Python 如何在R中构造易于扩展的蒙特卡罗模型
我有一个简单的公司模型，它有两个农场，每个农场种两种作物（苹果和梨）。第一步是将树的数量乘以每棵树上的果实数量 模拟每棵树上的果实数量（跨农场和作物） 在R中建模时，我至少面临三个决策：Python 如何在R中构造易于扩展的蒙特卡罗模型,python,r,simulation,montecarlo,Python,R,Simulation,Montecarlo,我有一个简单的公司模型，它有两个农场，每个农场种两种作物（苹果和梨）。第一步是将树的数量乘以每棵树上的果实数量 模拟每棵树上的果实数量（跨农场和作物） 在R中建模时，我至少面临三个决策： 如何构造变量 如何模拟 如何将模拟变量与非模拟变量相乘 我希望即使我添加了另一种作物和/或农场，它也能工作——理想情况下，即使我添加了另一个维度，例如作物品种（Granny Smith等）。我还想按名称而不是索引号来指代农场和农作物 以下是我提出的方法。这是可行的，但很难添加另一个维度，而且代码也很多。有没
- 如何构造变量
- 如何模拟
- 如何将模拟变量与非模拟变量相乘
farms <- c('Farm 1', 'Farm 2');
crops <- c('Pear', 'Apple');
params <- c('mean','sd');
numTrees <- array(0, dim=c(length(farms), length(crops)), dimnames=list(farms,crops));
fruitPerTree <- array(0, dim=c(length(farms), length(varieties), length(params)),
dimnames=list(farms,varieties,params));
# input data e.g.
numTrees['Farm 1', 'Pear'] = 100
# and
fruitPerTree['Farm 1', 'Pear', 'mean'] = 50
fruit_per_tree = {}
fruit_per_tree[('Farm 1', 'Pear')] = (50, 15) # normal params
sim_fruit_per_tree = {key: random.normal(*params, size=num_sims)
for key, params in fruit_per_tree.items() }
sim_total_fruit = {key: sim_fruit_per_tree[key]*num_trees[key] for key in num_trees }
在R中也有简单的方法吗？谢谢 以下是我将如何设置这样的模拟：
#for reproducibility
set.seed(42)
#data
farms <- data.frame(farm=rep(1:2, each=2),
trees=sample(100, 4),
crop=rep(c("pear", "apple")),
mean=c(100, 200, 70, 120),
sd=c(30, 15, 25, 20))
#n
n <- 100
#simulation
fruits <- t(matrix(rnorm(n*nrow(farms), farms$mean, farms$sd), ncol=n))
#check
colMeans(fruits)
#[1] 101.10215 200.06649 68.01185 120.05096
library(reshape2)
fruits <- melt(fruits, value.name="harvest_per_tree")
farms$i <- seq_len(nrow(farms))
farm_sim <- merge(farms, fruits, by.x="i", by.y="Var2", all=TRUE)
names(farm_sim)[7] <- "sim_i"
#multiply with number of trees
farm_sim$harvest_total <- farm_sim$harvest_per_tree * farm_sim$trees
head(farm_sim)
# i farm trees crop mean sd sim_i harvest_per_tree harvest_total
# 1 1 1 92 pear 100 30 1 110.89385 10202.234
# 2 1 1 92 pear 100 30 2 145.34566 13371.801
# 3 1 1 92 pear 100 30 3 139.14609 12801.440
# 4 1 1 92 pear 100 30 4 96.00036 8832.033
# 5 1 1 92 pear 100 30 5 26.78599 2464.311
# 6 1 1 92 pear 100 30 6 94.84248 8725.508
library(ggplot2)
ggplot(farm_sim, aes(x=sim_i, y=harvest_total, colour=factor(farm))) +
geom_line() +
facet_wrap(~crop)
#用于再现性
种子（42）
#资料
农场如果我理解正确，您将对n个农场的水果总产量进行建模，每个农场都有k种作物（这里，n=k=2）。每个农场都有一些不同品种的树木，每个农场的生产力（果实/树木）是一个随机变量，分布在N（μ，σ）上，其中μ和σ取决于农场和品种
因此，对于输入，我们构造了一个数据框，params
，包含5列：农场、作物、树木、平均值和sd
。然后，每行包含给定农场/作物组合的树数、每棵树的平均生产率和每棵树的生产率变化。这些是输入
如果我们在树的层次上建模，那么给定农场中给定品种的每棵树的果实产量为：
rnorm(trees,mean,sd)
也就是说，输出是长度=#树的随机样本，平均值和sd适合给定的品种和农场。那么这个品种/农场所有树木的总产量就是上面向量的总和，总产量就是所有农场/作物的总和
所有这些都给了我们一次蒙特卡罗模型的迭代。为了确定总产出的分布，我们必须重复这个过程若干次。幸运的是，在R中，这相当简单：
set.seed(1)
farms <- c('Farm 1', 'Farm 2')
crops <- c('Pear', 'Apple')
