CHAPTER 8

REFERENCES

Alho, J. (1990): Stochastic methods in population forecasting. Interna­

tional Journal of Forecasting, 6(4), 521-530.

Athreya, K. B., McDonald, D., Ney, P. (1978a): Coupling and the Renewal

Theorem. Amer. Math. Monthly, Vol.85, No.10, 809-814.

Athreya, K. B., McDonald, D., Ney, P. (1978b): Limit Theorems for Semi­

Markov Processes and Renewal Theory for Markov Chains. Ann. Prob­

ability, Vol.6, No.5, 788-797.

Bachi, R. (1965): "Analysis of Geographical Data on Internal Migration."

In: United Nations. World Population Conference (Belgrade), Vol IV.

1967. Pp. 475-479.

Bai, D.S., and Kim, S. (1979): "Estimation of Transition Probabilities in a

Two-State Markov Chain". Comm. Stat.: Theory Methods, A8(6),591-

599.

Bailey, N. T. J. (1964): The Elements of Stochastic Processes with Applica­

- tions to the Natural Sciences. Wiley, New York.

Bartholomew, D. J. (1982): Stochastic Models for Social Processes. 3rd Ed.,

Wiley, New York.

152

Bartlett, M. S. (1978): An Introduction to Stochastic Processes. 3rd Ed.,

Cambridge University Press, Cambridge, England.

Basawa, I.V. and Prakasa Rao, B.L.S. (1980): Statistical Inference for

Stochastic Processes. Academic Press, New york.

Bayarri, M. J., and Berger J. 0. (2004): The Interplay of Bayesian and

Frequentist Analysis. Statistical Science, 19(1), 58-80.

Berger, J.O. (1985): Statistical Decision Theory and Bayesian Analysis.

2nd Ed., Springer-Verlag, New York.

Bernardo, J. M., and Munoz, J. (1993): Bayesian analysis of population

evolution. The Statistician, 42( 4): 541-550.

Bernardo, J. M., and Smith, A. F. M. (1994): Bayesian Theory. Wiley,

New York.

Bhat, U. N. (1984): Elements of Applied Stochastic Processes. 2nd Ed.,

Wiley, New York.

Bhat, U. N., and Miller, G. K. (2002): Elements of Applied Stochastic

Processes. Wiley, New York.

Bharucha, A.T. and Reid (1960): Elements of the Theory of Markov Pro­

cesses and Their Applications. McGraw-Hill, New York.

Bhattacharya, R.N. and Waymire, R.E. (1990): Stochastic Processes with

Applications. Wiley, New York.

153

Bijak, J. (2005): "Bayesian Methods in International Migration Forecast­

ing''. European Population Conference 2006, Liverpool, United King­

dom.

Billard, L. and Meshkani, M. R. (1995): "Estimation of Stationary Markov

Chain." J. Amer. Stat. Assoc., 90, 307-315.

Billingsley, P. (1961): Statistical Inference for Markov Processes. University

of Chicago Press, Chicago.

Billingsley, P. (1961): "Statistical Methods in Markov Chains'1• Ann. Math.

Stat., 32, 12-40.

Biswas, S. (1988): Stachastic Processes in Demography and Applications.

Wiley Eastern Limited.

Box, G. E. P., and Tiao, G. C. (1973): Bayesian Inference in Statistical

Analysis. Reading, MA: Addition-Wesley.

Brown, L. A. (1970): On the use of Markov chains in movement research.

Economic Geography, 46(Suppl.), 393-403.

Carlin, B. P., and Louis, T. A. (1996): Bayes and Empirical Bayes Methods

for Data Analysis. Chapman & Hall, London.

Carlsson, G, (1958): Social Mobility and Class Structure. CWK Gleerup,

Lund, Sweden.

Chung, K. L. (1967): Markov Chains With Stationary Transition Probabil­

ities. 2nd Ed., Springer-Verlag, New York.

