the correlated pseudomarginal method the pseudomarginal algorithm is a metropolis hastings type scheme which samples asymptotically from a target probability density when we can only estimate unbiasedly an unnormalized version of it in a bayesian context it is a state of the art posterior simulation technique when the likelihood function is intractable but can be estimated unbiasedly by using monte carlo samples however for the performance of this scheme not to degrade as the number t of data points increases it is typically necessary for the number n of monte carlo samples to be proportional to t to control the relative variance of the likelihood ratio estimator appearing in the acceptance probability of this algorithm the correlated pseudomarginal method is a modification of the pseudomarginal method using a likelihood ratio estimator computed by using two correlated likelihood estimators for random effects models we show under regularity conditions that the parameters of this scheme can be selected such that the relative variance of this likelihood ratio estimator is controlled when n increases sublinearly with t and we provide guidelines on how to optimize the algorithm on the basis of a non standard weak convergence analysis the efficiency of computations for bayesian inference relative to the pseudomarginal method empirically increases with t and exceeds two orders of magnitude in some examples

a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

the bgk model with external confining potential existence long time behaviour and time periodic maxwellian equilibria we study global existence and long time behaviour for the inhomogeneous nonlinear bgk model for the boltzmann equation with an external confining potential for an initial datum f0 0 with bounded mass entropy and total energy we prove existence and strong convergence in l1 to a maxwellian equilibrium state by compactness arguments and multipliers techniques of particular interest is the case with an isotropic harmonic potential in which boltzmann himself found infinitely many time periodic maxwellian steady states this behaviour is shared with the boltzmann equation and other kinetic models for all these systems we study the multistability of the time periodic maxwellians and provide necessary conditions on f0 to identify the equilibrium state both in l1 and in lyapunov sense under further assumptions on f these conditions become also sufficient for the identification of the equilibrium in l1

efficient implementation of markov chain monte carlo when using an unbiased likelihood estimator summary when an unbiased estimator of the likelihood is used within a metropolis hastings chain it is necessary to trade off the number of monte carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain using many monte carlo samples will typically result in metropolis hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples however the computing time required to construct the likelihood estimator increases with the number of samples under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated we provide guidelines on the number of samples to select we illustrate our results by considering a stochastic volatility model applied to stock index returns

bayesian semiparametric wiener system identification we present a novel method for wiener system identication the method relies on a semiparametric i e a mixed parametric nonparametric model of a wiener system we use a state space model for the linear dynamical system and a nonparametric gaussian process model for the static nonlinearity we avoid making strong assumptions such as monotonicity on the nonlinear mapping stochastic disturbances entering both as measurement noise and as process noise are handled in a systematic manner the nonparametric nature of the gaussian process allows us to handle a wide range of nonlinearities without making problem specic parameterizations we also consider sparsity promoting priors based on generalized hyperbolic distributions to automatically infer the order of the underlying dynamical system we derive an inference algorithm based on an ecient particle markov chain monte carlo method referred to as particle gibbs with ancestor sampling the method is proled on two challenging identication problems with good results blind wiener system identication is handled as a special case

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

particle efficient importance sampling abstract the efficient importance sampling eis method is a general principle for the numerical evaluation of high dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers despite a number of successful applications in high dimensions it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases we solve this problem by recognising that the eis framework has an offline sequential monte carlo interpretation the particle eis method is based on non standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density we apply the method for a range of univariate and bivariate stochastic volatility specifications we also develop a new application of the eis approach to state space models with student s t state innovations our results show that the particle eis method strongly outperforms both the standard eis method and particle filters for likelihood evaluation in high dimensions we illustrate the efficiency of the method for bayesian inference using the particle marginal metropolis hastings and importance sampling squared algorithms

dynamic phase transition for decoding algorithms the state of the art error correcting codes are based on large random constructions random graphs random permutations etc and are decoded by linear time iterative algorithms because of these features they are remarkable examples of diluted mean field spin glasses both from the static and dynamic points of view we analyze the behavior of decoding algorithms by mapping them onto statistical physics models this allows us to understand the intrinsic i e algorithm independent features of this behavior

