Page 37

Line 9 should read “the simplified notation μQf instead of (μQ)(f) or μ(Qf).”

Maurice Charbit, 17 Jan 2008

Page 46

Second item should read QW : (W × C) ×

David Haight, 5 Nov 2007

Page 53

Line after (3.1) should read “μ_n denotes the product distribution μ^⊗(n+1) on (Yⁿ⁺¹,^⊗(n+1))”

Thiery Balser, 2 Feb 2007

Page 56

Integrand on the right hand side of (3.9) should read f(x_k)ϕν,0:n|n(y0:n,dx0:n)

Thiery Balser, 6 Feb 2007

Page 58

Last paragraph before Section 3.1.4: should read “This notation also constitutes”

Drew Creal, 7 Dec 2006

Page 61

Third sentence from bottom: should read “For HMMs” (not HHMs)

Drew Creal, 7 Dec 2006

Page 63

Equation (3.22) should read ϕν,k(f) = cν,k⁻¹ ∫ f(x′)∫ ϕν,k−1(dx)Q(x,dx′)g_k(x′)

Maurice Charbit, 17 Jan 2008

Page 138

Equation (5.47) shoud read k+1|k−1 = A_kk|k−1 + R_kÛk|k−1 = A_kk|k−1

Antoine Pichot, 9 Mar 2009

Page 149

Equation (5.104) should read μ_X|Y = Σ_X|Y

Tommaso Proietti, 9 Jul 2009

Page 78

Line 12 should read “particular expressions like E[∑ _k=0ⁿs(X_k)∣Y0:n] and E[(∑ _k=0ⁿs(X_k))²∣Y0:n],”

Maurice Charbit, 17 Jan 2008

Page 91

Line 19 should read “If ξ has a density f”

Maurice Charbit, 17 Jan 2008

Page 141

The ARE expression in Remark 5.2.12 should be Σ = AΣA^t − AΣB^t(BΣB^t + SSt)⁻¹BΣA^t + RRt.

Cornelius Probst, 13 Aug 2012

Page 123

Algorithm 5.1.2 should read “computed during the forward filtering pass (Algorithm 5.1.1)”

Maurice Charbit, 17 Jan 2008

Page 135

The last term in (5.33) should be E(Y Xt)

Maurice Charbit, 17 Jan 20087

Page 139

(5.55) should read Cov(k+1|k) = A_k Cov(k|k−1)A_k^t + HkΓ_kHk^t

François Roueff, 16 May 2007

Page 154

The reference below (5.121) should be to (5.11) rather than (5.12)

Maurice Charbit, 17 Jan 2008

Page 155

Line 7 of Section 5.2.6 shoudl read “is a Markov chain on a finite set C,”

Maurice Charbit, 17 Jan 2008

Page 180

π_i should be π_k

Federica Citterio, 15 Apr 2017

Page 184

π_k(x|x_k−1,x_k) should be π_k(x|x_k−1,x_k+1) (three times)

Maurice Charbit, 17 Jan 2008

Page 188

(6.18) should read exp−

Hossein Gholami, 27 Mar 2007

Page 201

In algorithm 6.3.4, last equation on page 201 shoud read Σ0|n(c) = Σ0|0(c) − Σ0|0(c)⁻¹Π_0|nΣ0|0(c)

Drew Creal, 12 Dec 2006

Page 202

Algorithm 6.3.4 should read Σk|n(c) = Σk|k(c) − Σk|k(c)⁻¹Π_k|nΣk|k(c)

Drew Creal, 7 Dec 2006

Page 204

First two equations of Example 6.3.7 have misplaced commas and the second one should read Y _k = μ_Y (C_k,2) + B(C_k,2)W_k + S(C_k,2)V _k

Drew Creal, 7 Dec 2006

Pages 222–231

In Sections 7.2.2.2 (starting from Example 7.2.4), 7.2.2.3, and, 7.2.2.4, the use of T_k is not consistent with its definition in (7.15) and throughout these pages, T_k needs to be understood as T_k−1 in the sense of (7.15)

Jimmy Olsson, 24 Jul 2007

Page 224

Last line of Section 7.2.2.2 should read “where the current local likelihood g_k(x) = g_k(x,Y _k) is large,”

Jimmy Olsson, 24 Jul 2007

Page 213

In last sentence of the page, the claim that “SIR ν,M,N is an unbiased estimate of μ(f)” is incorrect (the valid statement is given by the equation below)

Jimmy Olsson, 12 Jun 2007

Page 216

In (7.10), R_i(x_l,⋅) should be R_l(x_l,⋅)

Jimmy Olsson, 12 Jun 2007

Page 225

In the last equation, R(c) should be R(x)

Maurice Charbit, 17 Jan 2008

Page 226

Line -6 should read “the Hessian of log t_k(x,⋅) at the mode.”

