Stochastic Models for Social Processes: A Review and Bibliography

Armitage P. H. Smith C. S. Alper P. , ‘Decision Models for Educational Planning’, Allen Lane, The Penguin Press, London, 1969.

Armitage P. H. Phillips C. M. Davies J. , ‘Towards a model of the upper secondary school system’ (with discussion), J. Roy. Statist. Soc., A, Vol. 133, 1970, pp. 166–205.

Kamat A. R. , ‘Estimating wastage in a course of education,’ Sankhya, B, Vol. 30, 1968, pp. 5–12.

Kamat A. R. , ‘Mathematical schemes for describing progress in a course of education’, Sankhya, B, Vol. 30, 1968, pp. 13–24.

Kamat A. R. , ‘A stochastic model for progress in a course of education’, Sankhya, B, Vol. 30, 1968, pp. 25–32.

Kodama F. , ‘An approach to the analysis of vocational education and training requirements’, Man. Sci., Vol. 17, 1970, B178–B191.

Marshall K. T. Oliver R. M. , ‘A constant-work model for student attendance and enrolment’, Operat. Res., Vol. 18, 1970, pp. 193–206.

OECD ‘Mathematical Models in Educational Planning’, OECD, Paris, 1967.

Pollard A. H. , ‘Some hypothetical models in systems of tertiary education’, Aust. J. Statist., Vol. 12, 1970, pp. 78–91.

Pollard A. H. , ‘Minimum rate of progress formulae at universities’, Aust. J. Statist., Vol. 12, 1970, pp. 92–103.

Thonstad T. , ‘Education and Manpower: Theoretical Models and Empirical Applications’, Oliver and Boyd, Edinburgh and London, 1969.

Zemach Rita , ‘A State-Space Model for Resource Allocation in Higher Education’, IEEE Trans. of Systems Science and Cybernetics, Vol. SSC-4, No. 2, 1968.

Bartholomew D. J. , ‘The statistical approach to manpower planning’, Statistician, Vol. 20, 1971, pp. 3–26.

Bartholomew D. J. Morris B. R. (eds.), ‘Aspects of Manpower Planning’, English Universities Press, London, 1971.

Bartholomew D. J. Smith A. R. (eds.), ‘Manpower and Management Science’, English Universities Press, London, 1971.

Bibby J. , ‘A model to control for the biasing effects of differential wastage’, J. Indust. Rel., Vol. 8, 1970, pp. 418–420.

Bowey A. M. , Labour stability curves and labour stability', Brit. J. Indust. Rel., Vol. 7, 1969, pp. 69–84.

Butler A. D. , ‘The distribution of numbers promoted and leaving in a graded organization’, Statistician, Vol. 20, 1971, pp. 69–84.

Dill W. R. Gaver D. P. Weber W. L. , ‘Models and modelling for manpower planning’, Man. Sci., Vol. 13, 1966, B142–166.

Forbes A. F. , ‘Non-parametric methods for estimating the survivor function’, Statistician, Vol. 20, 1971, pp. 27–52.

Hyman R. , ‘Economic motivation and labour stability’, Brit. J. Indust. Rel., Vol. 8, 1970, pp. 159–178.

Marshall K. T. , ‘A Comparison of Two Personnel Prediction Models’ United States Naval Postgraduate School, 1971.

Marshall M. L. , ‘Some statistical methods of forecasting wastage’, Statistician, Vol. 20, 1971, pp. 53–68.

Merck J. W. , ‘A Mathematical Model of Personnel Structure of Large Scale Organizations Based on Markov Chains’, Ph.D. Thesis, Duke University, North Carolina, 1961.

Sabolo Y. , ‘A structural approach to the projection of occupational categories and its application to South Korea and Taiwan’, Internat. Labour Review, Vol. 103, 1971, pp. 131–155.

Smith A. R. (ed.), ‘Models of Manpower Systems’, English Universities Press, London, 1971.

