Mike West, Duke University  

Mike West
The Arts & Sciences Professor of Statistics & Decision Sciences
Department of Statistical Science
Duke University

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Bayesian Forecasting and Dynamic Models
Mike West and Jeff Harrison

This list includes some points of clarification of text, as well as minor corrections, for the 2nd Edition, 1st Printing (1997). These have been corrected/clarified in the 1999 2nd printing.

Note that we use some basic TeX notation, e.g., "X_t" is "X" subscripted "t", and so forth

Chapter 2

  • p34, line 7
    In " ... is a local linear ..." the word "linear" should read "constant"
  • p39, Theorem 2.2 (b) ... X_{t+k} should be X_t(k)
  • p44, Theorem 2.3, three lines from the end of the proof.
    ... C_t=A_t/V ... should read ... C_t=A_t V ...
  • p49, Section 2.4.1, third displayed equation.
    The lower limit on summation should be j=0 not j=o and the upper limit should be t-2
    the subscript t-j+1 on a in the sum should be t-j-1

Chapter 3

  • p74, line 14
    The final v_t should be the greek nu_t
  • p91, Section 3.5, line 2
    In { F_t, 1,V_t, W,t } the W,t should of course be W_t

Chapter 4

  • p104, l19, part (a)
    in N[0,W] the matrix W should be W_t
  • p109, line 3
    In W^*_t the matrix W should be W , i.e., in bold font
  • p117, Theorem 4.5 under "Retrospective Recurrence Relations" in the table
    B_v in the first line should be in bold font
  • p126, Section 4.9.4, line 3
    Harrison (1996b) should be Harrison (1996)
  • p127, Section 4.9.4, last line
    Harrison (1996b) should be Harrison (1996)
  • p138, Exercise 2(b)
    D_t should be D_{t-1}
  • p140, Exercise 11(d)
    reference to "Theorem 4.7" should be "Theorem 4.5"

Chapter 5

  • p160, Section 5.5.1, line 5.
    Harrison (1996a) should be Harrison (1997)
  • p161-162 -- a type-setting glitch only. The "diamond" symbol indicating the end of the Proof of Theorem 5.4 should appear after the proof, at the foot of page 161 -- it has slipped over onto the top of p162.
  • p154-160, part (ii) of Definitions 5.7 to 5.11 inclusive
    Definitions of "canonical equivalent models" also require initial priors to be related as in the basic definition of equivalent models, second displayed equation of Definition 5.4 (line 11 on p152)
  • p160-162
    Though based on normal models, the results here do indeed depend only on the forms of the mean and variance recursions in constant DLMS, as stated at the start of Section 5.5.1. So they are applicable under traditional least squares, Kalman filtering and Bayesian least squares assumptions, for example.
  • p161, Definition 5.12
    The definition requires a condition to hold for all non-zero vectors. In fact, the condition holds for zero vectors as well, so the definition should omit the adjective non-zero
  • p164, line 1
    the word observable should be omitted
  • p172, Exercises 3 and 4
    the state vector elements \theta_{t1} and \theta_{t2} are scalars and so should not be in bold font
  • p173, Exercise 4(c)
    ... the DLM is observable ... should read ... the DLM is unobservable ...
  • p174, Exercise 8(b)
    "... final n-1 elements" should be "... final n elements"
  • p174, Exercise 9(a)
    the second element of F should be 1 (one) not 0 (zero)

Chapter 6

  • p205, Question 9(a)
    Theorem 4.7(i) and (ii) should be Theorem 4.5(i) and (ii)

Chapter 8

  • p265, Question (7)
    In the definition of the frequency \omega the term arccos{\sqrt(1+g^2)} should read arccos{ 1 / \sqrt(1+g^2)}
  • p266, Question (11) part (b)
    In the expression for \rho_t the element \omega_{t2} in the second term should be \omega_{t-1,1}

Chapter 9

  • p275, line 10 (first line after displayed updating equations)
    In the expression for Q_t the term C_{t-1} should, of course, be R_t
  • p302, line 4.
    West (1996a) should be West (1997)
  • p304, Section 9.6.1, line 9-10
    Prado and West (1996) should be Prado and West (1997)
  • p306, line 6 and last line
    Prado and West (1996) should be Prado and West (1997)

Chapter 10

  • p362, Table 10.4, 2nd line under "Information"
    \delta is missing from the T dof; it should read
      (\theta_t|D_{t-1}) \sim T_{\delta n_{t-1}}[a_t,R_t]
  • p362, Table 10.4, 2nd line under "Forecast:"
    In the equation for Q_t the term S_{t-1} should be k_t S_{t-1}
  • p364, in the final equation for n_t(-k) the term + \delta n_{t-k+1} should be +\delta n_t(-k+1)

Chapter 11

  • p383, Section 11.3.1, line 1 of para 2
    The first-order polynomial model ... should be The second-order polynomial model ...
  • p416, l3.
    Add reference to Harrison and Lai (1999)
  • p417, Section 11.6.3, line 10
    \mu=E(X_i|\eta)=\dot a(\eta) not \dot g(\eta)

Chapter 12

  • p469 at the top:
    • p_t^*(j_t) should be p_t^*(j_t,j_{t-1}) in both its definition in the displayed equation of line 4 and in the summation of line 5
    • The summation of line 5 should be over index j_{t-1} not j_t
    • Similarly, p_t^*(j_{t-1}) should be p_t^*(j_t,j_{t-1}) in the displayed equation of line 9

Chapter 14

  • p529, equation (14.33)
    lines 2-4 of this equation are missing the divisor /q_t, as should be clear from equation (14.31).

