Kaipio, J., and Somersalo, E., 2004, "*Statistical and Computational Inverse Problems*" (Applied Mathematical Sciences, Vol. 160 ), Springer-Verlag, Berlin.

Maybeck, P., 1979, "*Stochastic Models, Estimation and Control*", Academic Press, New York.

Winkler, R., 2003, "*An Introduction to Bayesian Inference and Decision*", Probabilistic Publishing, Gainsville, FL.

Kaipio, J., Duncan, S., Seppanen, A., Somersalo, E., and Voutilainen, A., 2005, “State Estimation for Process Imaging,” "*Handbook of Process Imaging for Automatic Control*", D.Scott and H.McCann, eds., CRC Press, Boca Raton, FL.

Kalman, R., 1960, “A New Approach to Linear Filtering and Prediction Problems,” ASME J. Basic Eng., 82 , pp. 35–45.

[CrossRef]Sorenson, H., 1970, “Least-Squares Estimation: From Gauss to Kalman,” IEEE Spectrum, 7 , pp. 63–68.

[CrossRef]Welch, G., and Bishop, G., 2006, *An Introduction to the Kalman Filter*, UNC, Chapel Hill, Report No. TR 95-041.

Arulampalam, S., Maskell, S., Gordon, N., and Clapp, T., 2001, “A Tutorial on Particle Filters for On-Line Non-Linear/Non-Gaussian Bayesian Tracking,” IEEE Trans. Signal Process., 50 , pp. 174–188.

[CrossRef]Ristic, B., Arulampalam, S., and Gordon, N., 2004, "*Beyond the Kalman Filter*", Artech House, Boston.

Doucet, A., Godsill, S., and Andrieu, C., 2000, “On Sequential Monte Carlo Sampling Methods for Bayesian Filtering,” Stat. Comput., 10 , pp. 197–208.

[CrossRef]Liu, J., and Chen, R., 1998, “Sequential Monte Carlo Methods for Dynamical Systems,” J. Am. Stat. Assoc., 93 , pp. 1032–1044.

[CrossRef]Andrieu, C., Doucet, A., and Robert, C., 2004, “Computational Advances for and From Bayesian Analysis,” Stat. Sci., 19 , pp. 118–127.

[CrossRef]Johansen, A., and Doucet, A., 2008, “A Note on Auxiliary Particle Filters,” Stat. Probab. Lett., 78 (12), pp. 1498–1504.

[CrossRef]Carpenter, J., Clifford, P., and Fearnhead, P., 1999, “An Improved Particle Filter for Non-Linear Problems,” IEE Proc., Radar Sonar Navig., 146 , pp. 2–7.

[CrossRef]Del Moral, P., Doucet, A., and Jasra, A., 2007, “Sequential Monte Carlo for Bayesian Computation,” "*Bayesian Statistics*", Vol. 8 , Oxford University Press, Cary, North Carolina, pp. 1–34.

Del Moral, P., Doucet, A., and Jasra, A., 2006, “Sequential Monte Carlo Samplers,” J. R. Stat. Soc., 68 , pp. 411–436.

[CrossRef]Andrieu, C., Doucet, A., Singh, S. S., and Tadic, V. B., 2004, “Particle Methods for Charge Detection, System Identification and Control,” Proc. IEEE, 92 , pp. 423–438.

[CrossRef]Hammersley, J. M., and Hanscomb, D. C., 1964, "*Monte Carlo Methods*", Chapman and Hall, London.

Gordon, N., Salmond, D., and Smith, A. F. M., 1993, “Novel Approach to Nonlinear and Non-Gaussian Bayesian State Estimation,” IEE Proc. F, Radar Signal Process., 140 , pp. 107–113.

[CrossRef]Orlande, H., Dulikravich, G., and Colaço, M., 2008, “Application of Bayesian Filters to Heat Conduction Problem,” "*EngOpt 2008—International Conference on Engineering Optimization*", J.Herskovitz, ed., Rio de Janeiro, Brazil, June 1–5.

Pitt, M., and Shephard, N., 1999, “Filtering via Simulation: Auxiliary Particle Filters,” J. Am. Stat. Assoc., 94 (446), pp. 590–599.