154

Cinlar, E. (1975): Introduction to Stochastic Processes. Englewood Cliffs,

NJ: Prentice-Hall.

Congdon, P. (2003): Applied Bayesian Modelling. Chichester: John Wiley.

Courgeau, D. (1995): Migration theories and behavioural models. Interna­

tional Journal of Population Geography, 1(1): 19-27.

Cox, D. R. (1962): Renewal Theory. Methuen, London.

Cox, D. R. and Miller, H. D. (1965): The Theory of Stochastic Processes.

Methuen, London.

Cox, D. R., and Lewis, P. A. W. (1966): The Statistical Analysis of Series

of Events. Chapman & Hall, London.

Cushing, B. (2005): Specification of Functional Form in models of Popu­

lation Migration. Southern Regional Science Association Conference:

Arlington, VA, April 7-9, 2005.

Davidon, W. C. (1959): Variable metric methods for minimisation. AEC

Research and Development Report ANL-5990, Argonne National Lab­

oratory, Chicago.

Davis, P. J., and Rabinowitz, P. (1984): Methods of Numerical Integration.

2nd Ed., Orlando, FL: Academic Press.

De Beer, J. (1997): The effect of uncertainty of migration on national popu­

lation forecasts: the case of the Netherlands. Journal of Official Statis­

tics, 13(3), 227-243.

155

Deely, J., and Lindley, D. V. (1981): "Bayes Empirical Bayes.'' J. Amer.

Statist. Assoc., 76, 833-841.

Derman, C. (1970): Finite State Markovian Decision Processes. Academic

Press, New York.

Drake, A. W. (1967): Fundamentals of Applied Probability Theory. McGraw­

Hill, New York.

Dustmann, C. (1997): Return migration, uncertainty and precautionary

savings. Journal of Development Economics, 52(2), 295-316.

Dynkin, E. B. (1965): Theory of Markov Processes. Academic Press, New

York.

Ethier, S. N., Kurtz, T. G. (1986): Markov Processes1 Characterization and

Convergence. John Wiley, New York.

Evans, G. (1993): Practical Numerical Integration. Wiley, New York.

Fishman, G. (1978): Principles of Discrete Event Simulation. John Wiley,

New York.

Feller, W. (1968): An Introduction to Probability Theory and its Applica­

tions. VoL I, 3rd Ed., John Wiley & Sons, New York.

Feller, W. (1971): An Introduction to Probability Theory and its Applica­

tions. Vol. II, John Wiley & Sons, New York.

Ferguson, T. S. (1967): Mathematical Statistics: A Decision Theoretic Ap­

proach. Academic Press, New York.

156

Ferguson, T. S. (1996): A Course In Large Sample Theory. Chapman &

Hall, London.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin1 D. B. (1995): Bayesian

Data Analysis. Chapman & Hall, London.

Ginsberg1 R. B. (1971): Semi-Markov Processes and Mobility. Journal of

Mathematical Sociology, 1(1), 233-262.

Glass, D. V. (1954): Social Mobility in Britain. Routledge and Kegan Paul,

London.

Goldstein, H. (2003): Multivariate Statistical Models. Arnold, London.

Goodman, L. A. (1961): Statistical Methods for the 'Mover-Stayer' Model.

J. Amer. Stat. Assoc. 56, 841-868.

Greenwood M. (1985): Human Migration: Theory, Models and Empirical

Studies. Journal of Regional Science 251 521-544.

Grenander, U. (1981): Abstract Inference. Wiley, New York.

Haggstrom, 0. (2002): Finite Markov Chains and Algorithmic Applications.

Cambridge University Press, Cambridge.

Harris, J. R., and Todaro, M. P. (1970): Migration, unemployment and de­

velopment: A two sector analysis. American Economic Review, 60(1),

126-142.

157

Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky (1999):

Bayesian Model Averaging: A Tutorial. Statistical Science, 14(4), 382-

417.