params <- expand.grid(farms=farms,crops=crops)
params$trees<- 100
params$mean <- 50
params$sd <- 10
n.iterations<- 1000
output <- function(i,p) {
pp <- p[3:5] # trees, mean, sd for each farm/crop
# fruit = total output for each farm/crop combination
fruit <- colSums(apply(pp,1,function(x)rnorm(x[1],x[2],x[3])))
return(sum(fruit)) # grand total output
}
dist <- sapply(1:n.iterations,output,params)
print(c(mean=mean(dist),sd=sd(dist)),quotes=F,digits=4)
# mean sd
# 19997.5 198.8
hist(dist, main="Distribution of Total Output",
sub=paste(n.iterations,"Iterations"),xlab="Total Fruit Output")
最后，我敦促大家考虑每棵树的输出比正常情况更可能是泊松分布。如果使用rpois（…）
而不是rnorm（…）
重新运行模拟，则总体sd会稍低（~150而不是~200）。以下是我的问题的一般解决方案。我从罗兰的方法开始，并对其进行了更新，使分布、参数和尺寸都可以轻松更改
distSim <- function(nSims, simName, distFn, dimList, paramList, constList) {
#
# Simulate from a distribution across all the dimensions.
#
# Args:
# nSims: integer, e.g. 10000
# simName: name of the output column, e.g. 'harvestPerTree'
# distFn: distribution function, e.g. rnorm
# dimList: list of dimensions,
# e.g. list(farms=c('farm A', 'farm B'), crops=c('apple', 'pear', 'durian'))
# paramList: list of parameters, each of length = product(length(d) for d in dimList),
# to be passed to the distribution function,
# e.g. list(mean=c(10,20,30,5,10,15), sd=c(2,4,6,1,2,3))
# constList: optional vector of length = product(length(d) for d in dimList)
# these are included in the output dataframe
# e.g. list(nTrees=c(10,20,30,1,2,3))
#
# Returns:
# a dataframe with one row per iteration x product(d in dimList)
#
# expand out the dimensions into a dataframe grid - one row per combination
df <- do.call(expand.grid, dimList);
nRows <- nrow(df);
# add the parameters, and constants, if present
df <- cbind(df, paramList);
if (!missing(constList)) {
df <- cbind(df, constList);
}
# repeat this dataframe for each iteration of the simulation
df <- do.call("rbind",replicate(nSims, df, simplify=FALSE));
# add a new column giving the iteration number ('simId')
simId <- sort(rep(seq(1:nSims),nRows));
df <- cbind(simId, df);
# simulate from the distribution
df[simName] <- do.call(distFn, c(list(n=nrow(df)), df[names(paramList)]))
return(df);
}
还要注意的是，您还可以以一种很好的索引方式定义输入值；e、 g.如果你定义
numTrees2 <- array(0, dim=c(length(farms), length(crops)), dimnames=tree_dimList);
numTrees2['Farm A','apple'] = 200;
# etc
numTrees2循环不需要rnorm
完全矢量化，并接受mean
和sd
的矢量。另外，我可能不会在这里使用数组。长格式的data.frame或data.table应该更容易使用。我只能重复：不需要循环。一次调用rnorm
（或rpois
）就足够了。谢谢你-我喜欢你的方法，尽管罗兰的方法更符合我的想法。非常感谢！谢谢罗兰。我将修改您的答案，以避免使用重塑命令：farms
gg <- do.call(rbind,
lapply(c(100,1000,10000),
function(n)cbind(n=n,total=sapply(1:n,output,params))))
gg <- data.frame(gg)
library(ggplot2)
ggplot(gg)+
geom_histogram(aes(x=total, y=..density.., fill=factor(n)))+
scale_fill_discrete("Iterations")+
facet_wrap(~n)
