shadow hybrid monte carlo an efficient propagator in phase space of macromolecules shadow hybrid monte carlo shmc is a new method for sampling the phase space of large molecules particularly biological molecules it improves sampling of hybrid monte carlo hmc by allowing larger time steps and system sizes in the molecular dynamics md step the acceptance rate of hmc decreases exponentially with increasing system size n or time step t this is due to discretization errors introduced by the numerical integrator shmc achieves an asymptotic o n1 4 speedup over hmc by sampling from all of phase space using high order approximations to a shadow or modified hamiltonian exactly integrated by a symplectic md integrator shmc satisfies microscopic reversibility and is a rigorous sampling method shmc requires extra storage modest computational overhead and a reweighting step to obtain averages from the canonical ensemble this is validated by numerical experiments that compute observables for different molecules ranging from a small n alkane butane with four united atoms to a larger solvated protein with 14 281 atoms in these experiments shmc achieves an order magnitude speedup in sampling efficiency for medium sized proteins sampling efficiency is measured by monitoring the rate at which different conformations of the molecules dihedral angles are visited and by computing ergodic measures of some observables

a direct approach to conformational dynamics based on hybrid monte carlo recently a novel concept for the computation ofessentialfeatures of the dynamics of hamiltonian systems such as molecular dynamics has been proposed the realization of this concept had been based on subdivision techniques applied to the frobenius perron operator for the dynamical system the present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework this approach allows us to define the phrase conformation in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations in a first step the frequency of conformational changes is characterized in statistical terms leading to the definition of some markov operatortthat describes the corresponding transition probabilities within the canonical ensemble in a second step a discretization oftvia specific hybrid monte carlo techniques is shown to lead to astochasticmatrixp with these theoretical preparaions an identification algorithm for conformations to be presented in a later paper is applicable it is demonstrated that the discretization oftcan be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked numerical results for the n pentane molecule and the triribonucleotide adenylyl 3 5 cytidylyl 3 5 cytidin are given and interpreted

a krylov stability corrected coordinate stretching method to simulate wave propagation in unbounded domains the krylov subspace projection approach is a well established tool for the reducedorder modeling of dynamical systems in the time domain in this paper we address the main issues obstructing the application of this powerful approach to the time domain solution of exterior wave problems we use frequency independent perfectly matched layers to simulate the extension to infinity pure imaginary stretching functions based on zolotarev s optimal rational approximation of the square root are implemented leading to perfectly matched layers with a controlled accuracy over a complete spectral interval of interest a new krylov based solution method via stabilitycorrected operator exponents is presented which allows us to construct reduced order models roms that respect the delicate spectral properties of the original scattering problem the roms are unconditionally stable and are based on a renormalized bi lanczos algorithm we give a theoretical foundation of our method and illustrate its performance through a number of numerical examples in which we simulate two dimensional electromagnetic wave propagation in unbounded domains including a photonic waveguide example the new algorithm outperforms the conventional finitedifference time domain method for problems on large time intervals

poisson equations associated with a homogeneous and monotone function necessary and sufficient conditions for a solution in a weakly convex case abstract given a monotone and homogeneous self mapping f of the n dimensional positive cone a communication matrix m f is introduced and a family f of functions is obtained by multiplying each component of f by arbitrary positive numbers assuming that f satisfies a weak form of convexity a necessary and sufficient criterion on the structure of m f is given so that each function in f has a nonlinear eigenvalue an alternative necessary and sufficient condition in terms of the recession function of f is also provided

numerical integrators for the hybrid monte carlo method we construct numerical integrators for hamiltonian problems that may advantageously replace the standard verlet time stepper within hybrid monte carlo and related simulations past attempts have often aimed at boosting the order of accuracy of the integrator and or reducing the size of its error constants order and error constant are relevant concepts in the limit of vanishing step length we propose an alternative methodology based on the performance of the integrator when sampling from gaussian distributions with not necessarily small step lengths we construct new splitting formulae that require two three or four force evaluations per time step limited proof of concept numerical experiments suggest that the new integrators may provide an improvement on the efficiency of the standard verlet method especially in problems with high dimensionality