Hogg, R. V. and Craig, A. T. (1995): Introduction to Mathematical Statis­

tics. Prentice Hall, New York.

Hogg, R. V. and Tanis, E. A. (1993): Probability and Statistical Inference.

4 e/d, Macmillan, New York.

Hossain, J., and Seal, B. (2007): " A measure of equality of states and its

estimation based on migration". Submitted.

Hossain, J., and Seal, B. (2007): " Sample size required for estimation

procedure of migration". Submitted.

Household, A. S. (1964): The Theory of Matrices in Numerical Analysis.

Blaisdell, New york.

Howard, R. A. (1960): Dynamic Programming and Markov Processes. Cam­

bridge, MA: MIT Press.

Jaynes, E.T. (1968): "Prior probabilities." IEEE Transactions on Systems

Science and Cybematics, SSC-4, 227-241.

Jeffreys, H. (1939): Theory of Probability. Oxford University Press, Oxford.

Johnson, N.L., and Kotz, S. (1969): Distributions in Statistics: Discrete

Disributions. John Willy & Sons, New york.

158

Johnson, N.L., and Kotz, S. (1970a): Distributions in Statistics: Continuous

Univariate Disatributions. Vol. 1, John Willy & Sons, New york.

Johnson, N.L., and Kotz, S. (1970b): Distributions in Statistics: Continu­

ous Univariate Disatributions. Vol. 2, John Willy & Sons, New york.

Johnson, N. L., and Kotz, S. (1972): Continuous Multivariate Distributions.

John Wi11y & Sons, New york.

Johnson, N. L. 1 Kotz, 8., and Balakrishnan, N. (1994): Continuous Uni­

variate Disatributions. Vol. 2, John Willy & Sons, New york.

Johnson, N. L., Kotz, 8., and Balakrishnan, N. (1997): Discrete Multivariate

Disatributions. John Willy & Sons, New york.

Joseph, g. (1974): A Markov Analysis of Age/Sex Differences in Inter­

regional Migration in Britain. Regional Studies, 9(2), 69-78.

Kadane, J. B. (1984): Robastness of Bayesian Analysis. North-Holland,

Amsterdam.

Kalbfleisch, J. D., and Lawless, J. F. (1984): ,,Least-squares Estimation of

Transition Probabilities from Aggregate Data." Canad. J. Btat., 12(3),

169-182.

Karlin, S. and Taylor H. (1975): A First Course in Stochastic Processes.

Academic Press, New York.

Karlin, S. and Taylor H. (1981): A Second Course in Stochastic Processes.

Academic Press, New York.

159

Karlin, S. and Taylor H. (1998): An Introduction to Stochastic Modelling.

Academic Press, New York.

Karr, A. F. (1991): Point Processes and Their Statistrical Inference. 2nd

Ed., Marcel Dekker, New York.

Katz, J. L. and Burford, R. L. (1988): "Estimating Mean Time to Absorp­

tion for a Markov Chain with Limited Information." Applied Stochastic

Models and Data Analysis, 4, 217-230.

Kau, James and Sirnans C. F. (1976): "New, Repeat, and Return Migration:

A Study of Migrant Types." Southern Economic Journal, 43, 144-1148.

Keilson, J. (1979): Markov Chain Models-Rarity and Exponentiality. Springer­

Verlag, Berlin.

Kemeny, J. G. and Snell, J. L. (1976): Finite Markov Chains. Springer­

Verlag) New York.

Kendal, M. G., Stuart, A., and Ord, J. K. (1987): The Advanced Theory of

Statistics. Vol. I, 5th Ed., Griffin, London.

Kennedy, W. G., and Gentle, J. E. (1980): Statistical Computing. Marcel

Dekker, New York.

Keyfitz, N. (1968): Introduction to the Mathematics of Population. Univer­

sity of California Press, Berkeley, CA.

160

Keyfitz, N. (1980): Multidimensionality in Population Analysis. IIASA

Report RR-80-33. International Institute for Applied System Analysis,

Laxen burg.