Stoikov V. , ‘The effect of changes in quits and hires on the length-of-service composition of employed workers’, Brit. J. Indust. Rel., Vol. 9, 1971, pp. 255–233.

Wilson N. A. B. (ed.), ‘Manpower Research’, English Universities Press, London, 1969.

White Harrison C. , ‘Control and evolution of aggregate personnel: Flows of men and jobs’, Admin. Sci. Quarterly, Vol. 14, 1969, pp. 4–11.

Vroom V. H. MacCrimmon K. R. , ‘Towards a stochastic model of managerial careers’, Admin. Sci. Quarterly, Vol. 13, 1968, pp. 26–46.

Hodge R. W. , ‘Occupational mobility as a probability process’, Demography, Vol. 3, 1966, pp. 19–34.

Land K. , ‘Duration of residence and prospective migration’, Demography, Vol. 6, 1969, pp. 133–140.

Long L. H. , ‘On measuring geographic mobility’, J. Amer. Statist. Ass., Vol. 65, 1970, pp. 1195–1203.

McGinnis R. , ‘A stochastic model of social mobility’, Amer. Soc. Rev., Vol. 33, 1968, pp. 712–721.

Marshall M. L. , ‘The Use of Probability Distributions for Comparing the Turnover of Families in a Residential Area’, London Papers in Regional Science, Vol. 2. (Urban and Regional Planning), ed. Wilson A. G. , Pion, London, 1971, pp. 171–193.

Morrison P. , ‘Duration of residence and prospective migration: The evaluation of a stochastic model’, Demography, Vol. 4, 1967, pp. 533–561.

Ostry S. Sunter A. , ‘Canadian job vacancy survey: A measure of labour demand’, J. Amer. Statist. Ass., Vol. 65, 1970, pp. 1059–1070.

Sykes Z. M. , ‘Some stochastic versions of the matrix model for population dynamics’, J. Amer. Statist. Ass., Vol. 64, 1969, pp. 111–130.

Theodorescu R. Vaduva I. , ‘A mathematical demographic model concerning the dynamics of specialists’, Studii Cereetari Mat., Vol. 19, 1967, pp. 329–337.

White Harrison C. , ‘Matching vacancies and mobility’, J. Pol. Econ., Vol. 78, 1970, pp. 97–105.

White Harrison C. , ‘Chains of Opportunity’, Harvard University Press, Cambridge, Mass., 1970.

Bowers R. V. , ‘The direction of the intra-societal diffusion’, Amer. Soc. Review, Vol. 2, 1937, pp. 826–836.

de Fleur Melvin L. , ‘A mass communication model of stimulus response relationships: An experiment in leaflet message diffusion’, Sociometry, Vol. 19, 1956, pp. 12–36.

Griliches Z. , ‘Hybrid corn: An exploration in the economics of technological change’, Econometrica, Vol. 25, 1957, pp. 501–522.

Griliches Z. , ‘Hybrid corn and the economics of innovation’, Science, Vol. 132, 1960, pp. 275–280.

Hägerstrand T. , ‘The propogation of innovation waves’, Lund Studies in Geography, Ser. B, No. 4, 1952.

Hägerstrand T. , ‘Innovation diffusion as a spatial process’, The University of Chicago Press, Chicago and London, 1967.

Hill Richard J. , ‘An experimental investigation of the logistic model of message diffusion’, Social Forces, Vol. 36, 1957, pp. 21–26.

Harary F. Ross I. C. , ‘The number of complete cycles in a communication network’, J. Soc. Psych., Vol. 40, 1954, pp. 329–333.

Mansfield E. , ‘Technical change and the rate of imitation’, Econometrica, Vol. 29, 1961, pp. 741–766.

Pemberton H. E. , ‘The curve of culture diffusion rate’, Amer. Soc. Review, Vol. 1, 1936, pp. 547–556.

Pemberton H. E. , ‘The spatial order of culture diffusion’, Sociology and Social Research, Vol. 22, 1938, pp. 246–251.

Rogers E. , ‘Diffusion of Innovations’, Free Press, Glencoe, New York, 1962.