the nose poincare method for constant temperature molecular dynamics we present a new extended phase space method for constant temperature canonical ensemble molecular dynamics our starting point is the hamiltonian introduced by nose to generate trajectories corresponding to configurations in the canonical ensemble using a poincare time transformation we construct a hamiltonian system with the correct intrinsic timescale and show that it generates trajectories in the canonical ensemble our approach corrects a serious deficiency of the standard change of variables nose hoover dynamics which yields a time reversible system but simultaneously destroys the hamiltonian structure a symplectic discretization method is presented for solving the nose poincare equations the method is explicit and preserves the time reversal symmetry in numerical experiments it is shown that the new method exhibits enhanced stability when the temperature fluctuation is large extensions are presented for nose chains holonomic constraints and rigid bodies

hamiltonian monte carlo sampling in bayesian empirical likelihood computation summary we consider bayesian empirical likelihood estimation and develop an efficient hamiltonian monte carlo method for sampling from the posterior distribution of the parameters of interest the method proposed uses hitherto unknown properties of the gradient of the underlying log empirical likelihood function we use results from convex analysis to show that these properties hold under minimal assumptions on the parameter space prior density and the functions used in the estimating equations determining the empirical likelihood our method employs a finite number of estimating equations and observations but produces valid semiparametric inference for a large class of statistical models including mixed effects models generalized linear models and hierarchical bayes models we overcome major challenges posed by complex non convex boundaries of the support routinely observed for empirical likelihood which prevent efficient implementation of traditional markov chain monte carlo methods like random walk metropolis hastings sampling etc with or without parallel tempering a simulation study confirms that our method converges quickly and draws samples from the posterior support efficiently we further illustrate its utility through an analysis of a discrete data set in small area estimation

gaussian spectral rules for the three point second differences i a two point positive definite problem in a semi infinite domain we suggest an approach to grid optimization for a second order finite difference scheme for elliptic equations a model problem corresponding to the three point finite difference semidiscretization of the laplace equation on a semi infinite strip is considered we relate the approximate boundary neumann to dirichlet map to a rational function and calculate steps of our finite difference grid using the pade chebyshev approximation of the inverse square root it increases the convergence order of the neumann to dirichlet map from second to exponential without increasing the stencil of the finite difference scheme and losing stability

risk sensitive optimal control for markov decision processes with monotone cost the existence of an optimal feedback law is established for the risk sensitive optimal control problem with denumerable state space the main assumptions imposed are irreducibility and anear monotonicity condition on the one step cost function a solution can be found constructively using either value iteration or policy iteration under suitable conditions on initial feedback law

risk sensitive control of markov processes in countable state space in this paper we consider infinite horizon risk sensitive control of markov processes with discrete time and denumerable state space this problem is solved by proving under suitable conditions that there exists a bounded solution to the dynamic programming equation the dynamic programming equation is transformed into an isaacs equation for a stochastic game and the vanishing discount method is used to study its solution in addition we prove that the existence conditions are also necessary

reflectionless truncation of target area for axially symmetric anisotropic elasticity this paper presents an approach to numerical simulation of seismic wave propagation in anisotropic elastic media in cylindrical coordinates by means of conservative finite difference scheme on staggered grids an original low cost domain distension based on optimal grids is proposed to restrict computational domain

multipoint metropolis method with application to hybrid monte carlo abstract we propose the multipoint metropolis algorithm as an extension of the orientational bias monte carlo of frenkel and smit a ratio statistics similar to that in the metropolis algorithm is introduced to maintain the detailed balance the multipoint idea can be applied to improve the efficiency of a general markov chain based monte carlo algorithm to illustrate we describe two variations of the idea the random grid metropolis and the multipoint hybrid monte carlo and apply them to a number of examples

optimal scaling of discrete approximations to langevin diffusions we consider the optimal scaling problem for proposal distributions in hastings metropolis algorithms derived from langevin diffusions we prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate independently of the target distribution the asymptotically optimal acceptance rate is 0 574 we show that as a function of dimension n the complexity of the algorithm is o n1 3 which compares favourably with the o n complexity of random walk metropolis algorithms we illustrate this comparison with some example simulations