Julien Cornebise, 1 Jun 2008

Page 230

In Example 7.2.6: First two equations of the EKF approximation should read Kk(x) = 2σ_u²ba_k−1(x)⁻¹ and m_k(x) = a_k−1(x) + Kk(x)

Drew Creal, 7 Dec 2006

Page 231

Line 4 of second paragraph should read “[...] contained in g₁ is large compared to that provided [...]”.

Julien Cornebise, 27 Jan 2009

Page 232

Equation (7.32) should read IS k,N = ∑ _i=1^Nf(ξik)

Maurice Charbit, 17 Jan 2008

Page 253

Last paragraph of Section 8.1 should read “the updated empirical approximation 0:k+1|k+1 should approximate the distribution defined in [...]”

Cornelius Probst, 2 Aug 2010

Page 253

First two sentences after Algorithm 8.1.1, Algorithm 8.1.1 should be Algorithm 7.3.4 (twice)

Tobias Rydén, 12 Apr 2007

Page 331

Rhs of (9.59) should read∑ _i=1^M_Nβk|n(ξ_k^N,i)ψ_k|n(ξ_k^N,i)∑ _i=1^M_Nβk|n(ξ_k^N,i)

Ajay Jasra, 7 Feb 2010

Page 332

ψ_k|n(x) should be defined as Fk|nFn−1|nf(x) − Fk|nFn−1|nf(x₀)

Ajay Jasra, 7 Feb 2010

Page 332

In the rewriting of Δ_k,n^N(f), the upper index in the summation in the numerator should be M_N

Ajay Jasra, 7 Feb 2010

Page 408

Equation (11.9) should read _i∑ _j=i0^{i j}

Michael Egert, 12 Mar 2007

Page 413

The rightmost term in the second unumbered equation should read E[∇_θ log f(ξi; ⁱ⁻¹)∣ⁱ⁻¹]

Michael Egert, 12 Mar 2007

Page 416

In (11.23), the sum should read ∑ _j=i0^{i j}

Michael Egert, 12 Mar 2007

Page 432

The right hand side of the first unnumbered equation should read ∑ _i=1^∞γ_i+1²∥∇_θψ( ⁱ)∥² ∫ |S(x)|²p(x; ⁱ)λ(dx)

Michael Egert, 12 Mar 2007

Page 433

In Theorem 11.3.6 and below, H(θ_⋆) should be J(θ_⋆) (three times)

Michael Egert, 12 Mar 2007

Page 434

Proof of Lemma 11.3.7 should read ∇_θψ[θ(s)]s −∇_θc[θ(s)] = 0 (11.51), ∇_θℓ[θ(s)] = −∇_θ²F[s;θ(s)]∇_sθ(s)h(s) (11.53) and ∇_sℓ[θ(s)] = −^t∇_θ²F[s;θ(s)]∇_sθ(s)h(s) (11.54) for consistent gradient notations

Michael Egert, 12 Mar 2007

Page 435

should be

Michael Egert, 12 Mar 2007

Page 436

should be (twice)

Michael Egert, 12 Mar 2007

Page 487

Unnumbered formula on top of page should read ∏ _j²

Oscar Rueda, 2 Apr 2008

Page 501

First sentence of second paragraph of Section 13.3 should read “parameters estimates in HMMs” (not HHMs)

Olivier Cappé, 11 Dec 2006

Page 35

Unnumbered display in Definition 2.1.1: g should be q

David Carter, 23 Mar 2006

Page 57

Seven lines after (3.12): should read “as defined in (3.11) and (3.12)”

Drew Creal, 18 Dec 2005

Page 58

One line before section 3.1.4: should read “depend on the distribution”

Drew Creal, 18 Dec 2005

Page 64

In (3.27): ϕν,k(f) = ϕν,k|k−1(fg_k) should be ϕν,k(f) = cν,k⁻¹ϕν,k|k−1(fg_k)

Tobias Rydén, 16 Feb 2006

Page 81

First three sum should have k = 0 as lower index (rather k = 1)

Olivier Cappé, 25 Jul 2006

Page 93

Statement of Lemma 4.3.5 should read “For any ξ and ξ′ in...”