Kingman, J. F. C. (1969): " Markov Population Processes." J. Appl. Prob.,

6 1-18.

Koslowski, R. (2004): Possible steps towards an international regime for

mobility and security. Global Commission on International Migration.

Kulldroff, Gunnar (1955): Migration Probabilities. Lund series in Geogra­

phy, Series B, Human Geography, No. 14, Royal University of Lund

(Sweden).

Kupiszewski, M. (2002): Modelowanie dynamiki przemian ludnosci w warunk­

ach wzrostu znaczenia migracji miedzynarodowych [Modelling popula­

tion dynamics considering the increasing role of international migra­

tion}. Institute of Geography and Spatial Organisation, Polish Academy

of Sciences, Warsaw.

Lange, K. (1995): "Application of the Dirichlet Distribution to forensic

match probabilities." Genetica, 96: 107-117.

Lange, K. (1995b): "A quasi-newton accleration of the EM algorithm.n

Statistica Sinica, 5, 1-18.

Law, A. and Kelton, W. (1992): Simulation Modelling and Analysis. 2nd

Ed., McGraw-Hill, New york.

161

Lee, E. S. (1966): A Theory of Migration. Demogmphy, 3(1), 47-57.

Lee, T. C., Judge, G. G., and Zellner, A. (1970): Estimating the Parameters

of the Markov Probability Model From Aggregate Time Series Data.

Amsterdam: North-Holland.

Lehman, E. L. ( 1983): Theory of Point Estimation. 2nd Ed., John Wiley

& Sons, New York.

Lehman, E. L. (1986): Testing Statistical Hypotheses. 2nd Ed., John Wiley

& Sons, New York.

Li, W. K., and Kwok, M. C. 0. (1990): 11 Some results on the Estimation of

Higher Order Markov Chain." Comm. Stat.: Simulat. Comp., 19(1),

363-380.

Lindley, D. V. (2000): The Philosophy of Statistics. The Statistician, 49(3),

293-337.

Lipset, S. M., and Bendix, R. (1960): Social Mobility in Industrial Societies.

The University of California Press, Berkley.

MacPherson, D. W. (2004): Irregular migration and health. Global Com­

mission on International Migration, Geneva.

Maritz, J.S. and Lwin, T. (1989): Empirical Bayes Methods. 2nd Ed.,

Chapman & Hall, London.

162

Marks, E. L., Seltzer, W., and Krotki, K. J. (1974): Population Growth

Estimation: A Handbook of Vital Statistics Measurement. The Popu­

lation Council, New York.

Martin, J. J. (1967): Baysian Decision Problems and Markov Chains. Wi­

ley, New york.

Massey, D.S., and Zenteno, R. M. (1999): The dynamics of mass migration.

Proceedings of the National Academy of Sciences of the U.S.A., 96(9),

5328-5335.

McDonald, D. (1978): "On semi-Markov and semi-regenerative Processes

I." Zeitschrift fur Wahrscheinlichkeitstheorie Verw. Gebiete, 42, 261-

277.

McDonald, D. (1978): "On semi-Markov and semi-regenerative Processes

II." Annals of Probability, Vol.6, No.61 995-1014.

McDonald, D. (1980): "On the Poisson approximation to the multinomial

distribution." Canadian Journal of Statistics, Vol.8, No.1, 115-118.

McGinnis, R., Myers, G. C., and Pilger, J. (1963): Internal migration as

a stochastic process. Paper for the 34th session of the International

Statistical Institute, Ottawa, 21-29 August.

McLachlan, G. Krishnan, T. (1997): The EM Algorithm and Extensions.

John Wiley & Sons, New York.

Medhi, J. (1987): Stochastic Processes. Wiley Eastern Limited.

163

Meyn, S. P. and Tweedie, R. L. (1993): Markov Chains and Stochastic

Stability. Springer-Verlag, New York.