[CrossRef]Liu, J., and West, M., 2001, “Combined Parameter and State Estimation in Simulation-Based Filtering,” "*Sequential Monte Carlo Methods in Practice*", A.Doucet, N.de Freitas, and N.Gordon, eds., Springer-Verlag, New York, pp. 197–217.

Sisson, S. A., Fan, Y., and Tanaka, M. M., 2009, “Sequential Monte Carlo Without Likelihoods,” Proc. Natl. Acad. Sci. U.S.A., 104 , pp. 1760–1765, Errata, 2007.

[CrossRef]Batchelor, G. K., 2000, "*An Introduction to Fluid Dynamics*", Cambridge University Press, Cambridge.

Versteeg, H., and Malalasekera, W., 2007, "*An Introduction to Computational Fluid Dynamics: The Finite Volume Method*", Prentice-Hall, Englewood Cliffs, NJ.

Van Doormal, J. P., and Raithby, G. D., 1984, “Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flow,” Numer. Heat Transfer, 7 , pp. 147–163.

[CrossRef]Raithby, G. D., and Torrance, K. E., 1974, “Upstream-Weighted Differencing Schemes and Their Application to Elliptic Problems Involving Fluid Flow,” Comput. Fluids, 2 , pp. 191–206.

[CrossRef]Saad, Y., and Schultz, M., 1985, “Conjugate Gradient-Like Algorithms for Solving Non-Symmetric Linear Systems,” Math. Comput., 44 (170), pp. 417–424.

[CrossRef]Colaço, M. J., and Orlande, H. R. B, 1999, “A Comparison of Different Versions of the Conjugate Gradient Method of Function Estimation,” Numer. Heat Transfer, Part A, 36 (2), pp. 229–249.

[CrossRef]Colaço, M. J., and Orlande, H. R. B, 2001, “Inverse Problem of Simultaneous Estimation of Two Boundary Heat Fluxes in Parallel Plate Channels,” J. Braz. Soc. Mech. Eng., 23 (2), pp. 201–215.

[CrossRef]Colaço, M. J., and Orlande, H. R. B, 2001, “Inverse Forced Convection Problem of Simultaneous Estimation of Two Boundary Heat Fluxes in Irregularly Shaped Channels,” Numer. Heat Transfer, Part A, 39 , pp. 737–760.

[CrossRef]Colaço, M. J., Dulikravich, G. S., and Martin, T. J., 2004, “Optimization of Wall Electrodes for Electro-Hydrodynamic Control of Natural Convection During Solidification,” Mater. Manuf. Processes, 19 (4), pp. 719–736.

[CrossRef]Colaço, M. J., and Orlande, H. R. B, 2004, “Inverse Natural Convection Problem of Simultaneous Estimation of Two Boundary Heat Fluxes in Irregular Cavities,” Int. J. Heat Mass Transfer, 47 , pp. 1201–1215.

[CrossRef]Colaço, M. J., Dulikravich, G. S., and Martin, T. J., 2005, “Control of Unsteady Solidification via Optimized Magnetic Fields,” Mater. Manuf. Processes, 20 (3), pp. 435–458.

[CrossRef]Colaço, M. J., and Dulikravich, G. S., 2006, “A Multilevel Hybrid Optimization of Magnetohydrodynamic Problems in Double-Diffusive Fluid Flow,” J. Phys. Chem. Solids, 67 , pp. 1965–1972.

[CrossRef]Colaço, M. J., and Dulikravich, G. S., 2007, “Solidification of Double-Diffusive Flows Using Thermo-Magneto-Hydrodynamics and Optimization,” Mater. Manuf. Processes, 22 , pp. 594–606.

[CrossRef]Beck, J. V., and Arnold, K. J., 1977, "*Parameter Estimation in Engineering and Science*", Wiley Interscience, New York.

Calvetti, D., and Somersalo, E., 2007, "*Introduction to Bayesian Scientific Computing*", Springer, New York.

Tan, S., Fox, C., and Nicholls, G., 2006, "*Inverse Problems*" (Course Notes for Physics 707), University of Auckland, Auckland, New Zealand.

Lee, P. M., 2004, "*Bayesian Statistics*", Oxford University Press, London.

Gamerman, D., and Lopes, H. F., 2006, "*Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference*", 2nd ed., Chapman and Hall/CRC, Boca Raton, FL.

