# Only prior sampled: Help to setup time series analysis with intrinsic auto-regressive model

**URL:** <https://discourse.mc-stan.org/t/only-prior-sampled-help-to-setup-time-series-analysis-with-intrinsic-auto-regressive-model/19022>\
**Category:** brms\
**Created:** [November 1, 2020, 8:08pm UTC](https://discourse.mc-stan.org/t/only-prior-sampled-help-to-setup-time-series-analysis-with-intrinsic-auto-regressive-model/19022 "2020-11-01T20:08:31Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![thauffe](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/thauffe/32/9804_2.png) [@thauffe](https://discourse.mc-stan.org/u/thauffe)\
**Post date:** [November 1, 2020, 8:08pm UTC](https://discourse.mc-stan.org/t/only-prior-sampled-help-to-setup-time-series-analysis-with-intrinsic-auto-regressive-model/19022/1 "2020-11-01T20:08:31Z")

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- Operating System: Ubuntu 16.04
- brms Version: 2.14.0

Dear forum,

I want to use brms (great package!) for an intrinsic auto-regressive model for time series analysis (see e.g. [Chen & Ficetola](https://onlinelibrary.wiley.com/doi/abs/10.1111/1755-0998.12949)).

With my current setup brms seems to sample from the prior only. Does anyone has an idea what goes wrong here?

To demonstrate the prior-only sampling, there is a sample example below.  
With the autoregressive AR(1) model, the autocorrelation is correctly inferred and the true values are correctly predicted by the FitAr1 model.  
With the intrinsic auto-regressive model, the prediction interval is the same for all data points.  
When shuffling the data (i.e. removing the temporal autocorrelation), the intrinsic auto-regressive model shows the same estimates for the autocorrelation parameter sdcar as before (FitCar2 vs. FitCar1). In contrast, the AR(1) model (FitAr2) correctly infers the lack of autocorrelation.

Thanks a lot for any suggestions,  
Torsten

```
library(brms)

# Helper function similar to 
# https://gitlab.com/wtchen/DNA_CAR_model/-/blob/master/ts_analysis.R
# but faster/less memory hungry
###########################################################
adjacency_matrix <- function(S, Degree = 1) {
  A <- matrix(0, S, S)
  for (i in 1:S) {
    BeforeDiag <- (i - Degree):(i - 1)
    BeforeDiag <- BeforeDiag[BeforeDiag >= (i - Degree) & BeforeDiag > 0]
    AfterDiag <- (i + 1):(i + Degree)
    AfterDiag <- AfterDiag[AfterDiag <= S]
    A[i, c(BeforeDiag, AfterDiag)] <- 1
  }
  return(A)
}
# Create some data
################
N <- 100
X <- seq(-5, 5, length.out = N)
Y <- 1 + 2 * X + rnorm(N, sd = 0.1)
Df <- data.frame(X = X, Y = Y, Group = "A")

AdjMat <- adjacency_matrix(N)
rownames(AdjMat) <- colnames(AdjMat) <- Df$Group 

# AR1 Model
FitAr1 <- brm(Y ~ ar(p = 1, gr = Group, cov = FALSE),
             data = Df,
             data2 = list(W = AdjMat),
             chains = 1, cores = 1)
summary(FitAr1)
# True values well predicted
head(Df)
head(predict(FitAr1)) 

# icar Model
FitCar1 <- brm(Y ~ car(W, gr = Group, type = "icar"),
              data = Df,
              data2 = list(W = AdjMat),
              chains = 1, cores = 1)
summary(FitCar1)
# High uncertainty for values
head(Df)
head(predict(FitCar1)) 

# Shuffle data (removes autocorrelation)
################################
Df <- Df[sample(N),]
# AR1 Model
FitAr2 <- brm(Y ~ ar(p = 1, gr = Group, cov = FALSE),
             data = Df,
             data2 = list(W = AdjMat),
             chains = 1, cores = 1)
# ar[1] with large uncertainty because shuffling removes autocorrelation
summary(FitAr2) 

# icar Model
FitCar2 <- brm(Y ~ car(W, gr = Group, type = "icar"),
              data = Df,
              data2 = list(W = AdjMat),
              chains = 1, cores = 1)
# Same sdcar then for FitCar1
summary(FitCar2)

```

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<div class="post-metadata">

**Author:** ![thauffe](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/thauffe/32/9804_2.png) [@thauffe](https://discourse.mc-stan.org/u/thauffe)\
**Post date:** [November 3, 2020, 8:16am UTC](https://discourse.mc-stan.org/t/only-prior-sampled-help-to-setup-time-series-analysis-with-intrinsic-auto-regressive-model/19022/2 "2020-11-03T08:16:33Z")

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I think I found the solution: The car model works when the grouping factor gr within car() is unique for each observation.

The only thing to modify in the minimal example would be:

```
Df <- data.frame(X = X, Y = Y, Group = as.character(1:N))

```

Is it possible to tag the threat with something like _solved_?

Best,  
Torsten

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**Author:** ![hhau](https://avatars.discourse-cdn.com/v4/letter/h/2bfe46/32.png) [@hhau](https://discourse.mc-stan.org/u/hhau)\
**Post date:** [November 3, 2020, 7:57pm UTC](https://discourse.mc-stan.org/t/only-prior-sampled-help-to-setup-time-series-analysis-with-intrinsic-auto-regressive-model/19022/3 "2020-11-03T19:57:07Z")

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Good to hear you found a solution.

There should be an option to mark your comment ‘as a solution’ (but I don’t think you can for your original post).