Morrison, D. G., Massy, W. F., and Silverman, F. N. (1971): The effect of

non-homogeneous populations on Markov steady state probabilities. J.

Amer. Statist. Assoc., Vol 66, 268-274.

Mukherjee1 S. P., and Basu, R. (1979): Measures of Social and Occupational

Mobility. Demography India, Vol 8, 236-246.

Mukherjee, S. P., and Chattopadhyay, A. K. (1985): Renewal Theoretic

Measurement of Occupational Mobility. Calcutta Statist. Assoc. Bull.,

Vol 34, 207-213.

Mukherjee, S. P., and Chattopadhyay, A. K. (1986b): Measures of mobility

and some associated inference problems. Demography India, Vol 15(2),

269-280.

Mukhopadhyay, P. (1998): Theory and Methods of Servey Sampling. Prentice­

Hall.

Petersen, W. (1968): "A General Topology of Migration." In Charles B.

Nam (ed.), Population and Society1 Pp. 288-297, Houghton-Mifflin

Company, New york.

Plane, D. A. (1993): Demographic Influences on Migration. Regional Stud­

ies, 27(4), 375-383.

Prabhu, N. U. (1965): Stochastic Processes. Macmillan, New york.

164

Prais, S. J. (1955a): Measuring Social Mobility. J. Roy. Stat. Soc., A118,

56-66.

Prais, S. J. (1955b): The Formal Theory of Social Mobility. Population

Studies, 9, 72-81.

Prakasa Rao, B. L. S. (1987): Asymptotic Theory of Statistical Inference.

Wiley, New York.

Prakasa Rao, B. L. S. (1999): Statistical Inference for Diffusion Type Pro­

cesses. Wiley, New York.

Press, S. J. (2003): Subjective and Objective Bayesian Statistics: Principles)

Models and Applications. 2nd Ed., Wiley, New York.

Puterman, M. L. (1994): Markov Decision Theory. Wiley, New York.

Raiffa, H. and Schlaifer, R. (1961 ): Applied Statistical Decision Theory.

Division of Research , Graduate School of Business Administration,

Harvard University.

Renshaw (1991): Modelling Biological Populations in Space and Time. Cam­

bridge University Press, Cambridge, England.

Ripley, B. D. (1987): Stochastic Simulation. Wiley, New York.

Robbins, H. (1955): "An Empirical Bayes Approach to Statistics." in Pro­

ceedings of the Third Berkeley Symposium on Mathematical Statistics

and Probability, I, Berkeley, University of California Press, 157-164.

165

Rogers, A. (1966): A Markovian Policy Model of Interregional Migration.

Papers of the Regional Science Association, 17, 205-224.

Rogers, A. (1975): Introduction to Multiregional Mathematical Demography.

John Wiley, New York.

Rogerson, P. A. (1984): New Directions in Modelling of Interregional Mi­

gration. Economic Geography, 60(2), 111-121.

Rogoff, N. (1953):Recent Trends in Occupational Mobility. Thee Free Press

of Glencoe, Glencoe.

Ross, S. M. (1983): Stochastic Processes. Wiley, New york.

Ross, S. M. (1992): Applied Probability Models with Optimization Applica­

tions. Dover Publications, New York.

Ross, S. M. (1994): Introduction to Probability Models. 6th Ed., Academic

Press, New York.

Ross, S. M. (2002): Simulation. 3rd Ed., Academic Press, San Diego.

Schechtman, Joseph B. (1949): Population Transfer in Asia. New York,

Hallsby Press.

Schefer, J. (1998): Analysis of Incomplete Multivariate Data by Simulation.

Prentice-Hall.

Schwarzacher, W. (1972): "The Semi-Markov as a General Sedimentation

Model." Mathematical models of Sedimentary Processes, (D. F. Mer­

rium, ed.), New York: Plenum Press.

166

Seneta, E. (1981): Non-negative Matrices and Markov chains. 2nd Ed.,

Springer-Verlag, New york.