Wang, J., and Zabaras, N., 2004, “A Bayesian Inference Approach to the Stochastic Inverse Heat Conduction Problem,” Int. J. Heat Mass Transfer, 47 , pp. 3927–3941.

[CrossRef]Wang, J., and Zabaras, N., 2004, “A Computational Statistics Approach to Stochastic Inverse Problems and Uncertainty Quantification in Heat Transfer,” "*Proceedings of the VI World Conference on Computational Mechanics*", Beijing, China, Sept. 5–10.

Mota, C. A. A., Orlande, H. R. B., Wellele, O., Kolehmainen, V., and Kaipio, J., 2009, “Inverse Problem of Simultaneous Identification of Thermophysical Properties and Boundary Heat Flux,” High Temp. – High Press., 38 , pp. 171–185.

Orlande, H. R. B., Kolehmainen, V., and Kaipio, J. P., 2007, “Reconstruction of Thermal Parameters Using a Tomographic Approach,” Int. J. Heat Mass Transfer, 50 , pp. 5150–5160.

[CrossRef]Emery, A. F., 2007, “Estimating Deterministic Parameters by Bayesian Inference With Emphasis on Estimating the Uncertainty of the Parameters,” "*Proceedings of the Inverse Problem, Design and Optimization Symposium*", G.Dulikravich, H.Orlande, and M.Colaco, eds., Miami Beach, FL, Vol. 1 , pp. 266–272.

Mota, C., Orlande, H., De Carvalho, M., Kolehmainen, V., and Kaipio, J., 2010, “Bayesian Estimation of Temperature-Dependent Thermophysical Properties and Transient Boundary Heat Flux,” Heat Transfer Eng., 31 , pp. 570–580.

[CrossRef]Naveira-Cotta, C., Orlande, H., and Cotta, R., 2010, “Integral Transforms and Bayesian Inference in the Identification of Variable Thermal Conductivity in Two-Phase Dispersed Systems,” Numer. Heat Transfer, 57 , pp.173–202.

[CrossRef]Naveira-Cotta, C., Cotta, R., and Orlande, H., 2010, “Inverse Analysis of Forced Convection in Micro-Channels With Slip Flow via Integral Transforms and Bayesian Inference,” Int. J. Therm. Sci., 49 , pp. 879–888.

[CrossRef]Naveira-Cotta, C., Orlande, H., Cotta, R., and Nunes, J., 2010, “Integral Transforms, Bayesian Inference, and Infrared Thermography in the Simultaneous Identification of Variable Thermal Conductivity and Diffusivity in Heterogeneous Media,” "*Proceedings of the International Heat Transfer Conference IHTC14*", Washington, DC, Aug. 8–13, Paper No. IHTC14-22511.

Fudym, O., Orlande, H. R. B., Bamford, M., and Batsale, J. C., 2008, “Bayesian Approach for Thermal Diffusivity Mapping From Infrared Images With Spatially Random Heat Pulse Heating,” J. Phys.: Conf. Ser., 135 , pp. 12–42.

[CrossRef]Massard, H., Fudym, O., Orlande, H. R. B., and Batsale, J. C., 2010, “Nodal Predictive Error Model and Bayesian Approach for Thermal Diffusivity and Heat Source Mapping,” C. R. Méc., 338 , pp. 434–449.

[CrossRef]Orlande, H., Colaço, M., and Dulikravich, G., 2008, “Approximation of the Likelihood Function in the Bayesian Technique for the Solution of Inverse Problems,” Inverse Probl. Sci. Eng., 16 (6), pp. 677–692.

[CrossRef]Parthasarathy, S., and Balaji, C., 2008, “Estimation of Parameters in Multi-Mode Heat Transfer Problems Using Bayesian Inference—Effect of Noise and

*a priori*,” Int. J. Heat Mass Transfer, 51 , pp. 2313–2334.

[CrossRef]Kaipio, J., and Fox, C., “The Bayesian Framework for Inverse Problems in Heat Transfer,” Heat Transfer Eng., 32 (9), pp. 718–753.

[CrossRef]Godsill, S., Doucet, A., and West, M., 2004, “Monte Carlo Smoothing for Nonlinear Time Series,” J. Am. Stat. Assoc., 99 , pp. 156–168.

[CrossRef]Doucet, A., Freitas, N., and Gordon, N., 2001, "*Sequential Monte Carlo Methods in Practice*", Springer, New York.