The Bayesian Estimation Tools package provides a suite of tools for estimation and analysis of a number of pre-packaged models. The internal GAUSS Bayesian models provide quickly accessible, full-stage modeling including data generation, estimation, and post-estimation analysis. Modeling flexibility is provided through control structures for setting modeling parameters, such as burn-in periods, total iterations and others.

Data generation tools for building hypothetical data sets:

Univariate and multivariate linear models

Autoregressive error terms (AR)

Hierarchical Bayes (HB)

Probit and logit data

Supported models for Markov Chain Monte Carlo (MCMC) Estimation:

Univariate and multivariate linear models

Autoregressive error terms (AR)

Hierarchical Bayes (HB)

Probit model

Dynamic two-factor model

Structural vector autoregressive (SVAR)

Flexible, user defined MCMC estimation parameters including:

Number of saved iterations

Skipped iterations

Burn-in iterations

Total number of iterations

Inclusion of intercept

Optional graph and results output

Elective maximum likelihood estimation (MLE) initialization

Thorough computations including:

Draws for all parameters at each iteration

Posterior mean of parameters

Posterior standard deviation of parameters

Predicted variable values and residuals

Correlation matrix between observed and predicted data

PDF values and corresponding PDF graphs

Log-likelihood values (when applicable)

Sample output report for probit model

```Model Type: Probit regression model
*************************************************************
Possible underlying (unobserved) choice generation:
Agent selects one alternative:
Y[ij] = X[j]*beta_i + epsilon[ij]
epsilon[ij]~N(0,Sigma)
*************************************************************
Y[ij] is mvar vector
Y[ij] is utility from subject i, choice set j, alternative k
where	i = 1, ..., numSubjects
j = 1, ..., numChoices
k = 1, ..., numAlternatives - 1
*************************************************************
X[j] is numAlternative x rankX for choice j
*************************************************************
Pick alternative k if:
Y[ijk] > max( Y[ijl] )
for all k < mvar+1 and l not equal to k
Select base alternative if max(Y)<0
*************************************************************
Observed model:
*************************************************************
Choice vector C[ij] is a numAlternative vector of 0/1
beta_i = Theta'Z[i] + delta[i]
delta[i]~N(0,Lambda)
*************************************************************

Summary stats of independent data

*****************************************
Summary stats for X variables
*****************************************

Variable        Mean              STD              MIN              MAX
X1          0.33333          0.47538             0                1
X2          0.33333          0.47538             0                1
X3          0.33333          0.47538             0                1
X4          0.28648          0.20641        -0.083584          0.71157
X5          0.083333         0.59065            -1                1

*****************************************
Summary stats for Z variables
*****************************************

Variable        Mean            STD             MIN             MAX
Y1         -0.10328         1.1582         -6.1714          3.7266
Y2         -0.23821         1.1428         -6.1295          3.2853
Y3         -0.28473         1.2776         -5.4752           4.58

*****************************************
Summary stats for dependent variables
*****************************************

Variable        Mean             STD             MIN              MAX
Y1         -0.10328          1.1582         -6.1714          3.7266
Y2         -0.23821          1.1428         -6.1295          3.2853
Y3         -0.28473          1.2776         -5.4752            4.58

***********************************
MCMC Analysis Setup
***********************************
Total number of iterations:     1100.0
Total number of saved iterations:     1000.0
Number of iterations in transition period:     100.00
Number of iterations between saved iterations:     0.0000
Number of obs:    60.000
Number of independent variables:    5.0000
(excluding deterministic terms)
Number of dependent variables:    3.0000

********************************
MCMC Analysis Results
********************************

***********************************
Error Standard Deviation
***********************************
Variance-Covariance Means(Sigma)

Equation        Y1               Y2               Y3
Y1         0.20831         0.078641         -0.12772
Y2         0.078641        0.26217          -0.078051
Y3        -0.12772        -0.078051                1

***********************************
Error Standard Deviation
***********************************
Variance-Covariance Means (Lambda)

Equation        Beta1        Beta2           Beta3         Beta4            Beta5
Beta1       0.038024       0.0084823      0.0050414     -0.010463       -0.0044786
Beta2       0.0084823      0.038058       0.0061952     -0.0098521       0.0017846
Beta3       0.0050414      0.0061952      0.080755      -0.0086755       0.016158
Beta4      -0.010463      -0.0098521     -0.0086755      0.10271        -0.010493
Beta5      -0.0044786      0.0017846      0.016158      -0.010493        0.046216

***********************************
Theta for Z Equation     1.0000
***********************************

Variable         PostMean          PostSTD
Theta1          0.53176          0.43012
Theta2          0.43195          0.35411
Theta3        -0.011848       0.00015526
Theta4          -2.0511          -1.9772
Theta5           1.0605           1.1038

***********************************
Theta for Z Equation     2.0000
***********************************

Variable         PostMean          PostSTD
Theta1          0.90016          0.79037
Theta2          0.37388          0.19278
Theta3         -0.32424         -0.37066
Theta4          0.69154          0.85307
Theta5         -0.26623         -0.19126

***********************************
Theta for Z Equation     3.0000
***********************************

Variable         PostMean          PostSTD
Theta1         -0.24998          -0.2454
Theta2         -0.22883         -0.19728
Theta3        -0.043585         0.026509
Theta4         -0.29718         -0.30046
Theta5          0.52032          0.50741
```

Platform: Windows, Mac, and Linux

Requirements: GAUSS/GAUSS Engine/GAUSS Light v13.1 or higher