practical construction of modified hamiltonians one of the most fruitful ways to analyze the effects of discretization error in the numerical solution of a system of differential equations is to examine the modified equations which are equations that are exactly satisfied by the approximate discrete solution these do not actually exist in general but rather are defined by an asymptotic expansion in powers of the discretization parameter nonetheless if the expansion is suitably truncated the resulting modified equations have a solution which is remarkably close to the discrete solution in the case of a hamiltonian system of ordinary differential equations the modified equations are also hamiltonian if and only if the integrator is symplectic evidence for the existence of a hamiltonian for a particular calculation is obtained by calculating modified hamiltonians and monitoring how well they are conserved also energy drifts caused by numerical instability are better revealed by evaluating modified hamiltonians doing this calculation would normally be complicated and highly dependent on the details of the method even if differences are used to approximate derivatives a relatively simple procedure is presented here nearly independent of the internal structure of the integrator for obtaining highly accurate estimates for modified hamiltonians as a bonus of the method of construction the modified hamiltonians are exactly conserved by a numerical solution in the case of a quadratic hamiltonian

phase transitions for controlled markov chains on infinite graphs this paper is concerned with some long run average cost problems for controlled markov chains with a denumerable state space the criterion to be optimized contains both reward and penalty functions as a trade off between reward and penalty we observe certain phase transition phenomena our results also provide a stochastic optimal control interpretation for phase transitions of discrete homopolymers with finite attracting potentials

backward error analysis for numerical integrators backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods this is true in particular for the integration of hamiltonian systems where backward error analysis can be used to show that a symplectic method will conserve energy over exponentially long periods of time such results are typically based on two aspects of backward error analysis i it can be shown that the modified vector fields have some qualitative properties which they share with the given problem and ii an estimate is given for the difference between the best interpolating vector field and the numerical method these aspects have been investigated recently for example by benettin and giorgilli in j statist phys 74 1994 pp 1117 1143 by hairer in ann numer math 1 1994 pp 107 132 and by hairer and lubich in numer math 76 1997 pp 441 462 in this paper we aim at providing a unifying framework and a simplification of the existing results and corresponding proofs our approach to backward error analysis is based on a simple recursive definition of the modified vector fields that does not require explicit taylor series expansion of the numerical method and the corresponding flow maps as in the above cited works as an application we discuss the long time integration of chaotic hamiltonian systems and the approximation of time averages along numerically computed trajectories

three point finite difference schemes pade and the spectral galerkin method i one sided impedance approximation a method for calculating special grid placement for three point schemes which yields exponential superconvergence of the neumann to dirich let map has been suggested earlier here we show that such a grid placement can yield impedance which is equivalent to that of a spectral galerkin method or more generally to that of a spectral galerkin petrov method in fact we show that for every stable galerkin petrov method there is a three point scheme which yields the same solution at the boundary we discuss the application of this result to partial differential equations and give numerical examples we also show equivalence at one corner of a two dimensional optimal grid with a spectral galerkin method

multilevel coarse graining and nano pattern discovery in many particle stochastic systems in this work we propose a hierarchy of markov chain monte carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions each monte carlo step is composed by two or more sub steps efficiently coupling coarse and finer state spaces the method can be designed to sample the exact or controlled error approximations of the target distribution providing information on levels of different resolutions as well as at the microscopic level in both strategies the method achieves significant reduction of the computational cost compared to conventional markov chain monte carlo methods applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods

the no u turn sampler hamiltonian monte carlo hmc is a markov chain monte carlo mcmc algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many mcmc methods by taking a

generalized simulated annealing algorithms using tsallis statistics application to conformational optimization of a tetrapeptide a monte carlo simulated annealing algorithm based on the generalized entropy of tsallis is presented the algorithm obeys detailed balance and reduces to a steepest descent algorithm at low temperatures application to the conformational optimization of a tetrapeptide demonstrates that the algorithm is more effective in locating low energy minima than standard simulated annealing based on molecular dynamics or monte carlo methods

application of the difference gaussian rules to solution of hyperbolic problems two of the authors earlier suggested a method of calculating special grid steps for three point finite difference schemes which yielded exponential superconvergence of the neumann to dirichlet map we apply this approach to solve the two dimensional time domain wave problem and the 2 5 d elasticity system in cylindrical coordinates our numerical experiments exhibit exponential convergence at prescribed points with the cost per grid node close to that of the standard second order finite difference scheme the scheme demonstrates high accuracy with slightly more than two grid points per wavelength the reduction of the grid size by one order compared to the standard scheme with the equidistant grids is observed

