# One MCMC chain not moving

**URL:** <https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104>\
**Category:** Modeling\
**Tags:** cognitive-science\
**Created:** [October 3, 2017, 10:17pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104 "2017-10-03T22:17:35Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![wzhong](https://avatars.discourse-cdn.com/v4/letter/w/ba8739/32.png) [@wzhong](https://discourse.mc-stan.org/u/wzhong)\
**Post date:** [October 3, 2017, 10:17pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/1 "2017-10-03T22:17:35Z")

</div>

Hi,

I am fitting a complicated hierarchical reinforcement learning model, and I am having some problems with model diagnostics. Specifically, when I examine the trace plots for the group hyperparameters, one of the MCMC chains seems to be stationary for most variables (except for mu\_par[5]) while the other chains mix reasonably well (see below).

 ![stantrace_mupars](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/6/643e579bf00afcecba204da872e91590b336f53e.png)  
 ![stantrace_sigma](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/5/58818e27f644bf5d701746528a204c1ec4969676.png)

And here are the pairs plot, unfortunately the matrix is too large to fit both mu and sigma’s in the same plot…

 ![pairs_mupar](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/c/ceff15bcfd61036392376fe7d8b64edf8cfb743b.png)  
 ![pairs_sigma](https://canada1.discourse-cdn.com/flex030/uploads/mc_stan/original/2X/5/55128bf86e79adbf815947104c838be13be8bad5.png)

I placed the following priors:

```
mu_par[1:8] ~ normal(0,1);  
sigma[1:8] ~ normal(0,1);
	
mu_par[9:10] ~ normal(0,2);  
sigma[9:10] ~ cauchy(0,2);

```

And I ran the model with step size = 0.001 and adapt delta = 0.999. I also noticed that when I ran the model, one chain took less than 10 minutes to complete while the three other chains took between half-day to one day. I am wondering if it is the fast chain that is having some problem?  
I would be grateful if anyone can suggest what steps I should take to resolve this problem and what may be the cause of this issue. Thanks!

---

<div class="post-metadata">

**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [October 4, 2017, 1:35am UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/2 "2017-10-04T01:35:56Z")

</div>

> [@wzhong](#):
>
> And I ran the model with step size = 0.001 and adapt delta = 0.999. I also noticed that when I ran the model, one chain took less than 10 minutes to complete while the three other chains took between half-day to one day. I am wondering if it is the fast chain that is having some problem?

Quite likely. You can look at the list generated by `get_sampler_params()`. Presumably one chain adapted very differently than the others.

---

<div class="post-metadata">

**Author:** ![wzhong](https://avatars.discourse-cdn.com/v4/letter/w/ba8739/32.png) [@wzhong](https://discourse.mc-stan.org/u/wzhong)\
**Post date:** [October 4, 2017, 4:29pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/3 "2017-10-04T16:29:26Z")

