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Posterior Sampling

 

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Posterior sampler: Lets you choose which MCMC algorithm to use, the random walk Metropolis with a normal proposal density, the slice sampler, the random walk Metropolis with a Student-t proposal density, the fixed blocking RWM with a normal proposal density, the fixed blocking RWM with a Student-t proposal density, the random blocking RWM with a normal proposal density, or the random blocking RWM with a Student-t proposal density.
Number of posterior draws per chain: Lets you select the total number of draws from the random-walk Metropolis algorithm or slice sampler for the DSGE model and for the Gibbs sampler for the VAR model with a steady state prior. Integer values between 1,000 and 2,000,000 draws as well as values from user input are supported. The selected value is also used by the gmhmaxlik optimization procedure.
Number of posterior sample batches to save per chain: Select how many times per MCMC chain that data will be saved to disk. Integer values between 1 and 10,000 are supported.
Number of parallel chains: Select how many parallel MCMC chains that YADA should run. Integer values between 1 and 50 are supported.
Number of posterior draws discarded as burn-in period: Select how many draws from the beginning of the MCMC chain that are discarded from the sample of posterior draws. Integer values between 0 and 1,000,000 as well as values from user input are supported. The selection is also used by the gmhmaxlik optimization procedure.
Method for estimating the inverse Hessian: Choose which general method that YADA should use for setting up an estimator of the inverse Hessian to be used for the proposal density of the random walk Metropolis algorithm. The methods are: (1) Output from the optimization routine; (2) Fitting of quadratic function to evaluated log posterior around the posterior mode; (3) Finite difference method; and (4) using "My estimate". For the second routine, the diagonal of the inverse Hessian is changed, while the correlation structure of (1) remains intact. For the 4th routine, you can use your own estimate of the inverse Hessian. YADA only requires that this estimate is stored in a Matlab mat-file under the variable name ParameterCovarianceMatrix. Such a matrix can, for example, be estimated using previous posterior draws. On the View menu the function Parameter Covariance Matrix can perform this task.
Maximum absolute correlation for inverse Hessian estimator: The user can change the maximum absolute correlation for the inverse Hessian estimator. The default is No restriction, bu values between 0 and 0.95 are supported. If you select a value such as 0.95, then this is only imposed on the inverse Hessian if some correlation is greater than 0.95 in absolute terms.
Scale factor for initializing the posterior sampler: You can choose a constant for influencing how the random walk Metropolis algorithm is initialized for a single chain. Values between 0 and 4 are supported. If this constant, c0, is set to 0, then the posterior mode is used for initialization. The initial value is otherwise a draw from a normal distribution with mean equal to the posterior mode, and covariance matrix given by the square of the constant times the selected inverse Hessian.
Scale factor for the posterior sampler: The constant c is squared and multiplied by the inverse Hessian estimator for the covariance matrix of the proposal density for the random walk Metropolis algorithm. For the slice sampler the constant c is multiplied by the selected standard deviation when setting up the hyperrectangle. This controls allows you to select a suitable value for c. Values between 0.05 and 4 are supported. The selection is also used by the gmhmaxlik optimization procedure.
Weight on randomization for initial values (multiple chains): This constant is used for initializing the parameters under multiple chains. Values between 0 and 1 are supported. A value of 0 means that the chain is started at the posterior mode. For other values, the initial value is drawn from a normal distribution with mean equal to the posterior mode and covariance matrix equal to you selected inverse Hessian estimator times 4 times the weight on randomization.
Maximum number of posterior draws to use for prediction: When estimating the predictive density YADA uses simulation where the number of paths per parameter value is determined on the Forecasting frame of the Miscellaneous tab. The current control allows you to select how many draws of the parameters from the posterior distribution that will be used. Integer values between 100 and the minimum of 1,000,000 and the number of posterior draws minus the number of burn-in draws are supported. The selection of parameters is by default given by equal distance.  This means that if you have selected to use 100 parameter draws and the total number of posterior draws after the burn-in period is 10,000, the selected draws will be 100 draws apart with the used draws being 1, 101, 201, ... , 9901. An alternative selections scheme supported by YADA is to randomize among the candidate draws. Such a selection is performed if the "Randomize draws from posterior distribution" option on the Tools frame of the Miscellaneous tab is check marked. The value for this setting is also used as the default value for the number of draws  for the prior sampling function.
Percentage use of posterior draws for impulse responses, etc.: For most other distributional calculations, such as the posterior distribution of impulse responses, variance decompositions, etc., YADA computes the number of draws to use from this percentage control. For example, if you have selected 550,000 posterior draws with 50,000 burn-in draws, then selecting 1% of the draws for posterior calculations means that 5,000 draws from the post burn-in sample will be used.

 

Additional Information

A more detailed description about the random walk Metropolis algorithm is found in Section 8.1, while the slice sampler is discussed in Section 8.2 of the YADA Manual.

 

 


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