exponential convergence through linear finite element discretization of stratified subdomains motivated by problems where the response is needed at select localized regions in a large computational domain we devise a novel finite element discretization that results in exponential convergence at pre selected points the key features of the discretization are a use of midpoint integration to evaluate the contribution matrices and b an unconventional mapping of the mesh into complex space named complex length finite element method cfem the technique is linked to pade approximants that provide exponential convergence of the dirichlet to neumann maps and thus the solution at specified points in the domain exponential convergence facilitates drastic reduction in the number of elements this combined with sparse computation associated with linear finite elements results in significant reduction in the computational cost the paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving laplace helmholtz and elastodynamics equations

a liouville operator derived measure preserving integrator for molecular dynamics simulations in the isothermal isobaric ensemble the constant pressure constant temperature npt molecular dynamics approach is re examined from the viewpoint of deriving a new measure preserving reversible geometric integrator for the equations of motion the underlying concepts of non hamiltonian phase space analysis measure preserving integrators and the symplectic property for hamiltonian systems are briefly reviewed in addition current measure preserving schemes for the constant volume constant temperature ensemble are also reviewed a new geometric integrator for the npt method is presented is shown to preserve the correct phase space volume element and is demonstrated to perform well in realistic examples finally a multiple time step version of the integrator is presented for treating systems with motion on several time scales

an efficient finite difference scheme for electromagnetic logging in 3d anisotropic inhomogeneous media we consider a problem of computing the electromagnetic field in 3d anisotropic media for electromagnetic logging the proposed finite difference scheme for maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis coercivity i e the complete discrete analogy of all continuous equations in every grid cell even for nondiagonal conductivity tensors a special conductivity averaging that does not require the grid to be small compared to layering or fractures and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity all of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3d geometries without sacrificing accuracy

optimal finite difference grids and rational approximations of the square root i elliptic problems the main objective of this paper is optimization of second order finite difference schemes for elliptic equations in particular for equations with singular solutions and exterior problems a model problem corresponding to the laplace equation on a semi infinite strip is considered the boundary impedance neumann to dirichlet map is computed as the square root of an operator using the standard three point finite difference scheme with optimally chosen variable steps the finite difference approximation of the boundary impedance for data of given smoothness is the problem of rational approximation of the square root on the operator s spectrum we have implemented zolotarev s optimal rational approx imant obtained in terms of elliptic functions we have also found that a geometrical progression of the grid steps with optimally chosen parameters is almost as good as the optimal approximant for bounded operators it increases from second to exponential the convergence order of the finite difference impedance with the convergence rate proportional to the inverse of the logarithm of the condition number for the case of unbounded operators in sobolev spaces associated with elliptic equations the error decays as the exponential of the square root of the mesh dimension as an example we numerically compute the green function on the boundary for the laplace equation some features of the optimal grid obtained for the laplace equation remain valid for more general elliptic problems with variable coefficients 2000 john wiley sons inc

stability of fdtd on nonuniform grids for maxwell s equations in lossless media in this paper we present practical stability conditions for the finite difference time domain method on nonuniform tensor product grids yee grids these stability conditions apply to maxwell s equations for inhomogeneous and lossless media rectangular domains are considered and the conditions are expressed in terms of the minimum spatial stepsizes of the grid and the maximum electromagnetic wave speed in the configuration the maximum wave speed is known as soon as the media are specified while the minimum spatial stepsizes are known after the configuration has been discretized for two dimensional configurations we present a number of numerical examples which illustrate the effectiveness of the proposed stability conditions

optimizing the perfectly matched layer the berenger perfectly matched layer or pml 4 3 is used in computational electromagnetism as a sponge layer to terminate finite element approximations of scattering problems an infinite perfectly matched layer creates no reflection for incident waves of any frequency or any incident direction and the waves decay exponentially in magnitude into the layer this property is lost when the layer is truncated since the truncation boundary generates a reflected wave discretization of the differential equations further changes the reflection coefficient of the layer in this talk we shall describe the pml in the simple case of a two dimensional electromagnetic problem the first part of this abstract is expository we shall show how to derive the layer using a change of variable approach 5 9 6 after this derivation we describe some new analysis to show the effects of truncating and discretizing the pml 9 we end by showing how to compute an optimal layer and make some remarks about pml for the full maxwell system