</div>

I ran the get\_sampler\_params() on the fit object and here are the outputs. It seems the pathological chain 3 has very small step size and very high energy.

```
  [[1]]
          accept_stat __stepsize__ treedepth __n_leapfrog__ divergent __energy__
     [1,] 1 7.450581e-12 2 3 0 1.306063e+19
     [2,] 0 1.001820e-02 0 1 1 1.499753e+18
     [3,] 0 9.514925e-04 0 1 1 1.499753e+18
     [4,] 0 4.885943e-05 0 1 1 1.499753e+18
     [5,] 0 1.916193e-06 0 1 1 1.499753e+18
     [6,] 0 6.717539e-08 0 1 1 1.499753e+18
     [7,] 0 2.286806e-09 0 1 1 1.499753e+18
     [8,] 0 7.918191e-11 0 1 1 1.499753e+18
     [9,] 1 2.863701e-12 4 15 0 1.492220e+18
    [10,] 1 2.583148e-12 7 127 0 5.344301e+17
    [11,] 1 2.513133e-12 1 1 0 2.224569e+17
    [12,] 1 2.585101e-12 2 3 0 2.215456e+17
    [13,] 1 2.771415e-12 3 7 0 2.177481e+17
    [14,] 1 3.064166e-12 1 1 0 2.016586e+17
    [15,] 1 3.466581e-12 1 1 0 2.005466e+17
    [16,] 1 3.989317e-12 1 1 0 1.991385e+17
    [17,] 1 4.648851e-12 1 1 0 1.972991e+17
    [18,] 1 5.466865e-12 1 1 0 1.948461e+17
    [19,] 1 6.470127e-12 2 3 0 1.914051e+17
    [20,] 1 7.690664e-12 1 1 0 1.745322e+17
    [21,] 1 9.166097e-12 2 3 0 1.689292e+17
    [22,] 1 1.094009e-11 4 15 0 1.426225e+17
    [23,] 1 1.306289e-11 2 3 0 4.811179e+16
    [24,] 1 1.559188e-11 1 1 0 4.346739e+16
    [25,] 1 1.859224e-11 1 1 0 4.201955e+16
    [26,] 1 2.213764e-11 1 1 0 4.009627e+16
    [27,] 1 2.631089e-11 1 1 0 3.761618e+16
    [28,] 1 3.120472e-11 1 1 0 3.453972e+16
    [29,] 1 3.692251e-11 2 3 0 3.057181e+16
    [30,] 1 4.357908e-11 1 1 0 1.845041e+16

    [[2]]
          accept_stat __stepsize__ treedepth __n_leapfrog__ divergent __energy__
     [1,] 0.0000000 0.0080000000 0 1 1 220443.72
     [2,] 1.0000000 0.0016261601 3 7 0 214171.69
     [3,] 1.0000000 0.0009514925 3 7 0 116666.99
     [4,] 1.0000000 0.0007017947 5 31 0 78637.18
     [5,] 1.0000000 0.0005809276 4 15 0 33377.93
     [6,] 1.0000000 0.0005148232 4 15 0 31327.58
     [7,] 1.0000000 0.0004766819 4 15 0 27454.79
     [8,] 1.0000000 0.0004546284 4 15 0 25573.87
     [9,] 1.0000000 0.0004426525 5 31 0 25263.59
    [10,] 1.0000000 0.0004374081 5 31 0 24022.68
    [11,] 0.9999997 0.0004368918 5 31 0 23087.26
    [12,] 1.0000000 0.0004398329 5 31 0 20927.98
    [13,] 1.0000000 0.0004453883 6 63 0 19680.25
    [14,] 0.9998862 0.0004529745 6 63 0 18248.85
    [15,] 0.9999979 0.0004620113 7 127 0 16891.33
    [16,] 0.9992086 0.0004725150 8 255 0 14261.29
    [17,] 0.9914343 0.0004829221 11 2047 0 12756.67
    [18,] 0.9992218 0.0004825939 12 4095 0 11649.08
    [19,] 0.9862694 0.0004944094 13 8191 0 11048.24
    [20,] 0.9954384 0.0004874687 13 8191 0 10491.81
    [21,] 0.9990575 0.0004944489 13 8191 0 10249.38
    [22,] 0.9948989 0.0005071214 13 8191 0 10220.08
    [23,] 0.9974357 0.0005138497 13 8191 0 10171.28
    [24,] 0.9962128 0.0005246038 13 8191 0 10163.10
    [25,] 0.9955914 0.0005336683 13 8191 0 10138.83
    [26,] 0.9997636 0.0005418895 13 8191 0 10128.69
    [27,] 0.9999868 0.0005567270 13 8191 0 10086.87
