Did anyone ever make any progress on this? I’d like to have an estimator that’s consistent with what is outlined in the Flegal & Jones paper.

It’s a little unclear to me from the documentation which method it uses for estimating the statistic. Also, I don’t want to switch over entirely to `MCMCChains`

- is there a way to call the autocorrelation time function on a given time series (of scalars)?

I understand why you may not want to commit the a Chain object in MCMCChains. About a year ago, the package maintainers split the diagnostics from MCMCChains and put them in standalone package: GitHub - TuringLang/MCMCDiagnosticTools.jl

I think this should have the features you want.

Indeed, this might be what I want, but I’m unsure of how to use it without falling back to the `chain`

datastructure. For instance, how would I get `MCMCDiagnosticTools`

to work with the following?

```
samples = cumsum(randn(10000));
ess_hat(samples)
```

just generates an error:

```
ERROR: MethodError: no method matching ess_rhat(::Vector{Float64})
Closest candidates are:
ess_rhat(::AbstractArray{<:Union{Missing, Real}, 3}; method, maxlag) at ~/.julia/packages/MCMCDiagnosticTools/kKCOf/src/ess.jl:208
Stacktrace:
[1] top-level scope
@ REPL[12]:1
```

According to the documentation, the function expects a three dimensional array.

```
help?> ess_rhat
search:
ess_rhat(
samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
)
Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the
method and a maximum lag of maxlag.
See also: ESSMethod, FFTESSMethod, BDAESSMethod
```

**Example**

```
using MCMCDiagnosticTools: ess_rhat
x = rand(1000, 10, 3)
ess,rhat = ess_rhat(x)
```

In your example, you do the following:

```
using MCMCDiagnosticTools: ess_rhat
samples = cumsum(randn(10000, 1, 1), dims=1);
ess,rhat = ess_rhat(samples)
```

You can also add more dimensions outside of `cumsum`

:

```
samples = [samples ;;;]
ess,rhat = ess_rhat(samples)
```