ACSS algorithm

Description

Adaptive Correlated Spike and Slab (ACSS) algorithm with/without adaptive burn-in Gibbs sampler. See paper of Yang, Z., Khare, K., & Michailidis, G. (2024) for details.

Usage

ACSS_gs(
  Y,
  X,
  a = 1,
  b = 1,
  c = 1,
  s,
  Max_burnin = 10,
  nmc = 5000,
  adaptive_burn_in = TRUE
)

Arguments

Value

A list with betahat: predicted beta hat from majority voting, and Gibbs_res: 5000 samples of beta, q and lambda^2 from Gibbs sampler.

Examples

## A toy example is given below to save time. The full example can be run to get better results
## by using X instead of X[, 1:30] and let nmc=5000 (default).

n = 30;
p = 2 * n;

beta1 = rep(0.1, p);
beta2 = c(rep(0.2, p / 2), rep(0, p / 2));
beta3 = c(rep(0.15, 3 * p / 4), rep(0, ceiling(p / 4)));
beta4 = c(rep(1, p / 4), rep(0, ceiling(3 * p / 4)));
beta5 = c(rep(3, ceiling(p / 20)), rep(0 , 19 * p / 20));
betas = list(beta1, beta3, beta2, beta4, beta5);

set.seed(123);
X = matrix(rnorm(n * p), n, p);
Y = c(X %*% betas[[1]] + rnorm(n));

## A toy example with p=30, total Gibbs steps=1100, takes ~0.6s
system.time({mod = ACSS_gs(Y, X[, 1:30], 1, 1, 1, sqrt(p), nmc = 100);})

mod$beta; ## estimated beta after the Majority voting
hist(mod$Gibbs_res$betamat[1,]); ## histogram of the beta_1
hist(mod$Gibbs_res$q); ## histogram of the q
hist(log(mod$Gibbs_res$lambdasq)); ## histogram of the log(lambda^2)
plot(mod$Gibbs_res$q); ## trace plot of the q
## joint posterior of model density and shrinkage
plot(log(mod$Gibbs_res$q / (1 - mod$Gibbs_res$q)), -log(mod$Gibbs_res$lambdasq),
    xlab = "logit(q)", ylab = "-log(lambda^2)",
    main = "Joint Posterior of Model Density and Shrinkage"); 

Economic data from the GLP paper

Description

A list contains the five data set used in the paper of Giannone, Lenza, and Primiceri (2021). Contains the following data sets: Macro1, Macro2, Micro1, Micro2, and Finance1

Usage

Econ_data

Format

## 'Econ_data' A list contains the five lists, as the 5 data sets

Macro1

A list with a vector and a data frame, 'Y' and 'X'. 'Y' is the response vector, with 659 observations in it. 'X' is the data frame contains all predictors, with n=659, p=130. It have the structure of time series data.

Macro2

A list with a vector and a data frame, 'Y' and 'X'. 'Y' is the response vector, with 90 observations in it. 'X' is the data frame contains all predictors, with n=90, p=69. It have the structure of sectional data.

Micro1

A list with a vector and a data frame, 'Y' and 'X'. 'Y' is the response vector, with 576 observations in it. 'X' is the data frame contains all predictors, with n=576, p=285. It have the structure of panel data with 48 units on 12 time points.

Micro2

A list with a vector and a data frame, 'Y' and 'X'. 'Y' is the response vector, with 312 observations in it. 'X' is the data frame contains all predictors, with n=312, p=138. It have the structure of panel data with 12 units on 26 time points.

Finance1

A list with a vector and a data frame, 'Y' and 'X'. 'Y' is the response vector, with 68 observations in it. 'X' is the data frame contains all predictors, with n=68, p=16. It have the structure of time series data.

Source

<https://www.econometricsociety.org/publications/econometrica/2021/09/01/economic-predictions-big-data-illusion-sparsity/supp/17842_Data_and_Programs.zip>

<https://research.stlouisfed.org/econ/mccracken/fred-databases/>

GLP algorithm

Description

Giannone, Lenza and Primiceri (GLP) algorithm with/without adaptive burn-in Gibbs sampler. See paper Giannone, D., Lenza, M., & Primiceri, G. E. (2021) and Yang, Z., Khare, K., & Michailidis, G. (2024) for details.

Most of the codes are from https://github.com/bfava/IllusionOfIllusion with our modification to make it have adaptive burn-in Gibbs sampler, and some debugs.