distSim <- function(nSims, simName, distFn, dimList, paramList, constList) {
#
# Simulate from a distribution across all the dimensions.
#
# Args:
# nSims: integer, e.g. 10000
# simName: name of the output column, e.g. 'harvestPerTree'
# distFn: distribution function, e.g. rnorm
# dimList: list of dimensions,
# e.g. list(farms=c('farm A', 'farm B'), crops=c('apple', 'pear', 'durian'))
# paramList: list of parameters, each of length = product(length(d) for d in dimList),
# to be passed to the distribution function,
# e.g. list(mean=c(10,20,30,5,10,15), sd=c(2,4,6,1,2,3))
# constList: optional vector of length = product(length(d) for d in dimList)
# these are included in the output dataframe
# e.g. list(nTrees=c(10,20,30,1,2,3))
#
# Returns:
# a dataframe with one row per iteration x product(d in dimList)
#
# expand out the dimensions into a dataframe grid - one row per combination
df <- do.call(expand.grid, dimList);
nRows <- nrow(df);
# add the parameters, and constants, if present
df <- cbind(df, paramList);
if (!missing(constList)) {
df <- cbind(df, constList);
}
# repeat this dataframe for each iteration of the simulation
df <- do.call("rbind",replicate(nSims, df, simplify=FALSE));
# add a new column giving the iteration number ('simId')
simId <- sort(rep(seq(1:nSims),nRows));
df <- cbind(simId, df);
# simulate from the distribution
df[simName] <- do.call(distFn, c(list(n=nrow(df)), df[names(paramList)]))
return(df);
}
dimList <- list(farms=c('farm A', 'farm B'), crops=c('apple', 'pear', 'durian'));
constList <- list(numTrees=c(10,20,30,1,2,3));
paramList <- list(mean=c(10,20,30,5,10,15), sd=c(2,4,6,1,2,3));
distSim(nSims=3, simName='harvestPerTree', distFn=rnorm, dimList=dimList,
paramList=paramList, constList=constList);
simId farms crops mean sd numTrees harvestPerTree
1 1 farm A apple 10 2 10 9.602849
2 1 farm B apple 20 4 20 20.153225
3 1 farm A pear 30 6 30 25.839825
4 1 farm B pear 5 1 1 1.733120
5 1 farm A durian 10 2 2 13.506135
6 1 farm B durian 15 3 3 11.690910
7 2 farm A apple 10 2 10 7.678611
8 2 farm B apple 20 4 20 22.119560
9 2 farm A pear 30 6 30 31.488002
10 2 farm B pear 5 1 1 5.366725
11 2 farm A durian 10 2 2 6.333747
12 2 farm B durian 15 3 3 13.918085
13 3 farm A apple 10 2 10 10.387194
14 3 farm B apple 20 4 20 21.086388
15 3 farm A pear 30 6 30 34.076926
16 3 farm B pear 5 1 1 6.159415
17 3 farm A durian 10 2 2 8.322902
18 3 farm B durian 15 3 3 9.458085
numTrees2 <- array(0, dim=c(length(farms), length(crops)), dimnames=tree_dimList);
numTrees2['Farm A','apple'] = 200;
# etc