    [28,] 0.9997677 0.0005721352 13 8191 0 10104.65
    [29,] 0.9973125 0.0005873873 13 8191 0 10112.70
    [30,] 0.9972249 0.0005987351 13 8191 0 10106.31

    [[3]]
          accept_stat __stepsize__ treedepth __n_leapfrog__ divergent __energy__
     [1,] 1 1.292470e-29 1 1 0 5.797633e+54
     [2,] 0 1.001820e-02 0 1 1 2.297321e+54
     [3,] 0 9.514925e-04 0 1 1 2.297321e+54
     [4,] 0 4.885943e-05 0 1 1 2.297321e+54
     [5,] 0 1.916193e-06 0 1 1 2.297321e+54
     [6,] 0 6.717539e-08 0 1 1 2.297321e+54
     [7,] 0 2.286806e-09 0 1 1 2.297321e+54
     [8,] 0 7.918191e-11 0 1 1 2.297321e+54
     [9,] 0 2.863701e-12 0 1 1 2.297321e+54
    [10,] 0 1.098229e-13 0 1 1 2.297321e+54
    [11,] 0 4.502938e-15 0 1 1 2.297321e+54
    [12,] 0 1.981857e-16 0 1 1 2.297321e+54
    [13,] 0 9.375834e-18 0 1 1 2.297321e+54
    [14,] 0 4.766257e-19 0 1 1 2.297321e+54
    [15,] 0 2.600133e-20 0 1 1 2.297321e+54
    [16,] 0 1.519193e-21 0 1 1 2.297321e+54
    [17,] 0 9.484620e-23 0 1 1 2.297321e+54
    [18,] 0 6.311388e-24 0 1 1 2.297321e+54
    [19,] 0 4.464805e-25 0 1 1 2.297321e+54
    [20,] 0 3.349092e-26 0 1 1 2.297321e+54
    [21,] 0 2.657007e-27 0 1 1 2.297321e+54
    [22,] 0 2.223961e-28 0 1 1 2.297321e+54
    [23,] 1 1.959293e-29 1 1 0 1.973148e+54
    [24,] 1 3.316111e-29 2 3 0 8.024776e+53
    [25,] 1 5.596571e-29 1 1 0 2.762145e+53
    [26,] 1 9.404855e-29 1 1 0 9.471475e+52
    [27,] 1 1.571930e-28 1 1 0 3.281367e+52
    [28,] 1 2.610904e-28 2 3 0 1.150290e+52
    [29,] 1 4.306664e-28 1 1 0 4.086772e+51
    [30,] 1 7.051335e-28 7 127 0 1.473304e+51

    [[4]]
          accept_stat __stepsize__ treedepth __n_leapfrog__ divergent __energy__
     [1,] 1 1.907349e-09 1 1 0 4.367587e+14
     [2,] 0 1.001820e-02 0 1 1 2.168011e+13
     [3,] 0 9.514925e-04 0 1 1 2.168011e+13
     [4,] 0 4.885943e-05 0 1 1 2.168011e+13
     [5,] 0 1.916193e-06 0 1 1 2.168011e+13
     [6,] 0 6.717539e-08 0 1 1 2.168011e+13
     [7,] 1 2.286806e-09 2 3 0 2.103727e+13
     [8,] 1 1.780050e-09 2 3 0 1.049278e+13
     [9,] 1 1.536878e-09 2 3 0 8.392762e+12
    [10,] 1 1.429097e-09 1 1 0 7.337860e+12
    [11,] 1 1.402603e-09 2 3 0 7.143783e+12
    [12,] 1 1.432455e-09 1 1 0 6.490294e+12
    [13,] 1 1.506772e-09 1 1 0 6.341383e+12
    [14,] 1 1.620191e-09 2 3 0 6.177983e+12
    [15,] 1 1.770938e-09 6 63 0 5.509423e+12
    [16,] 1 1.959400e-09 1 1 0 2.176023e+12
    [17,] 1 2.187394e-09 1 1 0 2.144719e+12
    [18,] 1 2.457771e-09 3 7 0 2.102302e+12
    [19,] 1 2.774181e-09 2 3 0 1.508265e+12
    [20,] 1 3.140953e-09 1 1 0 1.393930e+12
    [21,] 1 3.563005e-09 1 1 0 1.361079e+12
    [22,] 1 4.045802e-09 3 7 0 1.314966e+12
    [23,] 1 4.595326e-09 4 15 0 7.621139e+11
    [24,] 1 5.218050e-09 1 1 0 3.220273e+11
    [25,] 1 5.920936e-09 2 3 0 3.170939e+11
    [26,] 1 6.711416e-09 1 1 0 2.943347e+11
    [27,] 1 7.597392e-09 1 1 0 2.877424e+11
    [28,] 1 8.587230e-09 3 7 0 2.785319e+11
    [29,] 1 9.689752e-09 3 7 0 1.665425e+11
    [30,] 1 1.091423e-08 3 7 0 1.120353e+11

