Replacing Removed Syntaxes of estimate
The estimate function of the Bayesian linear
regression models conjugateblm, semiconjugateblm, diffuseblm, empiricalblm, and customblm returns only an estimated model and
an estimation summary table. The previous and current syntaxes for
estimate are:
[PosteriorMdl,estBeta,EstBetaCov,estSigma2,estSigma2Var,Summary] = estimate(...); % Now issues error [PosteriorMdl,Summary] = estimate(...); % Supported
Starting in R2019b, estimate returns the estimated model object
in the first output argument position and the estimation summary table in the second
output argument position. If you specify output arguments in subsequent positions, then
estimate issues this
error:
Too many output arguments.
To avoid the error, update your code by following this procedure.
Search your code for instances in which
estimatereturns any output argument positions after the first.In the identified instances, determine whether
estimatereturns marginal or conditional distribution estimates. If the call toestimateuses the'Beta'or'Sigma2'name-value pair argument, the function returns conditional distribution estimates. Otherwise,itreturns marginal distribution estimates.For instances returning marginal distribution estimates:
Return
PosteriorMdlandSummarywhen you callestimate.Estimate the marginal posterior statistics using the appropriate code in this table.
Output Argument PosteriorMdlIsconjugateblmObjectPosteriorMdlIsempiricalblmObjectestBetaorestBeta = PosteriorMdl.Mu;
estBeta = Summary.Mean(1:(end - 1));
orestBeta = Summary.Mean(1:(end - 1));
estBeta = mean(PosteriorMdl.BetaDraws,2);
EstBetaCovorEstBetaCov = Summary.Covariances(1:(end - 1),1:(end - 1));
EstBetaCov = PosteriorMdl.V/PosteriorMdl.B/(PosteriorMdl.A - 1);
orEstBetaCov = Summary.Covariances(1:(end - 1),1:(end - 1));
EstBetaCov = cov(PosteriorMdl.BetaDraws');
estSigma2orestSigma2 = Summary.Mean(end);
estSigma2 = 1/PosteriorMdl.B/(PosteriorMdl.A - 1);
orestSigma2 = Summary.Mean(end);
estSigma2 = mean(PosteriorMdl.Sigma2Draws);
estSigma2VarorestSigma2Var = Summary.Covariances(end,end);
estSigma2Var = 1/(PosteriorMdl.B^2*(PosteriorMdl.A - 1)^2*(PosteriorMdl.A - 2));
orestSigma2Var = Summary.Covariances(end,end);
estSigma2Var = var(PosteriorMdl.Sigma2Draws);
For examples, see Replace Removed Syntax When Estimating Analytical Marginal Posterior and Replace Removed Syntax When Estimating Numerical Marginal Posterior.
For instances returning conditional distribution estimates, you must return the estimation summary table
Summaryin the second output argument position. This table describes how to extract conditional posterior estimates fromSummary.Output Argument Estimation estBetaestBeta = Summary.Mean(1:end – 1);EstBetaCovEstBetaCov = Summary.Covariances(1:end – 1,1:end – 1)estSigma2estSigma2 = Summary.Mean(end)estSigma2VarestSigma2Var = Summary.Covariances(end,end)For an example, see Replace Removed Syntax When Estimating Conditional Posterior.
Replace Removed Syntax When Estimating Analytical Marginal Posterior
This example shows how to replace the removed syntax of estimate when it returns an analytical marginal posterior.
Consider a multiple linear regression model that predicts US real gross national product (GNPR) using a linear combination of industrial production index (IPI), total employment (E), and real wages (WR). Assume the following:
The intercept and three regression coefficients are random variables with a multivariate normal prior distribution conditional on the disturbance variance. The prior mean is a 4-D vector of zeros, and the prior covariance matrix is the 4-by-4 identity matrix scaled by 10,000.
The disturbance variance is a random variable with an inverse gamma prior distribution. The shape and scale parameter values are 3 and 1, respectively.