Ryan B. Gross N. C. , ‘The diffusion of hybrid seed corn in two Iowa communities’, Rural Sociology, Vol. 8, 1943, pp. 15–24.

Winthrop Henry , ‘Experimental results in relation to a mathematical theory of behavioural diffusion’, J. of Soc. Psych., Vol. 47, 1958, pp. 85–100.

Bailey N. T. J. , ‘Stochastic birth, death and migration processes for spatially distributed populations’, Biometrika, Vol. 55, 1968, pp. 189–198.

Bailey N. T. J. , ‘A perturbation approximation to the simple stochastic epidemic in a large population’, Biometrika, Vol. 55, 1968, pp. 199–209.

Becker N. G. , ‘The spread of an epidemic to fixed groups within the population’, Biometrics, Vol. 24, 1968, pp. 1007–1014.

Dietz K. , ‘Epidemics and rumours: A survey’, J. Roy. Statist. Soc., A., Vol. 130, 1967, pp. 505–528.

Downton F. , ‘A note on the ultimate size of a general stochastic epidemic’, Biometrika, Vol. 54, 1967, pp. 314–316.

Downton F. , ‘Epidemics with carriers: A note on a paper of Dietz’, J. Appl. Prob., Vol 4, 1967, pp. 264–270.

Gart J. J. , ‘The mathematical analysis of an epidemic with two kinds of susceptibles’, Biometrics, Vol. 24, 1968, pp. 557–566.

Hill R. T. Severo N. C. , ‘The simple stochastic epidemic for small populations with one or more initial infectives’, Biometrika, Vol. 56, 1969, pp. 183–196.

Ridler-Rowe C. J. , ‘On a stochastic model of an epidemic’, J. Appl. Prob., Vol. 4, 1967, pp. 19–33.

Severo N. C. , ‘Generalizations of some stochastic epidemic models’, Bull. Int. Statist. Inst., Vol. 42, Book 2, 1967, pp. 1064–1066.

Severo N. C. , ‘Solving non-linear problems in the theory of epidemics’, Bull. Int. Statist. Inst., Vol. 43, Book 2, 1969, pp. 226–228.

Severo N. C. , ‘The probabilities of some epidemic models’, Biometrika, Vol. 56, 1969, pp. 197–201.

Usher M. B. Williamson M. H. , ‘A deterministic matrix model for handling the birth, death and migration process of spatially distributed populations’, Biometrics, Vol. 26, 1970, pp. 1–12.

Yang Grace Lo , ‘Contagion in stochastic models for epidemics’, Ann. Math. Statist., Vol. 39, 1968, pp. 1863–1889.

Fein E. , ‘Demography and thermodynamics’, Amer. J. of Phys., Vol. 38, 1970, pp. 1373–1379.

Fisher J. W. Bristow M. R. Henderson L. , ‘An actuarial procedure for assessing the experience of mental hospital patients’, Bull. Int. Statist. Inst., Vol. 40, II, 1964, pp. 1102–1120.

Goodman L. A. , Stochastic models for the population growth of the sexes', Biometrika, Vol. 55, 1968, pp. 469–487.

Keyfitz M. , ‘Introduction to the Mathematics of Population’, Addison-Wesley, Reading, Mass., 1968.

Kuzma J. W. , ‘A comparison of two life table methods’, Biometrics, Vol. 23, 1967, pp. 51–64.

Liu P. T. Chow L. P. , ‘A stochastic approach to the prevalence of IUD: Example of Taiwan, Republic of China’, Demography, Vol 8, 1971, pp. 341–353.

Myers G. C. McGinnis R. Masnick G. , ‘The duration of residence approach to a stochastic model of internal migration’, Eugenics Quarterly, Vol. 14, 1967, pp. 121–126.

Pike M. C. , A note on Kimball's paper ‘Models for the estimation of competing risks from grouped data’, Biometrics, Vol. 26, 1970, pp. 579–581.