Chapter 15

  • p565, l1.
    Mueller, West and MacEachern (1996) should be 1997
  • p569, line -8.
    West (1996d) should be West (1996c)
  • p570, line -2
    singula-value should read singular-value
  • p571, Section 15.3.1, line 4.
    West (1996a,b,d) should be West (1996a,c, 1997)
  • p571, Section 15.3.1, line 5.
    West (1995 and 1996c) should be West (1995 and 1996b)
  • p578, line 1.
    West (1996c) should be West (1996b)
  • p579, line -3.
    West (1995, 1996a,b,c and d) should be West (1995, 1996a,b,c and 1997)

Chapter 16

  • p584, line -3
    The Barbosa and Harrison paper should be dated (1992) not (1989)

Chapter 17

  • p637, Bivariate Normal section
    The factor Q(.) in the exponent of the density function should be divided by 1-\rho_{ij}^2 and the arguments Q(x_1, x_2) should be Q(x_i, x_ j ) throughout
  • p649-651, on Common eigenvalues and Jordan forms
    This section implicitly assumes we are dealing with the system matrix G of an observable DLM. This should have been explicitly stated. In such cases, G *must* be similar to the precise Jordan form as stated (as clarified in Theorem 5.2, p155).

    Also add a note on the more general Jordan forms for G matrices of non-observable models that are used in the proof of Theorem 5.2 (based on general theory, such as Theorem 8.5, p 106, of E D Nerig, Linear Algebra and Matrix Theory, Wiley: New York, 1969). That is, any system matrix G with one eigenvalue e of multiplicity n can be reduced to a form diag( J_(r_1)(e),....., J_(r_m)(e)) with r_1+.....+r_m=n and where each J_(r_i)(e) is a standard Jordan block. This might even be the diagonal case where each r_i=1 when G =e I. This completes the general theory but is of little practical interest.

BIBLIOGRAPHY References to be added that were wrongly omitted:

  • O'Hagan, A., 1994, , "Kendall's Advanced Theory of Statistics, Volume 2B: Bayesian Inference", Edward Arnold, London.

Corrections to existing references:

  • p656: reference to Harrison, P.J., 1996a. Change to
      Harrison, P.J. , 1997. Convergence and the constant dynamic linear model. J. Forecasting 16, 287-292.
  • p656: Harrison, P.J., 1996b should be just 1996
  • p660: Prado, R., and West, M., 1996 ... etc .. should be changed to
      Prado, R., and West, M., 1997, Exploratory modelling of multiple non-stationary time series: Latent process structure and decompositions. In Modelling Longitudinal and Spatially Correlated Data, (T. Gregoire, Ed). New York: Springer-Verlag.
  • p664: West, M., 1996a. Change to
      West, M., 1997. Time series decomposition. Biometrika, 84, 489-494.
  • p664: West, M., 1996b becomes 1996a
  • p664: West, M., 1996c becomes 1996b
  • p664: West, M., 1996d becomes 1996c

New references to be added:

  • Aguilar, O., and West, M., 1998a, Analysis of hospital quality monitors using hierarchical time series models, Case Studies in Bayesian Statistics, Volume 4, C. Gatsonis, R.E. Kass, B. Carlin, A. Carriquiry, A. Gelman, I. Verdinelli and M.West (Eds), Springer-Verlag, New York.
  • Aguilar, O., and West, M., 1998b, Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. ISDS Discussion Paper 98-03, Duke University.
  • Aguilar, O., Huerta, G., Prado, R., and West, M., 1999, Bayesian inference on latent structure in time series (with discussion), Bayesian Statistics 6, J.O. Berger, J.M. Bernardo, A.P. Dawid, and A.F.M. Smith (Eds.), Oxford University Press.
  • Cooper, J.D., and Harrison, P.J., 1997, A Bayesian approach to modelling the observed bovine spongiform encephalopathy epidemic, J. Forecasting, 16, 355-374.
  • Harrison, P.J., and Lai, I.C.H., 1999, Statistical process control and model monitoring, J App. Stat. 26, 273-292.
  • Nerig, E.D., 1969, Linear Algebra and Matrix Theory, New York: Wiley.
  • Prado, R., Krystal, A.D., and West, M., 1999, Evaluation and comparison of EEG traces: Latent structure in non-stationary time series, J. Amer. Statist. Assoc., 94, -.