Create a normal-inverse-gamma conjugate prior model for the linear regression parameters. Set the number of predictors . Set the regression coefficient names to the corresponding variable names.
p = 3; PriorMdl = bayeslm(p,'ModelType','conjugate','VarNames',["IPI" "E" "WR"]);
Load the Nelson-Plosser data set. Create variables for the response and predictor series.
load Data_NelsonPlosser X = DataTable{:,PriorMdl.VarNames(2:end)}; y = DataTable{:,'GNPR'};
Before R2019b, estimate could return up to six outputs, each summarizing the posterior distribution. The previously supported syntax is:
[PosteriorMdl,estBeta,EstBetaCov,estSigma2,estSigma2Var,Summary] = estimate(PriorMdl,X,y);
For R2019b, estimate supports returning only two outputs: the posterior model PosteriorMdl and the estimation summary table Summary. Estimate the marginal posterior distribution by using the updated syntax. Return the posterior model and estimation summary table.
[PosteriorMdl,Summary] = estimate(PriorMdl,X,y);
Method: Analytic posterior distributions
Number of observations: 62
Number of predictors: 4
Log marginal likelihood: -259.348
| Mean Std CI95 Positive Distribution
-----------------------------------------------------------------------------------
Intercept | -24.2494 8.7821 [-41.514, -6.985] 0.003 t (-24.25, 8.65^2, 68)
IPI | 4.3913 0.1414 [ 4.113, 4.669] 1.000 t (4.39, 0.14^2, 68)
E | 0.0011 0.0003 [ 0.000, 0.002] 1.000 t (0.00, 0.00^2, 68)
WR | 2.4683 0.3490 [ 1.782, 3.154] 1.000 t (2.47, 0.34^2, 68)
Sigma2 | 44.1347 7.8020 [31.427, 61.855] 1.000 IG(34.00, 0.00069)
Compute posterior estimates by using the new procedure.
estBeta = PosteriorMdl.Mu % Posterior mean of coefficientsestBeta = 4×1
-24.2494
4.3913
0.0011
2.4683
EstBetaCov = Summary.Covariances(1:(end - 1),1:(end - 1)) % Posterior covariance of coefficientsEstBetaCov = 4×4
77.1246 0.7713 -0.0024 0.5311
0.7713 0.0200 -0.0000 -0.0295
-0.0024 -0.0000 0.0000 -0.0001
0.5311 -0.0295 -0.0001 0.1218
estSigma2 = Summary.Mean(end) % Posterior mean of disturbance varianceestSigma2 = 44.1347
estSigma2Var = Summary.Covariances(end,end) % Posterior variance of disturbance varianceestSigma2Var = 60.8709
Replace Removed Syntax When Estimating Numerical Marginal Posterior
This example shows how to replace the removed syntax of estimate when it returns a numerical marginal posterior.
Consider a multiple linear regression model that predicts US real gross national product (GNPR) using a linear combination of industrial production index (IPI), total employment (E), and real wages (WR). Assume the following:
The intercept and three regression coefficients are random variables with a multivariate normal prior distribution conditional on the disturbance variance. The prior mean is a 4-D vector of zeros, and the prior covariance matrix is the 4-by-4 identity matrix scaled by 10,000.
The disturbance variance is a random variable with an inverse gamma prior distribution. The shape and scale parameter values are 3 and 1, respectively.
Create a normal-inverse-gamma semiconjugate prior model for the linear regression parameters. Specify the number of predictors . Set the regression coefficient names to the corresponding variable names.
p = 3; PriorMdl = bayeslm(p,'ModelType','semiconjugate','VarNames',["IPI" "E" "WR"]);
Load the Nelson-Plosser data set. Create variables for the response and predictor series.
load Data_NelsonPlosser X = DataTable{:,PriorMdl.VarNames(2:end)}; y = DataTable{:,'GNPR'};
Before R2019b, estimate could return up to six outputs, each summarizing the posterior distribution. The previously supported syntax is:
[PosteriorMdl,estBeta,EstBetaCov,estSigma2,estSigma2Var,Summary] = estimate(PriorMdl,X,y);
For R2019b, estimate supports returning only two outputs: the posterior model PosteriorMdl and the estimation summary table Summary. Estimate the marginal posterior distribution by using the updated syntax. Return the posterior model and estimation summary table.