Seal H. L. , ‘Probability distributions of aggregate sickness durations’, Skand. Aktuarietidskrift, 3–4, 1970, pp. 193–204.

Sheps M. C. , ‘A review of models for population change’, Rev. Int. Statist. Inst., Vol. 39, 1971, pp. 185–196.

Bhargava T. N. Katz L. , ‘A stochastic model for a binary dyadic relation with applications to social and biological science’, Bull Int. Statist. Inst., Vol. 40, II, 1964, pp. 1055–1057.

Fararo T. J. Sunshine M. H. , ‘A Study of a Biased Friendship Net’, Youth Development Centre, Syracuse, New York, 1964.

Hiorns R. W. Harrison G. A. J. Boyce A. J. Küchemann C. F. ‘Mathematical analysis of the effects of movement on the relatedness between populations’, Ann. Hum. Genet., Vol. 32, 1969, pp. 237–250.

Hiorns R. W. Harrison G. A. Küchemann C. F. , ‘Social class relatedness in some Oxfordshire parishes’, J. Biosoc. Sci., Vol. 2, 1970, pp. 71–80.

Kadane J. B. Lewis G. , ‘The distribution of participation in group discussion: An empirical and theoretical appraisal’, Amer. Soc. Review, Vol. 34, 1969, pp. 710–723.

Rainio Kulleroo , ‘Stochastic processes of social contacts’, Scandinavian J. Psychology, Vol. 2, 1961, pp. 113–128.

White Harrison C. , ‘Chance models of systems of casual groups’, Sociometry, Vol. 25, 1962, pp. 153–172.

Horvath W. J. , ‘A statistical model for the duration of wars and strikes’, Behavioural Science, Vol. 13, 1968, pp. 18–28.

Weiss H. K. , ‘Stochastic models for the duration and magnitude of a “Deadly Quarrel”’, Operat. Res., Vol. 11, 1963, pp. 101–121.

Farquharson R. , ‘Theory of Voting’, Oxford University Press, 1969.

Hawkes A. G. , ‘An approach to the analysis of electoral swing’, J. Roy. Statist. Soc., A, Vol. 132, 1969, pp. 68–79.

Henry N. W. , ‘The retention model: A Markov chain with variable transition probabilities’, J. Amer. Statist. Ass., Vol. 66, 1971, pp. 264–267.

Theil H. , ‘The cube law revisited’, J. Amer. Statist. Ass., Vol. 65, 1970, pp. 1213–1219.

Takács L. , ‘On the fluctuations of election returns’, J. Appl. Prob., Vol. 7, 1970, pp. 114–123.

Aaker D. A. , ‘A new method of evaluating stochastic models of brand choice’, J. Marketing Research, Vol. 7, 1971, pp. 300–306.

Aaker D. A. , ‘The new-trier stochastic model of brand choice’, Man. Sci., Vol. 17, 1971, B435–B450.

Benjamin B. Maidand J. , ‘Operational research and advertising: Some experiments on the use of analogies’, Operat. Res. Quart., Vol. 9, 1958, pp. 207–217.

Bernhardt I. Mackenzie K. D. , ‘Some problems in using diffusion models for new products’ in Fisk G. (ed.), ‘Essays in marketing theory’, Allyn and Bacon, Boston, Mass., 1970.

Chatfield C. Goodhardt G. J. , ‘Beta-binomial model for consumer purchasing behaviour’, Appl. Stats., Vol. 19, 1970, pp. 240–250.

Ehrenberg A. S. C. , ‘Models of fact: Examples from marketing’, Man. Sci., Vol. 16, 1970, pp. 435–445.

Frank R. E. , ‘Brand choice as a probability process’, J. Business, Vol. 35, 1962, pp. 43–56.

Gupta S. K. Krishnan K. S. , ‘Mathematical models in marketing’, Operat. Res., Vol. 15, 1967, pp. 1040–1050.

Haines G. H. , ‘A theory of market behaviour after innovation’, Man. Sci., Vol. 10, 1964, pp. 634–666.