Tobias Rydén, 24 Feb 2006

Page 101

There should be only one integral sign in the rhs of (4.32)

Tobias Rydén, 17 Mar 2006

Page 135

Middle of the page: should read “also correspond to the first two moments”

Drew Creal, 18 Dec 2005

Page 138

In Remark 5.2.28: should read “In the general non-Gaussian model”

Drew Creal, 18 Dec 2005

Page 184

Three lines from the bottom: should read “the fact that this function”

Drew Creal, 18 Dec 2005

Page 194

Spurious extra word at the beginning of Section 6.3.1.2

Drew Creal, 18 Dec 2005

Page 226

Sentence above equation (7.21) should read “To choose the parameter”

Drew Creal, 18 Dec 2005

Page 227

Denominator of unnumbered equation after (7.23) should be σ_k⁻¹(x)^{−(η+1)∕2}

Olivier Cappé, 07 Dec 2005

Page 228

Text below Figure 7.7 should read “as the MCMC method in Figure 6.9 approximates”

Drew Creal, 18 Dec 2005

Page 256

In (8.8), f should be f_k+1

Olivier Cappé, 07 Jun 2006

Page 288

Below (9.1): should read “there is a range of results to assess the accuracy”

Drew Creal, 18 Dec 2005

Page 351

Last two lines of proof of Prop 10.1.4: maximal and maximum should be, respectively, minimal and minimum

Eva Mayer, 17 Apr 2006

Page 366

“Proposition (4.1.3) asserts...” should be “Proposition 4.1.3 asserts...”

Olivier Cappé, 22 Jun 2005

Page 392

Last line of proof of Theorem 10.5.4: “because” is misspelled

Eva Mayer, 17 Apr 2006

Page 406

First paragraph: should read “produces highly variable parameter estimates”

Drew Creal, 18 Dec 2005

Page 426

“eigenvalues of M(θ_⋆)” should be “eigenvalues of ∇_θM(θ_⋆)”

Jimmy Olsson, 29 Nov 2005

Page 427

(11.41) should be Sⁱ⁺¹S∘θ(Sⁱ) = G(Sⁱ), θⁱ⁺¹ = θ(Sⁱ⁺¹)

Jimmy Olsson, 29 Nov 2005

Page 431

Inline expression before (11.45) should be ⁱ = ⁱ⁻¹ + γ_ih( ⁱ⁻¹) + γ_iζⁱ

Jimmy Olsson, 29 Nov 2005

Page 432

First line of proof: Mⁱ = ∑ _j=1ⁱγ_jζ^j

Jimmy Olsson, 29 Nov 2005

Page 432

Last term in the rhs of the first unnumbered equation should be ∫ |S(x)|²p(x; ⁱ⁻¹)λ(dx)

Jimmy Olsson, 29 Nov 2005

Page 432

Line after the first unnumbered equation contains a spurious right parentheses

Jimmy Olsson, 29 Nov 2005

Page 445

Fifth line from the top: subscript should read −∞ < k < ∞

Eva Mayer, 17 Apr 2006

Page 454

Third line from the bottom: should read f_π instead of f_ϕ

Eva Mayer, 17 Apr 2006

Page 456

In the middle: should read μ₁ < μ₂... instead of μ_i < μ₂...

Eva Mayer, 17 Apr 2006

Page 456

Fourth line of Example 12.4.7: should read X_k = i instead of X_k = x

Eva Mayer, 17 Apr 2006

Page 461

Proof of Lemma 12.5.3: 1. should read ḣ_k,∞ instead of ḣ_k,−∞

Eva Mayer, 17 Apr 2006

Page 475

Sentence on first line should read “difficult to come up with”

Drew Creal, 18 Dec 2005

Page 517

Repeated word “an” in statement of Theorem 14.1.9

Drew Creal, 18 Dec 2005

Page 534

Repeated word “called” in Definition 14.2.26

Eva Mayer, 17 Apr 2006

Page 626

Uncapitalized proper names in ref. Barron (1985)

Olivier Cappé, 03 Aug 2005

Page 631

Repeated word “estimation” in ref. Doucet and Robert (2002)

Drew Creal, 18 Dec 2005

Page 631

Uncapitalized word “models” in ref. Elliott et al. (1995)

Olivier Cappé, 08 Jul 2005

Page 632

Typo in the title of Fearnhead (1998)

Olivier Cappé, 17 Jun 2006

Page 635

Incorrect formatting of authors in refs. Jacquier et al. (1994, 2004)

Olivier Cappé, 03 Aug 2005

Page 639

Meng, X.-L. and Dyk, D. V. (1997) should be Meng, X.-L. and Van Dyk, D. (1997)

Olivier Cappé, 16 Feb 2006

Pages 645-652

Page numbers in the index are ahead of the actual pages in the text : the discrepancy starts in part II (p. 347) with 2 pages and goes up to 6 pages for the material in parts III, IV (chapters 14 and 15 and appendices); corrected index available here

Olivier Cappé, 23 Nov 2005