[PosteriorMdl,Summary] = estimate(PriorMdl,X,y);
Method: Gibbs sampling with 10000 draws
Number of observations: 62
Number of predictors: 4
| Mean Std CI95 Positive Distribution
-------------------------------------------------------------------------
Intercept | -23.9999 9.0499 [-41.852, -6.163] 0.003 Empirical
IPI | 4.3933 0.1445 [ 4.112, 4.677] 1.000 Empirical
E | 0.0011 0.0003 [ 0.000, 0.002] 1.000 Empirical
WR | 2.4696 0.3571 [ 1.764, 3.169] 1.000 Empirical
Sigma2 | 46.9242 8.4732 [33.244, 66.309] 1.000 Empirical
Compute posterior estimates by using the new procedure.
estBeta = Summary.Mean(1:(end - 1)) % Posterior mean of coefficientsestBeta = 4×1
-23.9999
4.3933
0.0011
2.4696
EstBetaCov = Summary.Covariances(1:(end - 1),1:(end - 1)) % Posterior covariance of coefficientsEstBetaCov = 4×4
81.9002 0.8161 -0.0025 0.5843
0.8161 0.0209 -0.0000 -0.0303
-0.0025 -0.0000 0.0000 -0.0001
0.5843 -0.0303 -0.0001 0.1275
estSigma2 = Summary.Mean(end) % Posterior mean of disturbance varianceestSigma2 = 46.9242
estSigma2Var = Summary.Covariances(end,end) % Posterior variance of disturbance varianceestSigma2Var = 71.7952
Replace Removed Syntax When Estimating Conditional Posterior
This example shows how to replace the removed syntax of estimate when it returns a conditional posterior.
Consider a multiple linear regression model that predicts US real gross national product (GNPR) using a linear combination of industrial production index (IPI), total employment (E), and real wages (WR). Assume the following:
The intercept and three regression coefficients are random variables with a multivariate normal prior distribution conditional on the disturbance variance. The prior mean is a 4-D vector of zeros, and the prior covariance matrix is the 4-by-4 identity matrix scaled by 10,000.
The disturbance variance is a random variable with an inverse gamma prior distribution. The shape and scale parameter values are 3 and 1, respectively.
Create a normal-inverse-gamma conjugate prior model for the linear regression parameters. Specify the number of predictors . Set the regression coefficient names to the corresponding variable names.
p = 3; PriorMdl = bayeslm(p,'ModelType','conjugate','VarNames',["IPI" "E" "WR"]);
Load the Nelson-Plosser data set. Create variables for the response and predictor series.
load Data_NelsonPlosser X = DataTable{:,PriorMdl.VarNames(2:end)}; y = DataTable{:,'GNPR'};
Before R2019b, estimate could return up to six outputs; the latter five summarize the conditional posterior distribution. The previously supported syntax is:
[~,estBeta,EstBetaCov,estSigma2,estSigma2Var,Summary] = estimate(PriorMdl,X,y);
For R2019b, estimate supports returning only two outputs. The conditional posterior estimates are in the estimation summary table in the second output argument position.
Estimate the conditional posterior distribution of the regression coefficients given that the disturbance variance is 10. Return the estimation summary table by using the updated syntax.
[~,Summary] = estimate(PriorMdl,X,y,'Sigma2',10);Method: Analytic posterior distributions
Conditional variable: Sigma2 fixed at 10
Number of observations: 62
Number of predictors: 4
| Mean Std CI95 Positive Distribution
--------------------------------------------------------------------------------
Intercept | -24.2494 4.1803 [-32.443, -16.056] 0.000 N (-24.25, 4.18^2)
IPI | 4.3913 0.0673 [ 4.259, 4.523] 1.000 N (4.39, 0.07^2)
E | 0.0011 0.0002 [ 0.001, 0.001] 1.000 N (0.00, 0.00^2)
WR | 2.4683 0.1661 [ 2.143, 2.794] 1.000 N (2.47, 0.17^2)
Sigma2 | 10 0 [10.000, 10.000] 1.000 Fixed value
Compute posterior estimates by using the new procedure.
estBeta = Summary.Mean(1:end - 1) % Posterior mean of coefficientsestBeta = 4×1
-24.2494
4.3913
0.0011
2.4683
EstBetaCov = Summary.Covariances(1:end - 1,1:end - 1) % Posterior covariance of coefficientsEstBetaCov = 4×4
17.4748 0.1748 -0.0005 0.1203
0.1748 0.0045 -0.0000 -0.0067
-0.0005 -0.0000 0.0000 -0.0000
0.1203 -0.0067 -0.0000 0.0276
