metropolis_hastings() running too slow

[caioodantas]

I'm estimating an AnSchorheide-like model (available here: https://github.com/caioodantas/Behavioral-New-Keynesian-Model) but the runtime (10 hours predicted) is higher than what I get using Dynare (3 hours).

I'm using the following custom settings:

m <= Setting(:data_vintage, "820102") m <= Setting(:date_forecast_start, quartertodate("2007-Q4")) m <= Setting(:n_mh_simulations, 250000) m <= Setting(:n_mh_blocks, 5) m <= Setting(:mh_thin, 4) m <= Setting(:use_population_forecast, false) # Population forecast not available as data to turn off m <= Setting(:mh_cc, 0.6, "Jump size for Metropolis-Hastings (after initialization)")

Is there a way to speed up this process?

In Dynare I was using only 1 block with 1,250,000 simulations(replics), but when I try to use n_mh_simulations=1250000 in Julia I get:

ERROR: LoadError: InexactError: check_top_bit(UInt64, -1250000) Stacktrace: [1] throw_inexacterror(::Symbol, ::Type{UInt64}, ::Int64) at .\boot.jl:558 [2] check_top_bit at .\boot.jl:572 [inlined] [3] toUInt64 at .\boot.jl:683 [inlined] [4] UInt64 at .\boot.jl:713 [inlined] [5] convert at .\number.jl:7 [inlined] [6] setindex! at .\array.jl:847 [inlined] [7] _dataspace(::Tuple{Int64,Int64}, ::Tuple{}) at C:\Users\Samsung\.julia\packages\HDF5\T1b9x\src\HDF5.jl:1221

[chenwilliam77]

1. The setting :n_mh_blocks actually refers to the number of HDF5 blocks to be used, for memory reasons. The Setting :n_mh_param_blocks is probably the correct equivalent since I presume you're comparing parameter blocking. Furthermore, the setting :n_mh_simulations is the number of draws per block. Just making sure this is clear. You can check lines 116-136 in DSGE/src/defaults.jl to see descriptions on the Metropolis-Hastings settings.

2. I'm not sure why you're getting that error when using n_mh_simulations = 1250000 , but I suspect it's due to memory problems.

3. What data are you using? The data vintage you're using seems to not result in a working dataset for me.

4. I tried estimating your model. First, the rejection rate seems quite high given your choice of mh_cc (I get about 80-90%). Lowering mh_cc to .05 produces a rejection rate of 31% on average. Second, I get a time of roughly 1 - 1.2 min per 10000 draws (1000 draws per block for 10 blocks, where "block" here is a block of the HDF5 file being created), which would imply 2-2.5 hours for a Metropolis-Hastings estimation yielding 1.25 million draws (though it is possible that my machine is faster than yours).

I then also started an estimation of 10,000 draws per block, for 125 blocks, to get 1.25 million total draws (inclusive of draws that would be burned). My estimated runtime is 2 hours and 1 minute (takes about 1 minute per block).

My estimation script (after adding your Gabaix model to my local version of DSGE.jl)

using DSGE, ModelConstructors
m = Gabaix()
m <= Setting(:data_vintage, "181115")
m <= Setting(:date_forecast_start, quartertodate("2007-Q4"))
m <= Setting(:n_mh_simulations, 1000)
m <= Setting(:n_mh_blocks, 10)
m <= Setting(:mh_thin, 4)
m <= Setting(:mh_cc, .05)
df = load_data(m; try_disk = false, summary_statistics = :none)
data = df_to_matrix(m, df)
estimate(m, data)

5. It may be helpful if you could run

using DSGE, BenchmarkTools
m = Gabaix()
m <= Setting(:data_vintage, "181115")
m <= Setting(:date_forecast_start, quartertodate("2007-Q4"))
df = load_data(m; try_disk = false, summary_statistics = :none)
data = df_to_matrix(m, df)

@btime begin
    posterior(m, data)
end

I get 3.33 ms for the time it takes to calculate the log posterior once. This will help us get a sense of the difference in machine speed.

[caioodantas]

Thanks again, William.

The date start really didn't make sense. While the tests below were done using :date_forecast_start, quartertodate("2007-Q4"), the period I'm interested in is actually :date_forecast_start,quartertodate("1982-Q1")`.