Harary F. Lipstein B. , ‘The dynamics of brand loyalty: A Markovian approach’, Operat. Res., Vol. 10, 1962, pp. 19–40.

Kuehn A. A. , ‘A model of budget advertising’ in mathematical models and methods in marketing, (ed.) Bass R. D. , Irwin, Inc., Homewood, Illinois, 1961, pp. 302–356.

Kuehn A. A. , 'Consumer brand choice as a learning process, J. Advertising Research, Vol. 2, 1962, pp. 10–17.

Lee A. M. Burkart A. J. , ‘Some optimization problems in advertising media planning’, Operat. Res. Quart., Vol. 11, 1960, pp. 113–122.

Lee A. M. , ‘Decision rules for media scheduling: Static campaigns’, Operat. Res. Quart., Vol. 13, 1962, pp. 229–242.

Lee A. M. , ‘Decision rules for media scheduling: Dynamic campaigns’, Operat. Res. Quart., Vol. 14, 1963, pp. 365–372.

Maffei R. B. , ‘Brand preferences and simple Markov processes’, Operat. Res. Vol. 8, 1960, pp. 210–218.

Maffei R. B. , ‘Brand preferences and simple Markov processes’, in mathematical models and methods of marketing (ed.) Bass , R. D. Irwin, Inc., Homewood, Illinois, 1961, pp. 103–120.

Massey W. F. Montgomery D. B. Morrison D. G. , ‘Stochastic Models for Buying Behaviour’, The M.I.T. Press, Cambridge, Mass., 1970.

Montgomery D. B. , ‘Stochastic modelling of the consumer’, Industrial Management Review, 1967, pp. 31–42.

Montgomery D. B. , ‘A stochastic response model with application to brand choice’, Man. Sci., Vol. 15, 1969, pp. 323–337.

Morrison D. G. , ‘Testing brand-switching models’, J. Marketing Research, Vol. 3, 1966, pp. 401–409.

Nicosia F. M. , ‘New developments in advertising research: Stochastic models’, Proc. Amer. Ass. Public Opinion Research, 1967.

Padberg D. I. , ‘The use of Markov processes in measuring changes in market structure’, J. Farm. Economics, Vol. 44. 1962, pp. 189–199.

Simon L. S. Freimer M. , ‘Analytical Marketing’, Brace and World, Harcourt, 1970.

Styan G. P. H. Smith H. , ‘Markov chains applied to marketing’, J. Marketing Research, Vol. I, 1964, pp. 50–55.

Weinberg C. B. , ‘Response curves for a leaflet distribution—further analysis of the De Fleur data’, Operat. Res. Quart., Vol. 22, 1971, pp. 177–179.

Balleer M. , ‘The exclusion of sets of persons in sickness insurance considered as a Markov process’, Bla. Dtsch. Ges. Versichmath, Vol. 8, 1968, pp. 611–632.

Farrow S. C. Fisher D. J. H. Johnson D. B. , ‘Statistical approach to planning an integrated haemodialysis/transplantation programme’, British Medical Journal, Vol. 2, 1971, pp. 671–676.

Revelle C. Feldmann Lynn W. , ‘An optimization model of tuberculosis epidemiology gives a Markov process model for tuberculosis’, Man. Sci., Vol. 16, 1969, B190–B211.

Staff P. J. Vagholkar M. K. , ‘Stationary distributions of open Markov processes in discrete time with application to hospital planning’, J. Appl. Prob., Vol. 8, 1971, pp. 668–680.

Wood F. , ‘An Investigation into the Introduction of Progressive Patient Care’, M.Sc. Dissertation, University of Essex, 1969.

Champernowne D. G. , ‘A model of income distribution’, Economic J., Vol. 63, 1953, pp. 318–351.

Dryden M. , ‘Short-term forecasting of share prices: An information theory approach’, Scottish J. Political Economy, Vol. 15, 1968, pp. 227–249.

Kemp A. G. Reid G. C. , ‘The random walk hypothesis and the recent behaviour of equity prices’, Economica, Vol. 38, 1971, pp. 28–51.