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

bayesian inference for nonlinear structural time series models we consider efficient methods for likelihood inference applied to structural models in particular we introduce a particle filter method which concentrates upon disturbances in the markov state of the approximating solution to the structural model a particular feature of such models is that the conditional distribution of interest for the disturbances is often multimodal we provide a fast and effective method for approximating such distributions we estimate a neoclassical growth model using this approach an asset pricing model with persistent habits is also considered the methodology we employ allows many fewer particles to be used than alternative procedures for a given precision

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

sequential quasi monte carlo this is a written discussion of the paper sequential quasi monte carlo sampling by m gerber and n chopin following the presentation given before the royal statistical society in london on december 10th 2014

likelihood based estimation of latent generalized arch structures garch models are commonly used as latent processes in econometrics financial economics and macroeconomics yet no exact likelihood analysis of these models has been provided so far in this paper we outline the issues and suggest a markov chain monte carlo algorithm which allows the calculation of a classical estimator via the simulated em algorithm or a bayesian solution in o t computational operations where t denotes the sample size we assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 uk sectorial stock returns and compare it to existing approximate solutions

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

speeding up mcmc by efficient data subsampling we propose subsampling markov chain monte carlo mcmc an mcmc framework where the likelihood function for n observations is estimated from a random subset of m observations we introduce a highly

monte carlo smoothing for nonlinear time series we develop methods for performing smoothing computations in general state space models the methods rely on a particle representation of the filtering distributions and their evolution through time using sequential importance sampling and resampling ideas in particular novel techniques are presented for generation of sample realizations of historical state sequences this is carried out in a forward filtering backward smoothing procedure that can be viewed as the nonlinear non gaussian counterpart of standard kalman filter based simulation smoothers in the linear gaussian case convergence in the mean squared error sense of the smoothed trajectories is proved showing the validity of our proposed method the methods are tested in a substantial application for the processing of speech signals represented by a time varying autoregression and parameterized in terms of time varying partial correlation coefficients comparing the results of our algorithm with those from a simple smoother based on the filte

geometric convergence and central limit theorems for multidimensional hastings and metropolis algorithms we develop results on geometric ergodicity of markov chains and apply these and other recent results in markov chain theory to multidimensional hastings and metropolis algorithms for those based on random walk candidate distributions we find sufficient conditions for moments and moment generating functions to converge at a geometric rate to a prescribed distribution by phrasing the conditions in terms of the curvature of the densities we show that the results apply to all distributions with positive densities in a large class which encompasses many commonly used statistical forms from these results we develop central limit theorems for the metropolis algorithm converse results showing non geometric convergence rates for chains where the rejection rate is not bounded away from unity are also given these show that the negative definiteness property is not redundant

particle filters for continuous likelihood evaluation and maximisation in this paper a method is introduced for approximating the likelihood for the unknown parameters of a state space model the approximation converges to the true likelihood as the simulation size goes to infinity in addition the approximating likelihood is continuous as a function of the unknown parameters under rather general conditions the approach advocated is fast and robust and it avoids many of the pitfalls associated with current techniques based upon importance sampling we assess the performance of the method by considering a linear state space model comparing the results with the kalman filter which delivers the true likelihood we also apply the method to a non gaussian state space model the stochastic volatility model finding that the approach is efficient and effective applications to continuous time finance models and latent panel data models are considered two different multivariate approaches are proposed the neoclassical growth model is considered as an application

polynomial iterative algorithms for coloring and analyzing random graphs we study the graph coloring problem over random graphs of finite average connectivity c given a number q of available colors we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable depending on q we find with a one step replica symmetry breaking approximation the precise value of the critical average connectivity c q moreover we show that below c q there exists a clustering phase c in c d c q in which ground states spontaneously divide into an exponential number of clusters furthermore we extended our considerations to the case of single instances showing consistent results this leads us to propose a different algorithm that is able to color in polynomial time random graphs in the hard but colorable region i e when c in c d c q