Usage

GLP_gs(
  Y,
  X,
  a = 1,
  b = 1,
  A = 1,
  B = 1,
  Max_burnin = 10,
  nmc = 5000,
  adaptive_burn_in = TRUE
)

Arguments

Value

A list with betahat: predicted beta hat from majority voting, and Gibbs_res: 5000 samples of beta, q and lambda^2 from Gibbs sampler.

Examples

## A toy example is given below to save your time, which will still take ~10s. 
## The full example can be run to get BETTER results, which will take more than 80s, 
## by using X instead of X[, 1:30] and let nmc=5000 (default).

n = 30;
p = 2 * n;

beta1 = rep(0.1, p);
beta2 = c(rep(0.2, p / 2), rep(0, p / 2));
beta3 = c(rep(0.15, 3 * p / 4), rep(0, ceiling(p / 4)));
beta4 = c(rep(1, p / 4), rep(0, ceiling(3 * p / 4)));
beta5 = c(rep(3, ceiling(p / 20)), rep(0 , 19 * p / 20));
betas = list(beta1, beta3, beta2, beta4, beta5);

set.seed(123);
X = matrix(rnorm(n * p), n, p);
Y = c(X %*% betas[[1]] + rnorm(n));

## A toy example with p=30, total Gibbs steps=1100
system.time({mod = GLP_gs(Y, X[, 1:30], 1, 1, 1, 1, nmc = 100);})

mod$beta; ## estimated beta after the Majority voting
hist(mod$Gibbs_res$betamat[1,]); ## histogram of the beta_1
hist(mod$Gibbs_res$q); ## histogram of the q
hist(log(mod$Gibbs_res$lambdasq)); ## histogram of the log(lambda^2)
plot(mod$Gibbs_res$q); ## trace plot of the q
## joint posterior of model density and shrinkage
plot(log(mod$Gibbs_res$q / (1 - mod$Gibbs_res$q)), -log(mod$Gibbs_res$lambdasq),
    xlab = "logit(q)", ylab = "-log(lambda^2)",
    main = "Joint Posterior of Model Density and Shrinkage"); 

INSS algorithm

Description

INdependent Spike and Slab (INSS) algorithm with/without adaptive burn-in Gibbs sampler. See paper of Yang, Z., Khare, K., & Michailidis, G. (2024) for details.

Usage

INSS_gs(
  Y,
  X,
  a = 1,
  b = 1,
  c = 1,
  s,
  Max_burnin = 10,
  nmc = 5000,
  adaptive_burn_in = TRUE
)

Arguments

Value

A list with betahat: predicted beta hat from majority voting, and Gibbs_res: 5000 samples of beta, q and lambda^2 from Gibbs sampler.

Examples

## A toy example is given below to save time. The full example can be run to get better results
## by using X instead of X[, 1:30] and let nmc=5000 (default).

n = 30;
p = 2 * n;

beta1 = rep(0.1, p);
beta2 = c(rep(0.2, p / 2), rep(0, p / 2));
beta3 = c(rep(0.15, 3 * p / 4), rep(0, ceiling(p / 4)));
beta4 = c(rep(1, p / 4), rep(0, ceiling(3 * p / 4)));
beta5 = c(rep(3, ceiling(p / 20)), rep(0 , 19 * p / 20));
betas = list(beta1, beta3, beta2, beta4, beta5);

set.seed(123);
X = matrix(rnorm(n * p), n, p);
Y = c(X %*% betas[[1]] + rnorm(n));

## A toy example with p=30, total Gibbs steps=1100, takes ~0.6s
system.time({mod = INSS_gs(Y, X[, 1:30], 1, 1, 1, sqrt(p), nmc = 100);})

mod$beta; ## estimated beta after the Majority voting
hist(mod$Gibbs_res$betamat[1,]); ## histogram of the beta_1
hist(mod$Gibbs_res$q); ## histogram of the q
hist(log(mod$Gibbs_res$lambdasq)); ## histogram of the log(lambda^2)
plot(mod$Gibbs_res$q); ## trace plot of the q
## joint posterior of model density and shrinkage
plot(log(mod$Gibbs_res$q / (1 - mod$Gibbs_res$q)), -log(mod$Gibbs_res$lambdasq),
    xlab = "logit(q)", ylab = "-log(lambda^2)",
    main = "Joint Posterior of Model Density and Shrinkage");