```

And also I ran get\_adaptation\_info(), it is apparent that chain 3 has different behavior than the other chains.

```
[1] "# Adaptation terminated\n# Step size = 0.0173449\n# Diagonal elements of inverse mass matrix:\n# 0.12797, 0.207466, 0.0583861, 0.262218, 0.00274245, 0.0397579, 0.00743187, 0.0350643, 0.000489024, 0.000437928, 0.022354, 0.0277263, 0.0339336, 0.0482893, 0.230905, 0.0513686, 0.0457979, 0.798876, 0.184697, 1.32798, 0.0661912, 0.0772531, 0.195713, 0.0933529, 0.217419, 0.126162, 0.0941312, 0.223627, 0.0877216, 0.128143, 0.421813, 0.0891986, 0.0764124, 0.182436, 0.0938813, 0.0874292, 0.113718, 0.072941, 0.144466, 0.08523, 1.36977, 0.161513, 0.117778, 0.0814578, 0.0813858, 0.0887076, 0.107297, 0.0942244, 0.262298, 0.0753033, 0.293906, 0.229777, 0.117618, 0.126842, 0.20437, 0.263833, 0.276794, 0.214986, 0.153346, 0.151326, 0.272189, 0.149247, 0.0896074, 0.294099, 0.341472, 0.22304, 0.517192, 0.265631, 0.285168, 0.177408, 0.0806569, 0.0603476, 0.124002, 0.166297, 0.109847, 0.119436, 0.329544, 0.212882, 0.282552, 0.245942, 0.13614, 0.114498, 0.38946, 0.148072, 0.111022, 0.107911, 0.109772, 0... <truncated>

[[2]]
[1] "# Adaptation terminated\n# Step size = 0.0209994\n# Diagonal elements of inverse mass matrix:\n# 0.115718, 0.205785, 0.0537171, 0.244166, 0.00251715, 0.030784, 0.0075802, 0.0350458, 0.000519418, 0.000411778, 0.0228099, 0.0292809, 0.0376576, 0.0442331, 0.153228, 0.0532738, 0.0496571, 1.16481, 0.158387, 1.20273, 0.0565523, 0.0919289, 0.183975, 0.0947284, 0.204828, 0.138392, 0.0980136, 0.253032, 0.0799498, 0.171863, 0.413476, 0.103841, 0.0791864, 0.158471, 0.0881689, 0.0898936, 0.0998266, 0.0648375, 0.131384, 0.0835116, 1.0458, 0.172109, 0.113653, 0.0843148, 0.0817037, 0.0844458, 0.106355, 0.090414, 0.25457, 0.0675009, 0.242018, 0.177575, 0.0974645, 0.135264, 0.262727, 0.219498, 0.294108, 0.18109, 0.134527, 0.170718, 0.252306, 0.215155, 0.0913311, 0.327824, 0.38818, 0.268098, 0.365373, 0.296492, 0.323953, 0.168218, 0.0737963, 0.0632496, 0.1028, 0.154365, 0.102654, 0.124928, 0.321451, 0.235798, 0.274926, 0.282784, 0.135013, 0.130868, 0.29872, 0.145211, 0.11884, 0.118941, 0.111523, 0.4... <truncated>

[[3]]
[1] "# Adaptation terminated\n# Step size = 4.83033e-11\n# Diagonal elements of inverse mass matrix:\n# 9.90099e-06, 9.90101e-06, 9.90099e-06, 9.90099e-06, 0.00234474, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.91011e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, 9.90099e-06, ... <truncated>

[[4]]
[1] "# Adaptation terminated\n# Step size = 0.0239955\n# Diagonal elements of inverse mass matrix:\n# 0.11274, 0.186193, 0.0549136, 0.262421, 0.00312959, 0.0360401, 0.00655043, 0.0281247, 0.000581819, 0.000432995, 0.0234177, 0.0286032, 0.036863, 0.0515373, 0.353247, 0.0465309, 0.0419241, 1.1369, 0.136503, 1.20595, 0.0570064, 0.08132, 0.208696, 0.0785333, 0.175273, 0.125332, 0.0889874, 0.315583, 0.0905617, 0.143229, 0.448736, 0.10262, 0.0840417, 0.212294, 0.0953821, 0.0848, 0.102528, 0.0618765, 0.12662, 0.0817934, 1.14671, 0.196956, 0.133612, 0.0856085, 0.0832608, 0.0957021, 0.104368, 0.0980542, 0.265415, 0.0589645, 0.288139, 0.22046, 0.132964, 0.129785, 0.318438, 0.213677, 0.299509, 0.213899, 0.12354, 0.174327, 0.279038, 0.173186, 0.0745602, 0.327956, 0.290788, 0.230392, 0.37371, 0.292577, 0.305679, 0.168716, 0.072329, 0.0526341, 0.102998, 0.152814, 0.0998614, 0.116766, 0.373235, 0.231323, 0.262656, 0.242449, 0.135874, 0.127976, 0.276872, 0.156424, 0.129711, 0.11855, 0.116443, 0.417212... <truncated>