particle metropolis adjusted langevin algorithms this paper proposes a new sampling scheme based on langevin dynamics that is applicable within pseudo marginal and particle markov chain monte carlo algorithms we investigate this algorithm s theoretical properties under standard asymptotics which correspond to an increasing dimension of the parameters n our results show that the behaviour of the algorithm depends crucially on how accurately one can estimate the gradient of the log target density if the error in the estimate of the gradient is not sufficiently controlled as dimension increases then asymptotically there will be no advantage over the simpler random walk algorithm however if the error is sufficiently well behaved then the optimal scaling of this algorithm will be o n 1 6 compared to o n 1 2 for the random walk our theory also gives guidelines on how to tune the number of monte carlo samples in the likelihood estimate and the proposal step size

survey propagation for the cascading sourlas code we investigate how insights from statistical physics namely survey propagation can improve decoding of a particular class of sparse error correcting codes we show that a recently proposed algorithm time averaged belief propagation is in fact intimately linked to a specific survey propagation for which parisi s replica symmetry breaking parameter is set to zero and that the latter is always superior to belief propagation in the high connectivity limit we briefly look at further improvements available by going to the second level of replica symmetry breaking

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

statistical mechanics of low density parity check codes we review recent theoretical progress on the statistical mechanics of error correcting codes focusing on low density parity check ldpc codes in general and on gallager and mackay neal codes in particular by exploiting the relation between ldpc codes and ising spin systems with multispin interactions one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions corresponding to dynamical and thermodynamical transitions respectively as well as the behaviour of error exponents averaged over the corresponding code ensemble as a function of channel noise we also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature and show how these methods can be generalized to include other channel types and related communication problems

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

minimizing energy below the glass thresholds focusing on the optimization version of the random k satisfiability problem the max k sat problem we study the performance of the finite energy version of the survey propagation algorithm we show that a simple linear time backtrack decimation strategy is sufficient to reach configurations well below the lower bound for the dynamic threshold energy and very close to the analytic prediction for the optimal ground states a comparative numerical study on one of the most efficient local search procedures is also given

survey propagation at finite temperature application to a sourlas code as a toy model in this paper we investigate a finite temperature generalization of survey propagation by applying it to the problem of finite temperature decoding of a biased finite connectivity sourlas code for temperatures lower than the nishimori temperature we observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation as suggested recently by migliorini and saad for ldpc codes we show how the finite temperature 1rsb sp gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

the gaussian moment closure for gas dynamics the moment closure method of levermore applied to the boltzmann equation for rarefied gas dynamics leads to a hierarchy of symmetric hyperbolic systems of partial differential equations the euler system is the first member of this hierarchy of closures in this paper we investigate the next member the 10 moment gaussian closure we first reduce the collision term to an integral which may be explicitly evaluated for the special case of maxwell molecular interaction the resulting collision term for this case is shown to be equivalent to the term obtained by replacing the boltzmann collision operator with the bhatnagar gross and krook bgk approximation we then analyze the gaussian system applied to the canonical flow problem of a stationary planar shock an analytic shock profile for the gaussian closure is derived and compared with the numerical solutions of the boltzmann and navier stokes equations the results show reasonable agreement for weak shocks and close agreement between the downstream ga

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

specification estimation and evaluation of smooth transition autoregressive models abstract this article considers the application of two families of nonlinear autoregressive models the logistic lstar and exponential estar autoregressive models this includes the specification of the model based on simple statistical tests linearity testing against smooth transition autoregression determining the delay parameter and choosing between lstar and estar models are discussed estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model the proposed techniques are illustrated by examples using both simulated and real time series

cluster variation method in statistical physics and probabilistic graphical models the cluster variation method cvm is a hierarchy of approximate variational techniques for discrete ising like models in equilibrium statistical mechanics improving on the mean field approximation and the bethe peierls approximation which can be regarded as the lowest level of the cvm in recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models the foundations of the cvm are briefly reviewed and the relations with similar techniques are discussed the main properties of the method are considered with emphasis on its exactness for particular models and on its asymptotic properties the problem of the minimization of the variational free energy which arises in the cvm is also addressed and recent results about both provably convergent and message passing algorithms are discussed

