Dynamic Hamiltonian Monte Carlo in Stan Hamiltonian Monte Carlo use of gradient information and dynamic simulation reduce random walk Dynamic HMC adaptive simulation time Adaptation of algorithm parameters mass matrix and step size adaptation during warm-up Dynamic HMC specific diagnostics Aki.Vehtari@aalto.fi – @avehtari
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Dynamic Hamiltonian Monte Carlo in Stan
Hamiltonian Monte Carlouse of gradient information and dynamic simulation reducerandom walk
Dynamic HMCadaptive simulation time
Adaptation of algorithm parametersmass matrix and step size adaptation during warm-up
Michael Betancourt (2018). Scalable Bayesian Inferencewith Hamiltonian Monte Carlohttps://www.youtube.com/watch?v=jUSZboSq1zgMichael Betancourt (2018). A Conceptual Introduction toHamiltonian Monte Carlo. https://arxiv.org/abs/1701.02434http://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/Cole C. Monnahan, James T. Thorson, and Trevor A.Branch (2016) Faster estimation of Bayesian models inecology using Hamiltonian Monte Carlo.https://dx.doi.org/10.1111/2041-210X.12681
Uses gradient information for more efficient samplingAugments parameter space with momentum variablesSimulation of Hamiltonian dynamics reduces random walk
Uses gradient information for more efficient samplingAlternating dynamic simulation and sampling of the energylevel
Parameters: step size, number of steps in each chainNo U-Turn Sampling (NUTS) and dynamic HMC
adaptively selects number of steps to improve robustnessand efficiencydynamic HMC refers to dynamic trajectory lengthto keep reversibility of Markov chain, need to simulate intwo directionshttp://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/
Dynamic simulation is discretizedsmall step size gives accurate simulation, but requires morelog density evaluationslarge step size reduces computation, but increasessimulation error which needs to be taken into account in theMarkov chain
Uses gradient information for more efficient samplingAlternating dynamic simulation and sampling of the energylevelParameters: step size, number of steps in each chain
No U-Turn Sampling (NUTS) and dynamic HMCadaptively selects number of steps to improve robustnessand efficiencydynamic HMC refers to dynamic trajectory lengthto keep reversibility of Markov chain, need to simulate intwo directionshttp://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/
Dynamic simulation is discretizedsmall step size gives accurate simulation, but requires morelog density evaluationslarge step size reduces computation, but increasessimulation error which needs to be taken into account in theMarkov chain
Uses gradient information for more efficient samplingAlternating dynamic simulation and sampling of the energylevelParameters: step size, number of steps in each chainNo U-Turn Sampling (NUTS) and dynamic HMC
adaptively selects number of steps to improve robustnessand efficiencydynamic HMC refers to dynamic trajectory lengthto keep reversibility of Markov chain, need to simulate intwo directionshttp://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/
Dynamic simulation is discretizedsmall step size gives accurate simulation, but requires morelog density evaluationslarge step size reduces computation, but increasessimulation error which needs to be taken into account in theMarkov chain
Uses gradient information for more efficient samplingAlternating dynamic simulation and sampling of the energylevelParameters: step size, number of steps in each chainNo U-Turn Sampling (NUTS) and dynamic HMC
adaptively selects number of steps to improve robustnessand efficiencydynamic HMC refers to dynamic trajectory lengthto keep reversibility of Markov chain, need to simulate intwo directionshttp://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/
Dynamic simulation is discretizedsmall step size gives accurate simulation, but requires morelog density evaluationslarge step size reduces computation, but increasessimulation error which needs to be taken into account in theMarkov chain
Dynamic HMC using growing tree to increase simulationtrajectory until no-U-turn criterion stopping
max treedepth to keep computation in controlpick a draw along the trajectory with probabilities adjustedto take into account the error in the discretized dynamicsimulation
Mass matrix and step size adaptation in Stanmass matrix refers to having different scaling for differentparameters and optionally also rotation to reducecorrelationsmass matrix and step size adjustment and are estimatedduring initial adaptation phasestep size is adjusted to be as big as possible while keepingdiscretization error in control
After adaptation the algorithm parameters are fixed andsome further iterations included in the warmupAfter warmup store iterations for inferenceSee more details in Stan reference manual
Dynamic HMC using growing tree to increase simulationtrajectory until no-U-turn criterion stopping
max treedepth to keep computation in controlpick a draw along the trajectory with probabilities adjustedto take into account the error in the discretized dynamicsimulation
Mass matrix and step size adaptation in Stanmass matrix refers to having different scaling for differentparameters and optionally also rotation to reducecorrelationsmass matrix and step size adjustment and are estimatedduring initial adaptation phasestep size is adjusted to be as big as possible while keepingdiscretization error in control
After adaptation the algorithm parameters are fixed andsome further iterations included in the warmupAfter warmup store iterations for inferenceSee more details in Stan reference manual
Dynamic HMC using growing tree to increase simulationtrajectory until no-U-turn criterion stopping
max treedepth to keep computation in controlpick a draw along the trajectory with probabilities adjustedto take into account the error in the discretized dynamicsimulation
Mass matrix and step size adaptation in Stanmass matrix refers to having different scaling for differentparameters and optionally also rotation to reducecorrelationsmass matrix and step size adjustment and are estimatedduring initial adaptation phasestep size is adjusted to be as big as possible while keepingdiscretization error in control
After adaptation the algorithm parameters are fixed andsome further iterations included in the warmup
After warmup store iterations for inferenceSee more details in Stan reference manual
Dynamic HMC using growing tree to increase simulationtrajectory until no-U-turn criterion stopping
max treedepth to keep computation in controlpick a draw along the trajectory with probabilities adjustedto take into account the error in the discretized dynamicsimulation
Mass matrix and step size adaptation in Stanmass matrix refers to having different scaling for differentparameters and optionally also rotation to reducecorrelationsmass matrix and step size adjustment and are estimatedduring initial adaptation phasestep size is adjusted to be as big as possible while keepingdiscretization error in control
After adaptation the algorithm parameters are fixed andsome further iterations included in the warmupAfter warmup store iterations for inference
Dynamic HMC using growing tree to increase simulationtrajectory until no-U-turn criterion stopping
max treedepth to keep computation in controlpick a draw along the trajectory with probabilities adjustedto take into account the error in the discretized dynamicsimulation
Mass matrix and step size adaptation in Stanmass matrix refers to having different scaling for differentparameters and optionally also rotation to reducecorrelationsmass matrix and step size adjustment and are estimatedduring initial adaptation phasestep size is adjusted to be as big as possible while keepingdiscretization error in control
After adaptation the algorithm parameters are fixed andsome further iterations included in the warmupAfter warmup store iterations for inferenceSee more details in Stan reference manual