What is a MonteCarloMeasurement?
There are two defined MonteCarloMeasurements that one can make:
TimeSeries: stores the entire data stream as a time record for further analysis- The memory cost is $O(N)$.
- The worst-case cost to
push!data into a (pre-allocated)TimeSeriesis ammortized at $O(1)$.
AccumulatedSeries: accumulates the data stream into aBinningAccumulatorfromOnlineLogBinning.jl.- The memory cost is $O(\log N)$.
- The worst-case cost to
push!data into a (pre-allocated)AccumulatedSeriesis also $O(\log N)$.
As one can see, there are inherent tradeoffs to saving either type of MonteCarloMeasurement generated from a simulation. A TimeSeries provides the most sweep-to-sweep information regarding the evolution of a particular measurement, but can be cost-prohibitive in the limit of long simulations with many measurements. An AccumulatedSeries, on the other hand, is incredibly cheap to store, allowing for long runs with many different observables, but no fine detail about the temporal evolution can be recovered.
In light of these tradeoffs, we recommend storing a few of the slowest-evolving (scalar) observables as TimeSeries and storing all others as AccumulatedSeries.
After one is finished push!ing data into either Series, for example at the end of a Monte Carlo random walk, either MonteCarloMeasurement can be analyzed using a binning_analysis that returns a BinningAnalysisResult from OnlineLogBinning.jl. This provides as estimate of the mean of a given observable as well the variance of the mean (var_of_mean), assuming the data stream was correlated. Additionally, it provides other information about the stream, such as the effective uncorrelated length of the stream, etc. – see OnlineLogBinning.jl: Perform the Binning Analysis for details.
We extend the Measurements.jl interface for our MonteCarloMeasurement as well by dispatching on their measurement function which transforms either a TimeSeries or an AccumulatedSeries into a Measurement. One can then make use of the Measurements.jl package's propagation of error formulas, etc., for all of one's MonteCarloMeasurements.