```

What does this imply and is there any parameter I can change that can remedy this?

Thanks!

---

<div class="post-metadata">

**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [October 4, 2017, 4:37pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/4 "2017-10-04T16:37:46Z")

</div>

Often this can be avoided by specifying `init_r` to be some number less than its default value of 2. However, the fact that this issue can arise suggests that this posterior distribution is difficult to draw from (and the fact that `diverget__` is often 1 confirms it).

---

<div class="post-metadata">

**Author:** ![wzhong](https://avatars.discourse-cdn.com/v4/letter/w/ba8739/32.png) [@wzhong](https://discourse.mc-stan.org/u/wzhong)\
**Post date:** [October 4, 2017, 5:01pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/5 "2017-10-04T17:01:26Z")

</div>

Thanks, I will try that. Do I need to specify different inits for parameters too, or start with init\_r first?

---

<div class="post-metadata">

**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [October 4, 2017, 5:57pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/6 "2017-10-04T17:57:10Z")

</div>

Start with `init_r`

---

<div class="post-metadata">

**Author:** ![wlandau](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/wlandau/32/9846_2.png) [@wlandau](https://discourse.mc-stan.org/u/wlandau)\
**Post date:** [November 11, 2020, 6:17pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/7 "2020-11-11T18:17:16Z")

</div>

Are there any potential adverse consequences of setting `init_r` too low? Does it affect the distributions of the starting values for the parameters? Ideally, I would like them to be dispersed enough for potential scale reduction factors to still be valid.

---

<div class="post-metadata">

**Author:** ![bgoodri](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgoodri/32/4451_2.png) [@bgoodri](https://discourse.mc-stan.org/u/bgoodri)\
**Post date:** [November 11, 2020, 11:31pm UTC](https://discourse.mc-stan.org/t/one-mcmc-chain-not-moving/2104/8 "2020-11-11T23:31:12Z")

</div>

You might miss a mode, but I would say in general that the default value of `init_r` of 2 is more likely to be too big than too small.