In the speed test you suggested, I got 3.38 ms, so the remaining runtime difference might be due to our machines.

Using m <= Setting(:n_mh_simulations, 1000) m <= Setting(:n_mh_blocks, 10) I got 117 seconds, so it would take about 4 hours to complete the 1.25 million draws. Using 1982 as the starting date I get 137 seconds.

I didn't really get your point about :n_mh_param_blocks. Is there a function for automatic parameter blocking or should I just try multiple values out?

[chenwilliam77]

1. So you want to estimate the model on data from 1959:Q1 to 1981:Q4, with a forecast starting in 1982:Q1, correct? Note that after transformations, the data matrix seen by the estimation will just range from 1959:Q3 to 1981:Q4 since the first two quarters are used to calculate growth numbers (e.g. the GDP level is transformed to GDP growth). Just making sure you're setting up the data correctly.

2. Can you post your entire estimation script? I just want to be certain that any differences in timing between my results and yours are due to machine differences. I am mildly surprised that your machine is twice as slow when the calculation time of the posterior is almost identical.

3. There is "naive" automatic parameter blocking available. By default, we have

   m <= Setting(:n_mh_param_blocks, 1)

   meaning there is only one parameter block, as is the standard case for random-walk MH. However, it is known that blocking parameters can improve sampling efficiency. Since the FRBNY DSGE team has mostly moved toward using our SMC algorithm, we only got around to implementing a very naive parameter blocking scheme, which randomly allocates parameters into :n_mh_param_blocks (see generate_param_blocks) and updates each block on their own. So if you set

   m <= Setting(:n_mh_param_blocks, 5)

   our MH algorithm will randomly split the parameters of your model into 5 blocks during the set up of the algorithm and will block-update during sampling.

[caioodantas]

I did get a bit confused with the date specification, but the period I'm interested in is actually 1982:Q1 to 2007:Q4, so a bit longer than the one I was using before. Nevertheless, using 125 blocks of 10,000 draws I got it to run in 118 minutes.

I tried using m <= Setting(:n_mh_param_blocks, 5), but it ended up slowing the process down. I might try other values later.

The script I'm using now is

m = XGabaix() m <= Setting(:date_presample_start, quartertodate("1982-Q1")) m <= Setting(:date_forecast_start, quartertodate("2008-Q1")) m <= Setting(:n_mh_simulations, 10000) m <= Setting(:n_mh_blocks, 125) m <= Setting(:mh_thin, 4) m <= Setting(:mh_cc, .06) m <= Setting(:use_population_forecast, false) @time begin df = load_data(m, try_disk = false, check_empty_columns = false, summary_statistics = :none) data = df_to_matrix(m, df) estimate(m, data) end

Strangely, I'm not getting rejection rates as high as you reported with mh_cc=.06.

[chenwilliam77]

1. The mh_cc you originally reported was 0.6 (see your first post). A mh_cc = .06 is close to the one I ended up using (.05).

2. Your script looks fine. Glad to hear the estimation finished in 2 hours (and is thus faster than Dynare)

3. I would assume that parameter blocking will generally slow down the estimation because for each block draw you need to evaluate the likelihood. So a sample from the posterior with 5 blocks involves 5 calls of the likelihood. The gains from parameter blocking are in terms of efficiency, i.e. for the same number of draws, you're more likely to get a higher effective sample size per draw with blocking than without it. The gain in runtime from parameter blocking occurs from the fact that you can generally run MH for shorter chains due to the higher effective sample size per draw. I believe MCMCDiagnostics.jl should have some useful tools for assessing ESS. A relevant paper about blocking is this one.

[chenwilliam77]

Hi caioodantas,

I just remembered another feature of the DSGE.jl code which may suggest our code is even faster than Dynare. I don't know how the Dynare code for estimation works since I haven't looked into it, but the number of simulations (i.e. n_mh_simulations) in DSGE.jl will be the number of draws post-thinning. In other words, if you specify mh_thin = 4 as well as n_mh_simulations = 10000, under the hood, we are actually taking 40,000 draws and saving only every fourth draw. So if the Dynare code you ran that took 3 hours does not thin during the algorithm itself (i.e. run a total of 4 * 1,250,000 = 5,000,000 draws), then the DSGE.jl code should be even faster compared to Dynare.