使用贝叶斯推理寻找变量之间的关系

Question

我有很多数据，如下图，它们之间有关系。我想做一个方程来描述这种关系，比如 Power = a * WindSpeed ^ b 。如何使用贝叶斯推理找到 a 和 b？我想为此使用 R。

Answer 1

欢迎来到 SO，祝你好运。不要忘记关注评论（它们真的很相关，你可以增加获得答案的可能性）。请参阅下面使用 Bolstadt 包使用贝叶斯单变量回归的示例。

library(Bolstad)

# Simulation of Power vs Wind
# Power = 5 * Windspeed ^ 2
set.seed(123)
n <- 100

# y = Power
# x = WindSpeed
# e = error term

x <- (1:(25 * n))/ n
e <- rnorm(length(x)) / 10

# y = a * x ^ b
# log(y) = log(a) + b * log(x) + e  
# or
# in exponential form
y <- exp(log(5) + e) * x ^ 2

# bayes univariate linear regression model
z <- bayes.lin.reg(log(y), log(x))
# Standard deviation of residuals:  0.0943 
# Posterior Mean Posterior Std. Deviation
# -------------- ------------------------
#   Intercept:  6.076          0.0059657               
#   Slope:      1.996          0.0062209

# ------------------------------------------------
# pay attention the result of bayession regression
# are shifted for intercept by the mean
# is is accouted as below
intercept_shifted <- z$intercept$mean - z$slope$mean * mean(log(x))
intercept_shifted
# [1] 1.617218

# validate by standar linear model:
lm(log(y) ~ log(x))
# Coefficients:
#  (Intercept)       log(x)  
#  1.617        1.996  

a = exp(intercept_shifted) 
a
# [1] 5.039051
b = z$slope$mean
b
# [1] 1.996134

使用贝叶斯推理寻找变量之间的关系

Use bayesian inference to find relationship between variables

r

relationship

bayesian

inference