs during multiple sensor NLR-mediated immune responses. Despite their important role in sensor NLR-mediated immunity, knowledge of the specific, redundant, and synergistic functions of helper RNLs is limited. We demonstrate that the ADR1 and NRG1 families act in an unequally redundant manner in basal resistance, effector-triggered immunity (ETI) and regulation of defense gene expression. We define RNL redundancy in ETI conferred by some TNLs and in basal resistance against virulent pathogens. We demonstrate that, in Arabidopsis thaliana, the 2 RNL families contribute specific functions in ETI initiated by specific CNLs and TNLs. Time-resolved whole genome expression profiling revealed that RNLs and "classical" CNLs trigger similar transcriptome changes, suggesting that RNLs act like other CNLs to mediate ETI downstream of sensor NLR activation. Together, our genetic data confirm that RNLs contribute to basal resistance, are fully

Summary A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Lévy‐driven stochastic volatility model.

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We establish the theoretical validity of the estimators proposed and study their efficiency relative to the underlying MCMC algorithms. Finally, we illustrate the performance and limitations of the method on toy examples, on an Ising model around its critical temperature, on a high dimensional variable‐selection problem, and on an approximation of the cut distribution arising in Bayesian inference for models made of multiple modules.

Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to dataparallel algorithms such as the particle filter, or more generally Sequential Monte Carlo (SMC), which are increasingly used in statistical inference. SMC methods carry a set of weighted particles through repeated propagation, weighting and resampling steps. The propagation and weighting steps are straightforward to parallelise, as they require only independent operations on each particle. The resampling step is more difficult, as standard schemes require a collective operation, such as a sum, across particle weights. Focusing on this resampling step, we analyse two alternative schemes that do not involve a collective operation (Metropolis and rejection resamplers), and compare them to standard schemes (multinomial, stratified and systematic resamplers). We find that, in certain circumstances, the alternative resamplers can perform significantly faster on a GPU, and to a lesser extent on a CPU, than the standard approaches. Moreover, in single precision, the standard approaches are numerically biased for upwards of hundreds of thousands of particles, while the alternatives are not. This is particularly important given greater single-than double-precision throughput on modern devices, and the consequent temptation to use single precision with a greater number of particles. Finally, we provide auxiliary functions useful for implementation, such as for the permutation of ancestry vectors to enable in-place propagation.