Scott, D. (1992): Multivariate Density Estimation. Wiley, New York.

Serfling, J. (1979): Approximation Theorems of Mathetical Statistics. John

Wiley & Sons, New York.

Shorrocks, A. F. (1978): The Measurement of Mobility. Econometrica, Vol

46, 1013-1024.

Shryock, H. 8. 1 and Larmon, E. A. (1965): "Some Longitudanal Data on

Internal Migration." Demography, 2:579-592.

Shryock, H. S., Siegel, S. et al. (1976): The Methods and Materials of

Demography. Academic Press, New York.

Simonds, G. F. (1963): Introduction to Topology and Modern Analysis.

McGraw-Hill, Kogakusha Ltd.

Spilerman, S. (1972): The Analysis of Mobility Process by the Introduction

of Independent Variables into a Markov Chain. American Sociological

Review, 37(3), 277-294.

Spitzer, F. (1964): Principles of Random Walk. Springer-Verlag, New york.

Stouffer, S. A. (1940): Intervening opportunities: a theory relating mobility

and distance. American Sociological Review, 5(6): 845-867.

167

Sykes, Z. M. (1969): "Some Stochastic Versions of the Matrix Model for

Population Dynamics." Journal of American Statistical Association,

64(325): 111-130.

Taft, Donald R., and Robbins, Richard. (1955): International Migrations.

New York, Ronald Press Company.

Tanner, M. (1994): Tools for Statistical Inference. Springer-Verlag, New

York.

Thornthwaite, C. Warren. (1938): Internal Migration in the United States.

Philadelphia, University of Pennsylvania Press.

Tijms, H. C. (1994): Stochastic Models, An Algorithmic Approach. John

vViley, New york.

Titterington, D. M., Smith, A. F. M., Markov1 U. E. (1985): Statistical

Analysis of Finite Mixture Distributions. John Wiley & Sons, New

York.

United Nations. (1970): Methods of Measuring Internal Migration. Manu­

als on Methods of Estimating Population, Manual VI.

Vamathevan, S. (1961): Internal Migration in Ceylon, 1946-53. Monograph

No. 13. Ceylon, Department of Census and Statistics.

Weidlich, W., and Hagg, G. (1988): Interregional migration: dynamic the­

ory and comparative analysis. Springer, Berlin-Heidelberg.

168

West, D. G. (2001): Introduction to Graph Theory. 2nd Ed., Upper Saddle

River, NJ: Prentice-Hall.

White, D. J. (1993): Markov Decision Processes. John Wiley & Sons,

Chichester.

Willekens, F. (1995): multiregional demographic forecasting. Population Re­

search Centre Working Paper 95-1, University of Groningen, Gronin­

gen.

Wilson, A.G. (1981): Catastrophe Theory and Bifurcation. An Application

to Urban and Regional Systems. Croom Helm, London.

Withers, S. D. (2002): Quantitative methods: Bayesian inference, Bayesian

thinking. Progress in Human Geography, 26(4), 533-566.

Whittle, P. (1955): "Some distributions and moment formulae for the Markov

chains", J. R. S. S., B 17, 2235-242.

Whittle, P. (1968): "Equilibrium Distributions for an Open Migration Pro­

cess." J. Appl. Prob. 5 567-571.

Whittle, P. (1986): Systems in Stochastic Equilibrium. Wiley, New york.

Yausda, S. (1964): A Methodology Inquiry into Social Mobility. Amer.

Social Rev., Vol 29(1), 16-23.

Zachariah, K. C. (1964): A Historical Study of Internal Migration in the

Indian Sub-continent, 1901-31. New York, Asia Publishing House.

169

Zelinsky, W. (1971): The hypothesis of the mobility transition. Geographical

Review, 61(2), 219-249.

Zellner, A. (1971): An Introduction to Bayesian Inference in Econometrics.

Wiley, New York.

********************

170