higher order hybrid monte carlo algorithms we present a simple recursive iteration of the leapfrog discretization of newton s equations which leads to a removal of the finite step size error to any desired order this is done in a manner that preserves phase space areas and reversibility as required for use in the hybrid monte carlo method for simulating fermionic fields the resulting asymptotic volume dependence is exp ln ital v sup 1 2 we test the scheme on the 2 1 dimensional hubbard model

necessary and sufficient conditions for a solution to the risk sensitive poisson equation on a finite state space a markov chain with finite state space endowed with a cost function is considered the transition mechanism is stationary the observer has a constant risk sensitivity and the overall performance of the chain is measured by the risk sensitive long run average cost in this context the existence of solutions of the corresponding poisson equation for arbitrary cost function is characterized in terms of the communication properties of the transition matrix the result in this direction establishes that the poisson equation has a solution for each cost function if and only if the transition matrix has a unique recurrent class and a strong form of the doeblin condition holds

compensated optimal grids for elliptic boundary value problems a method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary the method is an extension of the optimal grid approach for elliptic problems based on optimal rational approximation of the associated neumann to dirichlet map in fourier space it is shown that using certain types of boundary discretization one can go from second order accurate schemes to essentially spectrally accurate schemes in two dimensional problems and to fourth order accurate schemes in three dimensional problems without any increase in the computational complexity the main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite difference stencil discretizing the differential operator on the boundary we illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication

application of the difference gaussian rules to solution of hyperbolic problems global expansion this work is the sequel to s asvadurov et al 2000 j comput phys 158 116 where we considered a grid refinement approach for second order finite difference time domain schemes this approach permits one to compute solutions of certain wave equations with exponential superconvergence an algorithm was presented that generates a special sequence of grid steps called optimal such that a standard finite difference discretization that uses this grid produces an accurate approximation to the neumann to dirichlet map it was demonstrated that the application of this approach to some problems in e g elastodynamics results in a computational cost that is an order of magnitude lower than that of the standard scheme with equally spaced gridnodes which produces the same accuracy the main drawback of the presented approach was that the accurate solution could be obtained only at some a priori selected points receivers here we present an algorithm that given a solution on the coarse optimal grid accurately reconstructs the solution of the corresponding fine equidistant grid with steps that are approximately equal to the minimal step of the optimal strongly nonuniform grid this expansion algorithm is based on postprocessing of the approximate solution is local in time but not in space and has a cost comparable to that of the discrete fourier transform an approximate inverse to the expansion procedure the reduction algorithm is also presented we show different applications of the developed procedures including refinement of a nonmatching grid numerical examples for scalar wave propagation and 2 5d cylindrical elasticity are presented

long time step methods for oscillatory differential equations considered are numerical integration schemes for nondissipative dynamical systems in which multiple time scales are present it is assumed that one can do an explicit separation of the rhs forces into fast forces and slow forces such that i the fast forces contain the high frequency part of the solution ii the fast forces are conservative and iii the reduced problem consisting only of the fast forces can be integrated much more cheaply than the full problem the fast forces are allowed to have low frequency components particular applications for which the schemes are intended include n body problems for which most of the forces are slow and nonlinear wave phenomena for which the fast forces can be propagated by spectral methods the assumption of cheap integration of fast forces implies that the overall cost of integration is primarily determined by the step size used to sample the slow forces a long time step method is one in which this step size exceeds half the period of the fastest normal mode present in the full system an existing method that comes close to qualifying is the impulse method also known as verlet i and r respa it is shown that it might fail though for a couple of reasons first it suffers a serious loss of accuracy if the step size is near a multiple of the period of a normal mode and second it is unstable if the step size is near a multiple of half the period of a normal mode proposed in this paper is a mollified impulse method having an error bound that is independent of the frequency of the fast forces it is also shown to possess superior stability properties theoretical results are supplemented by numerical experiments the method is efficient and reasonably easy to implement