Roberts H. V. , ‘Stock market “Patterns” and financial analysis: Methodological suggestions’, J. Finance, Vol. 14, 1959, pp. 1–10.

Rutherford R. S. G. , ‘Income distributions: A new model’, Econometrica, Vol. 23, 1955, pp. 277–294.

Tinbergen J. , ‘On the theory of income distribution’, Weltwirtschaftliches, Archiv. Bd., Vol. 77, 1956, pp. 10–31.

Tuck R. H. , ‘An Essay on the Economic Theory of Rank’, Blackwell, Oxford, 1954.

Wold H. O. A. Whittle P. , ‘A model explaining the Pareto distribution of wealth’, Econometrica, Vol. 25, 1957, pp. 591–595.

Dodd S. C. Christopher S. C. , ‘The Reactants Model’ in essays in Honour of George A. Lundberg, Behavioural Research Council, Great Barrington, Mass., 1968.

Fienberg S. E. , ‘Randomization and social affairs: The 1970 draft lottery’, Science, Vol. 171, 1971, pp. 255–261.

Henderson L. F. , ‘The statistics of crowd fluids’, Nature, Vol. 229, 1971, pp. 381–383.

Hill B. M. , ‘Zipf's Law and prior distributions for the composition of a population’, J. Amer. Statist. Ass., Vol. 65, 1970, pp. 1220–1232.

Horowitz A. Horowitz I. , ‘Entropy, Markov processes and competition in the brewing industry’, J. Indust. Econ., Vol. 16, 1968, pp. 196–211.

Jones J. M. , ‘A stochastic model for adaptive behaviour in a dynamic situation’, Man. Sci., Vol. 17, 1971, pp. 484–497.

Krenz R. D. , ‘Projection of farm numbers for North Dakota with Markov chains’, Agricultural Economics Research, Vol. 16, 1964, pp. 77–83.

Lee T. C. Judge G. C. Zellner A. , ‘Maximum likelihood and Bayesian estimation of transition probabilities’, J. Amer. Statist. Ass., Vol. 63, 1968, pp. 1162–1179.

Lee T. C. Judge G. C. Zellner A. , ‘Estimating the Parameters of the Markov Probability Model from Aggregate Time Data’, North Holland Publishing Co., 1970.

Mackenzie K. D. Barron F. H. , ‘Analysis of a decision making investigation’, Man. Sci., Vol. 17, 1970, B226–241.

McGuire T. W. , ‘More on least squares estimation of the transition matrix in a stationary first-order Markov process from sample population data’, Psychometrika, Vol. 34, 1969, pp. 335–345.

Reiger M. H. , ‘A two-state Markov model for behavioural chance’, J. Amer. Statist. Ass., Vol. 63, 1968, pp. 993–999.

Smith P. E. , ‘Markov chains, exchange matrices and regional development’, J. Regional Science, Vol. 3, 1961, pp. 27–36.

Barankin E. W. , ‘Towards the mathematics of a general theory of behaviour 1’, Ann. Insr. Statist. Math., Vol. 21, 1969, pp. 421–456.

Bartholomew D. J. Bassett E. E. , ‘Let's Look at the Figures: The quantitative approach to human affairs’, Penguin Books, London, 1971.

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Maslov P. P. , ‘Model building in sociological research’, Soviet Sociology, Vol. 1, 1962, pp. 11–23.

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Simon H. A. , ‘Models of Man, Social and Rational; mathematical essays on rational human behaviour in a social setting’, J. Wiley, New York, 1957.

Simon H. A. , ‘The Sciences of the Artificial’, M.I.T. Press, Cambridge, Mass., 1969.

Williams E. J. , ‘The development of biomathematical models’, Bull. Ins. Statist. Inst., Vol. 42, Book, 1, 1967, pp. 131–143.

Wold H. , ‘Non-experimental statistical analysis from the general point of view of scientific method’, Bull. Int. Statist. Inst., Vol. 42, Book 1, 1967, pp. 391–427.