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

a hybrid kinetic fluid model for solving the vlasov bgk equation our purpose is to derive a model for charged particles which combines a kinetic description of the fast particles with a fluid description of the slow ones in a previous paper a similar model was derived from a kinetic bgk equation that uses a constant relaxation time and does not include the effect of an electric field in this paper we consider a more general kinetic equation including an electric field and a varying relaxation time fast particles will be described through a collisional kinetic equation of vlasov bgk type while thermal particles will be modeled by a hydrodynamic model then we construct a numerical scheme for this model and validate the approach by presenting various numerical tests

an asymptotic preserving scheme for linear kinetic equation with fractional diffusion limit we present a new asymptotic preserving scheme for the linear boltzmann equation which under appropriate scaling leads to a fractional diffusion limit our scheme rests on novel micro macro decomposition to the distribution function which splits the original kinetic equation following a reshuffled hilbert expansion as opposed to classical diffusion limit a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter our idea is while solving the macro micro part in a truncated velocity domain truncation only depends on numerical accuracy to incorporate an integrated tail over the velocity space that is beyond the truncation and its major component can be precomputed once with any accuracy such an addition is essential to drive the solution to the correct asymptotic limit numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes

random k satisfiability problem from an analytic solution to an efficient algorithm we study the problem of satisfiability of randomly chosen clauses each with k boolean variables using the cavity method at zero temperature we find the phase diagram for the k 3 case we show the existence of an intermediate phase in the satisfiable region where the proliferation of metastable states is at the origin of the slowdown of search algorithms the fundamental order parameter introduced in the cavity method which consists of surveys of local magnetic fields in the various possible states of the system can be computed for one given sample these surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems one such algorithm is shown here for the k 3 satisfiability problem with very good performances

on some properties of markov chain monte carlo simulation methods based on the particle filter abstract andrieu et al 2010 prove that markov chain monte carlo samplers still converge to the correct posterior distribution of the model parameters when the likelihood estimated by the particle filter with a finite number of particles is used instead of the likelihood a critical issue for performance is the choice of the number of particles we add the following contributions first we provide analytically derived practical guidelines on the optimal number of particles to use second we show that a fully adapted auxiliary particle filter is unbiased and can drastically decrease computing time compared to a standard particle filter third we introduce a new estimator of the likelihood based on the output of the auxiliary particle filter and use the framework of del moral 2004 to provide a direct proof of the unbiasedness of the estimator fourth we show that the results in the article apply more generally to markov chain monte carlo sampling schemes with the likelihood estimated in an unbiased manner

a hybrid kinetic fluid model for solving the gas dynamics boltzmann bgk equation our purpose is to derive a hybrid model for particle systems which combines a kinetic description of the fast particles with a fluid description of the thermal ones in the present work fast particles will be described through a collisional kinetic equation of boltzmann bgk type while thermal particles will be modeled by means of a system of euler type equations then we construct a numerical scheme for this model this scheme satisfies exact conservation properties we validate the approach by presenting various numerical tests

convergence of a finite volume scheme for the vlasov poisson system we propose a finite volume scheme to discretize the one dimensional vlasov poisson system we prove that if the initial data are positive bounded continuous and have their first moment bounded then the numerical approximation converges to the weak solution of the system for the weak topology of l infty moreover if the initial data belong to bv the convergence is strong in c 0 0 t l 1 loc to prove the convergence of the discrete electric field we obtain an estimation in w 1 infty omega t then we have begin eqnarray f h t x v rightharpoonup f t x v textrm in l infty q t mbox weak star quad textrm as h rightarrow 0 e h t x rightarrow e t x textrm in c 0 overline omega t quad textrm as h rightarrow 0 end eqnarray where e f is the unique weak solution of the vlasov poisson system

instability of one step replica symmetry broken phase in satisfiability problems we reconsider the one step replica symmetry breaking 1rsb solutions of two random combinatorial problems k xorsat and k sat we present a general method for establishing the stability of these solutions with respect to further steps of replica symmetry breaking our approach extends the ideas of montanari and ricci tersenghi 2003 eur phys j b 33 339 to more general combinatorial problems it turns out that 1rsb is always unstable at sufficiently small clause density or high energy in particular the recent 1rsb solution to 3 sat is unstable at zero energy for m with m 4 153 on the other hand the sat unsat phase transition seems to be correctly described within 1rsb