Unbounded density

Estimation ML/Bayesian estimation
21

Thank you Prof. Pfeifer for answering my question. Many people say that mh_replic=10000 is too small. Based on your experience, do we have a domain about the values of mh_replic such that the estimation is usually acceptable in this domain?

22

Again, check the convergence diagnostics and the trace_plot results. I would always request at least 500000 draws as a first step.

23

Thank you Prof. Pfeifer for answering my question. Can you please specify how to find the trace_plot results? I can only find one related command in the dynare manual. this is: “generate_trace_plots(CHAIN_NUMBER)”. How to use this command? I add this command inside the estimation() command or other places?

24

It’s a command, not an option. You can either put it into the mod-file after the estimation-command or in Matlab’s command window.

25

Dear Prof. Pfeifer,

When I try mode_coupute=5, the model did not work, and the error is “Matrix must be positive definite”. However, when I try mode_compute=6, the model worked. Generally speaking, for some values of mode_compute, the model works, but for others, the model does not work. What can we conclude from this phenomenon? Does this mean something is wrong?

Thank you,
Alex

26

That is often a sign of trouble, and you should conduct further diagnostics as discussed. There are no general lessons drawn from this.

27

Thank you Prof. Pfeifer for answering my questions. In this case, what kind of diagnostics should be conducted based on your experience?

28

The mode_check-plots.

29

Thank you Prof. Pfeifer for answering my question. One more question is that I notice that the estimation does not work sometimes, but when you change the observables, it will work. Does this mean there is something wrong or it is normal?

30

Not necessarily. That can happen due to the informativeness of the time series. But it can also be a sign of a mistake in mapping the data to the model.

31

Thank you Prof. Pfeifer for answering my question. I heard people say that if the 90% HPD interval in Bayesian estimation is too narrow, it means that the parameter estimation is not good. Is this true? if it is true, how narrow is too narrow? Is there a quantitative standard to measure the narrowness of the confidence interval?

32

That can be true if it’s caused by the poor mixing of the Metropolis-Hastings algorithm. That’s why you must check the acceptance rate and the trace_plots. There is no hard rule what “too narrow” means. But for many parameters, people have some intuition on how precisely they can be estimated. If your estimates differ in their uncertainty by an order of magnitude, you have a problem.

33

Thank you Prof. Pfeifer for answering my question. I have a few more questions:

  1. As for trace_plots, the command is
    “trace_plot(options_,M_,estim_params_,’DeepParameter’,2,’parameter_name’)”, this command can only get the plot of one parameter. If I have 20 parameters, I have to write this command 20 times with different parameters’ names. Is my understanding correct?

  2. In order to know if the estimation results are good or not, we need to check the acceptance ration, trace_plot, mode_check_plot, multivariate convergence diagnostic, and priors and posteriors plot. There are 5 indicators. However, it is really hard to get perfect results in reality. I mean it is hard to have all the 5 indicators look prefect. Given this fact, I would like to know which indicator is the most important? Is there a ranking of importance of these 5 indicators?

34
  1. See the manual on the generate_trace_plots-command.
  2. The mode_check-plots and the acceptance ratio are only relevant for efficiently obtaining good MCMC results. If the trace_plots show good mixing and the convergence diagnostics are good, then you don’t care really care about these intermediate objects. The prior/posterior-plots will typically also look decent in this case.
35

Thank you Prof. Pfeifer for answering my questions. I really appreciate it.

36

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Thank you Prof. Pfeifer for answering my question. For the convergence diagnostics, we have three results: interval, m2 and m3. What are the differences between these three? which one is the most important one?

37

See

We mostly care about the first one.

38

Thank you Prof. Pfeifer for answering my questions.