Bayesian Estimation Tools

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The Bayesian Estimation Tools package provides a suite of pre-built tools for Bayesian estimation and analysis, including data generation, estimation, and post-estimation analysis.

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Overview

Posterior distribution of lambda
The Bayesian Estimation Tools package provides a suite of tools for estimation and analysis of a number of pre-packaged models. The internal 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.

Platform: Windows, Mac, and Linux

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

Features

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)

Examples

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

Product Inquiry

Bayesian Estimation Tools

More Views

Data generation tools for building hypothetical data sets:

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

Flexible, user defined MCMC estimation parameters including:

Thorough computations including:

Sample output report for probit model

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