# Bimodal Posteriors

**URL:** <https://forum.dynare.org/t/bimodal-posteriors/3536>\
**Category:** Dynare help (legacy posts)\
**Created:** [3 December 2013 13:01 UTC](https://forum.dynare.org/t/bimodal-posteriors/3536 "2013-12-03T13:01:04Z")\
**Posts on this page:** 1\
**Showing post:** 1

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**Author:** ![joepearlman1](https://forum.dynare.org/letter_avatar_proxy/v4/letter/j/b77776/32.png) [@joepearlman1](https://forum.dynare.org/u/joepearlman1)\
**Post date:** [3 December 2013 13:01 UTC](https://forum.dynare.org/t/bimodal-posteriors/3536/1 "2013-12-03T13:01:04Z")

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I wanted to test whether Dynare could estimate a non-invertible MA process, in particular y=eps-theta\*eps(-1), where theta\>1. I generated this process, and then estimated the parameters using the modfile below. The process was generated for 1000 periods using theta=0.5 and var(eps)=1.

First of all, the result is that it did estimate the non-invertible process (although using different priors I could get Dynare to estimate the equivalent invertible process).

However, what I would have anticipated is that since I used a flat prior (the uniform distribution) for the standard error, that the posterior would have been bimodal, with approximately equal likelihoods at theta and 1/theta. Instead the posterior was almost vertical at theta.

I have recently been wondering why it is that I so rarely see bimodal or indeed multimodal priors, and this adds to the mystery.

MODFILE:

//Simple MA(1) model

var y x;  
varexo eps;

parameters rho;  
rho = 0.90;

model;  
x = eps;  
y = -rho\*x(-1)+eps;  
end;

shocks;  
var eps; stderr 1;  
end;

steady;  
check;

estimated\_params;

//stderr eps, INV\_GAMMA\_PDF,1,200; //technology  
stderr eps, UNIFORM\_PDF,0.001,5; //technology  
//rho, BETA\_PDF, 0.4,0.2; //AR1 technology  
rho, NORMAL\_PDF, 1.25,2; //AR1 technology

end;

//stoch\_simul(irf=10) x y;  
varobs y;

estimation(datafile=y,mode\_compute=4,nobs=1000,  
prefilter=0,mh\_replic=5000,mh\_nblocks=2,mh\_jscale=0.40,mh\_drop=0.2);

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