MonteCarlo | Notes for Monte Carlo and implementations of algorithms

update:

My compilation command is ghc -O2 Montecarlo.hs. My random version is random-1.1, ghc version is 8.6.4, and my system is macOS Big Sur 11.1 (Intel chip). The command I used to test the speed is time ./Montecarlo 10000000, and the result it returns is real 0m17.463s, user 0m17.176s, sys 0m0.162s.

The following is a Haskell program that uses Monte Carlo to calculate pi. However, when the input is 10 million, the program ran for 20 seconds. The C program written in the same logic took only 0.206 seconds. Why is this, and how can I speed it up? Thank you all.

This is the Haskell version:

I'm trying to translate a pandas query into a SQL(ite) query. The main issue in my translation to SQL is trying to place a limit in a group.

Here is a setup (in python) of an example database.

I am using a Montecarlo simulation for predicting mpg in the mtcars data. I want to extract the coefficients of all the variables in the dataframe to compute how many times each car has lower mpg than the other car. For example how many times Toyota Corona has less predicted mpg than Datsun 710. This is my initial code using only two independent variables. I want to expand this selection to use all the variables in the data frame without manually have to include all the variables in the data frame. Is there any way I can do this?

What I am looking for is for a method in Python or any other way to solve this, for what I know there is one method, but I couldn't find it, in context what I am doing is calculate the probability of a pair, two pairs etc to appear in a poker play using Montecarlo method, at the moment I'm using the random.sample function to do that, but I want to use my own methods to generate random numbers that return numbers between 0-1, and I want to use Discrete Uniform Distribution in order to be sure that every number has the same probability to appear.

I apreciate any help you can give.

I am using the mob() function from partykit package and I am getting some problems when parsing the obtained model.

My main aim is to check approximately how large a sample size needs to be in order to detect the real structure of a data generating process (DGP) when breaks are present.

The code below performs a Montecarlo simulation of data with breaks and tries to identify if the break was captured by the M-fluctuation test or not.

More specifically, I want to make a count on the number of times over the total number of simulations (nreps) that the model actually captures the DGP, conditional on a fixed sample size (N) to get a feeling of how many data should I need to capture the real DGP.

At the end of the code, you can see the list that I get out of my simulations. The problem is that I cannot recover the information displayed on the console.

Additionally, I have some doubts about how to make the count of the "correctly identified models". For now, what I have in mind is to count as positive if the model has a break into the correct variable (z1) at the specified region (z1>0) with some tolerance into the break region for example if the break is at z1>0.1 or z1>-0.4 it is also valid as a positive for me. Therefore, is there any simple way of counting the models that have the stated characteristics?

I hope my example is clear enough for you to help me out. Thank you a lot in advance.

1. Ingredients to generate the DGP.

I'm trying to do a multiprocessed version of Monte Carlo Pi calculation.

However, I always get an error that says

TypeError: map() missing 1 required positional argument: 'iterable'

I read that the error can be fixed by using starmap but it doesn't work either for some reason.

I am searching for an equivalent function in R of the extremely convenient Stata command simulate. The command basically allows you to declare a program (reg_simulation in the example below) and then invoke such a program from simulate and store desired outputs.

Below is a Stata illustration of the usage of the simulate program, together with my attempt to replicate it using R.

Finally, my main question is: is this how R users will run a Montecarlo simulation? or am I missing something in terms of structure or speed bottlenecks? Thank you a lot in advance.

1. Defining reg_simulation program.

I want to use MonteCarlo function in MonteCarlo package in R which has one requirement among others as supply just one single function into the MonteCarlo package.

To run a simulation study, the user has to nest both - the generation of a sample and the calculation of the desired statistics from this sample - in a single function. This function is passed to MonteCarlo(). No additional programming is required (Vignette: The MonteCarlo Package).

Contrary to this vital condition, I have two different functions that suit my algorithm. I have used the MonteCarlo function as provided by the correct answer in this question for a method.

I want to use a different method thus, I write the following functions (function1 and function2) for it to be passed to MonteCarlo function as demonstrated below:

Here is the algorithm of what I want to do with R:

1. Simulate 10 time series data set from ARIMA model through arima.sim() function
2. Split the series into overlapping sub-series of possible 2s, 3s, 4s, 5s, 6s, 7s, 8s, and 9s.
3. For each size take a resample the blocks with replacement, for new series and obtain the best ARIMA model from the subseries from each block size through auto.arima() function.
4. Obtain for each subseries of each block sizes RMSE.

The below R functions get that done.

Here is the algorithm of what I want to do with R:

1. Simulate 10 time series data set from ARIMA model through arima.sim() function
2. Split the series into sub-series of possible 2s, 3s, 4s, 5s, 6s, 7s, 8s, and 9s.
3. For each size take a resample the blocks with replacement, for new series and obtain the best ARIMA model from the subseries from each block size through auto.arima() function.
4. Obtain for each subseries of each block sizes RMSE.

The below R function get that done.