risk sensitive control of discrete time markov processes with infinite horizon in this paper we study existence of solutions to the bellman equation corresponding to risk sensitive ergodic control of discrete time markov processes using three different approaches also for particular classes of systems asymptotics for vanishing risk factor is investigated showing that in the limit the optimal value for an average cost per unit time is obtained

an improved acceptance procedure for the hybrid monte carlo algorithm abstract the probability of accepting a candidate move in the hybrid monte carlo algorithm can be increased by considering a transition to be between windows of several states at the beginning and end of the trajectory with a particular state within the selected window then being chosen according to the boltzmann probabilities the detailed balance condition used to justify the algorithm still holds with this procedure provided the start state is randomly positioned within its window the new procedure is shown empirically to significantly improve the acceptance rate for a test system of uncoupled oscillators it also allows expectations to be estimated using data from all states in the windows rather than just states that are accepted

an extended krylov subspace model order reduction technique to simulate wave propagation in unbounded domains abstract in this paper we present a novel extended krylov subspace reduced order modeling technique to efficiently simulate time and frequency domain wavefields in open complex structures to simulate the extension to infinity we use an optimal complex scaling method which is equivalent to an optimized perfectly matched layer in which the frequency is fixed wavefields propagating in strongly inhomogeneous open domains can now be modeled as a non entire function of the complex scaled wave operator since this function contains a square root singularity we apply an extended krylov subspace technique to construct fast converging reduced order models specifically we use a modified version of the extended krylov subspace algorithm as proposed by jagels and reichel 14 since this algorithm allows us to balance the computational costs associated with computing powers of the wave operator and its inverse numerical experiments from electromagnetics and acoustics illustrate the performance of the method

on the continuum limit of a discrete inverse spectral problem on optimal finite difference grids we consider finite difference approximations of solutions of inverse stur m liouville problems in bounded intervals using three point finite difference sc hemes we discretize the equations on so called optimal grids constructed as follow s for a staggered grid with 2k points we ask that the finite difference operator a k k jacobi matrix and the sturm liouville differential operator share the k lowest eigenvalues and the values of the orthonormal eigenfunctions at one end of the interval this requirement determines uniquely the entries in the jacobi matrix which are grid cell averages of the coefficients in the continuum problem if these coefficients are known we can find the grid which we call optimal becau se it gives by design a finite difference operator with a prescribed spectr al measure we focus attention on the inverse problem where neither the coefficients n or the grid are known a key question in inversion is how to parametrize the coefficients i e how to choose the grid it is clear that to be successful this grid must be close to the optimal one which is unknown fortunately as we show here the grid dependence on the unknown coefficients is weak so the inversion can be done on a pr ecomputed grid for an a priori guess of the unknown coefficients this obse rvation leads to a simple yet efficient inversion algorithm which gives coefficien ts that converge pointwise to the true solution as the number k of data points tends to infinity the cornerstone of our convergence proof is showing that op timal grids provide an implicit natural regularization of the inverse problem by givin g reconstructions with uniformly bounded total variation the analysis is based on a novel explicit perturbation analysis of lanczos recursions and on a discrete

a comparison of generalized hybrid monte carlo methods with and without momentum flip the generalized hybrid monte carlo ghmc method combines metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta the standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step the implication is a trajectory reversal upon rejection which is undesirable when interpreting ghmc as thermostated molecular dynamics we show that a modified detailed balance condition can be used to implement ghmc without momentum flips the same modification can be applied to the generalized shadow hybrid monte carlo gshmc method numerical results indicate that ghmc gshmc implementations with momentum flip display a favorable behavior in terms of sampling efficiency i e the traditional ghmc gshmc implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of monte carlo samples the difference is more pronounced for ghmc we also numerically investigate the behavior of the ghmc method as a langevin type thermostat we find that the ghmc method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the ghmc method with momentum flip the same finding applies to gshmc

parameterization and bayesian modeling progress in statistical computation often leads to advances in statistical modeling for example it is surprisingly common that an existing model is reparameterized solely for computational purposes but then this new configuration motivates a new family of models that is useful in applied statistics one reason why this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood in a bayesian framework however a transformation of parameters typically suggests a new family of prior distributions we discuss examples in censored and truncated data mixture modeling multivariate imputation stochastic processes and multilevel models