This paper deals with the application of Bayesian methods to the estimation of two convective heat-transfer coefficients of a roof-mounted radiant barrier system. As part of an empirical validation of the thermal model of the roofing complex, a parametric sensitivity analysis highlighted the importance of convective coefficients in the thermal behavior of a roofing complex. A parameter estimation method is then used in order to find the values of the coefficients that lead to an improvement of the thermal model. However, instead of using a classical parameter estimation method, we used a Bayesian inference approach to parameter estimation. The aim of the paper is to introduce the basic concepts of this powerful method in this simple two-parameter case. We show that Bayesian methods introduce an explicit treatment of uncertainty in modeling and a corresponding measure of reliability for the conclusions reached.

1.
Medina
,
M. A.
, 2000, “
On the Performance of Radiant Barriers in Combination with Different Attic Insulation Levels
,”
Energy Build.
0378-7788,
33
(
1
), pp.
31
40
.
2.
Al-Asmar
,
H. R.
,
Jones
,
B.
,
W.
, and
Matteson
,
D.
, 1996, “
Experimental Evaluation of Attic Radiant Barriers (RP-577)
,”
ASHRAE Trans.
0001-2505,
102
(
1
), pp.
297
306
.
3.
Fairey
,
P.
, 1985, “
The Measured Side-by-Side Performance of Attic Radiant Barrier Systems in Hot and Humid Climates
,”
Proceedings of the 9th International Thermal Conductivity Conference
, Cookville, TN, pp.
481
496
.
4.
Hall
,
J. A.
, 1985, “
Performance Testing of Radiant Barriers
,”
Proceedings of the 3rd Annual Symposium on Improving Building Energy Efficiency in Hot and Humid Climates
, Arlington, TX, pp.
55
77
.
5.
Palomo del Barrio
,
E.
, and
Guyon
,
G.
, 2003, “
Parameters Space Analysis Tools for Empirical Model Validation. Part I. Theory and Computer Implementation
,”
Energy Build.
0378-7788,
35
(
10
), pp.
985
996
.
6.
Palomo del Barrio
,
E.
, and
Guyon
,
G.
, 2002, “
Using Parameters Space Analysis Techniques for Diagnosis Purposes in the Framework of Empirical Model Validation
,” Final Report, Task 22: Building Energy Analysis Tools,
International Energy Agency
.
7.
Bretthorst
,
G. L.
, 1990, “
An Introduction to Parameter Estimation Using Bayesian Probability
,”
Maximum Entropy and Bayesian Methods
,
P.
Fougere
, eds.,
Kluwer Academic Publishers
, Dordrecht, pp.
53
79
.
8.
Miranville
,
F.
, 2002, “
Mise en place d’une plate-forme expérimentale—réalisation et instrumentation d’un dispositif de caractérisation d’isolants minces réfléchissants
,” Ph.D. thesis, University of La Réunion, Saint-Denis, France.
9.
Boyer
,
H.
,
Garde
,
F.
,
Gatina
,
J. C.
, and
Brau
,
J.
, 1998, “
A Multimodel Approach to Building Thermal Simulation for Design and Research Purposes
,”
Energy Build.
0378-7788,
28
, pp.
71
78
.
10.
Boyer
,
H.
et al.
, 1996, “
Thermal Building Simulation and Computer Generation of Nodal Models
,”
Build. Environ.
0360-1323,
31
, pp.
207
214
.
11.
Miranville
,
F.
,
Boyer
,
H.
,
Mara
,
T.
, and
Garde
,
F.
, 2003, “
On the Thermal Behavior of Roof-Mounted Radiant Barriers Under Tropical and Humid Climatic Conditions: Modelling and Empirical Validation
,”
Energy Build.
0378-7788,
35
, pp.
997
1008
.
12.
Cole
,
R. J.
, and
Sturrock
,
N. S.
, 1977, “
The Convective Heat Exchange at External Surface Buildings
,”
Build. Environ.
0360-1323,
12
, pp.
207
214
.
13.
Fauconnier
,
R.
, and
Grelat
,
A.
, 1981, “
Thermique de l’habitat: Bases de la modélisation thermique
,”
Ann. Inst. Tech. Bat. Trav. Publics
1270-9840,
395
, pp.
123
138
.
14.
Mara
,
T. A.
,
Boyer
,
H.
, and
Garde
,
F.
, 2002, “
Parametric Sensitivity Analysis of a Test Cell Thermal Model Using Spectral Analysis
,”
ASME J. Sol. Energy Eng.
0199-6231,
124
, pp.
237
242
.
15.
Malakoff
,
D. M.
, 1999, “
Bayes Offers ‘New’ Way to Make Sense of Numbers
,”
Science
0036-8075
286
, pp.
1460
1464
.
16.
Cox
,
R. T.
, 1946, “
Probability, frequency and reasonable expectation
,”
Am. J. Phys.
0002-9505,
14
, pp.
1
13
.
17.
Bayes
,
T.
, 1763, “
An essay towards solving a problem in the doctrine of chances
,”
Philos. Trans. R. Soc. London
0370-2316,
53
, pp.
370
418
.
18.
de Laplace
,
P. S.
, 1812,
Théorie Analytique des Probabilités
,
Courcier Imprimeur
, Paris.
19.
Sivia
,
D. S.
, 1996,
Data Analysis: A Bayesian Tutorial
,
Oxford University Press
, Oxford, UK.
20.
Jaynes
,
E. T.
, 2003,
Probability Theory—The Logic of Science
,
Cambridge University Press
, Cambridge, UK.
21.
Jaynes
,
E. T.
, 1986, “
Bayesian Methods: General Background
,”
Maximum Entropy and Bayesian Methods in Applied Statistics
,
Cambridge University Press
, Cambridge, UK, pp.
1
25
.
22.
Loredo
,
T. J.
, 1990, “
From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics
,”
Maximum Entropy and Bayesian Methods
,
P.
Fougere
, ed.,
Kluwer Academic Publishers
,
Dordrecht
, pp.
81
142
.
23.
Bretthorst
,
G. L.
, 1990, “
Bayesian Model Selection: Examples Relevant to NMR
,”
Maximum Entropy and Bayesian Methods
,
P.
Skilling
, eds.,
Kluwer Academic Publishers
, Dordrecht, pp.
377
388
.
24.
Qian
,
S. S.
,
Stow
,
C. A.
, and
Borsuk
,
M. E.
, 2003, “
On Monte Carlo Methods for Bayesian Inference
,”
Ecol. Modell.
0304-3800,
159
, pp.
269
277
.
25.
Jeffreys
,
H.
, 1939,
Theory of Probability
,
Clarendon Press
, Oxford, UK.
26.
Seber
,
G. A. F.
, and
Wild
,
C. J.
, 1989,
Nonlinear Regression
,
Wiley and Sons
, New York.
27.
Ellison
,
A. M.
, 1996, “
An Introduction to Bayesian Inference for Ecological Research and Environmental Decision-Making
,”
Ecol. Appl.
1051-0761,
6
(
4
), pp.
1036
1046
.
28.
Bishop
,
C. M.
, 1995,
Neural Networks for Pattern Recognition
,
Oxford University Press
, Oxford, Chap. 10, pp.
398
401
.
You do not currently have access to this content.