## & Gynecology)

### BibTeX

@MISC{Ντζούφρας_&gynecology),

author = {Ι. Ντζούφρας and Π. Τσιαμυρτζής and Μάιος Ioannis Ntzoufras and Μαθημα Εισαγωγη and Στον Ελεγχο and Επιλογη Μοντελων Και and I. Ntzoufras and Απλοι Ελεγχοι Υποθεσεων and Εισαγωγή Εκ-των-υστερων Λόγος and Am. Jour Of Obsterics and Πιθανοτήτων Των Μοντέλων and Εκ-των-υστέρων Λόγος Πιθανοτήτων (posterior},

title = {& Gynecology)},

year = {}

}

### OpenURL

### Abstract

❙ X: Επίπεδο εστριόλης (estriol) των εγκύων γυναικών ❚ Υ i ~ Normal(μ i, σ 2) ❚ μ i =η i =α+βΧ i 6 … ΑΠΛΟΙ ΕΛΕΓΧΟΙ ΥΠΟΘΕΣΕΩΝ 6.1. Εισαγωγή: Εκ-των-Υστερων Λόγος

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Citation Context ...wish to measure the complexity of a focused model, both in its own right, say to assess the degrees of freedom of estimators, and as a contribution to model choice: for example, criteria such as BIC (=-=Schwarz, 1978-=-), AIC (Akaike, 1973), TIC (Takeuchi, 1976) and NIC (Murata et al., 1994) all trade off model fit against a measure of the effective number of parameters in the model. However, the foregoing discussio... |

1339 | Generalized Additive Models - Hastie, Tibshirani - 1990 |

1258 |
On information and sufficiency
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Citation Context ..., B. P. Carlin and A. van der Linde 2.3. True and estimated residual information The residual information in data y conditional on θ may be defined (up to a multiplicative constant) as −2log{p.y|θ/} (=-=Kullback and Leibler, 1951-=-; Burnham and Anderson, 1998) and can be interpreted as a measure of ‘surprise’ (Good, 1956), logarithmic penalty (Bernardo, 1979) or uncertainty. Suppose that we have an estimator ˜θ.y/ of the pseudo... |

1256 |
Information theory as an extension of the maximum likelihood principle
- Akaike
- 1973
(Show Context)
Citation Context ...omplexity of a focused model, both in its own right, say to assess the degrees of freedom of estimators, and as a contribution to model choice: for example, criteria such as BIC (Schwarz, 1978), AIC (=-=Akaike, 1973-=-), TIC (Takeuchi, 1976) and NIC (Murata et al., 1994) all trade off model fit against a measure of the effective number of parameters in the model. However, the foregoing discussion suggests that such... |

1152 |
Spatial interaction and the statistical analysis of lattice systems
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- 1974
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Citation Context ...ch αi .i = 1;:::;56/, γi are exchangeable random effects with a normal prior distribution having zero mean and precision λγ, and δi are spatial random effects with a conditional autoregressive prior (=-=Besag, 1974-=-) given by δi|δ\i ∼ normal ( 1 ni ∑ j∈Ai δj; 1 niλδ ) : A sum-to-zero constraint is imposed on the {δi} for identifiability, and weakly informative gamma(0.5,0.0005) priors are assumed for the random ... |

1127 |
Pattern Recognition and Neural Networks
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Citation Context ...y cannot be directly applied (Gelfand and Dey, 1994). The most ambitious attempts to tackle this problem appear in the smoothing and neural network literature (Wahba, 1990; Moody, 1992; MacKay, 1995; =-=Ripley, 1996-=-). This paper suggests Bayesian measures of complexity and fit that can be combined to compare models of arbitrary structure. In the next section we use an information theoretic argument to motivate a... |

1047 | Bayesian Theory - Bernardo, Smith - 1994 |

523 | Bayesian interpolation - Mackay - 1992 |

464 |
The Behavior of Maximum Likelihood Estimates under NonStandard Conditions.” Pp. 221-33
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Citation Context ...Takeuchi, 1976). Burnham and Anderson (1998) (page 244) pointed out that p Å = tr.JΣ/; (6) where Σ = J −1KJ −1 is the familiar ‘sandwich’ approximation to the variance–covariance matrix of the ˆθ.y/ (=-=Huber, 1967-=-). If pt .y/ = p.y|θt /, i.e. one of the models is true, then K = J and pÅ = p, the number of independent parameters in Θ. For example, in a fixed effect ANOVA model yi|θi ∼ N.θi; τ −1 i /; i = 1;:::;... |

446 | On Bayesian analysis of mixtures with an unknown number of components - Richardson, Green - 1997 |

318 | Random-Effects Models for Longitudinal Data - Laird, Ware - 1982 |

292 |
Approximate Inference in Generalized Linear Mixed Models
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Citation Context ...hood to posterior information. 5.4. Generalized linear mixed models We now consider the class of generalized linear mixed models with canonical link, in which g.µi/ = xT i α + zTi β, where β ∼ N.0;D/(=-=Breslow and Clayton, 1993-=-) and D is assumed known.Model Complexity and Fit 601 Using the same argument as for generalized linear models (Section 5.3), we find that pD ≈ tr[.X; Z/ T W.X; Z/V {.α; β/|y}] ≈ tr.V Å V −1 /; where... |

182 |
Bayesian model choice: asymptotics and exact calculations
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(Show Context)
Citation Context ...tion of the number of parameters in each model (Kass and Raftery, 1995), but in complex hierarchical models parameters may outnumber observations and these methods clearly cannot be directly applied (=-=Gelfand and Dey, 1994-=-). The most ambitious attempts to tackle this problem appear in the smoothing and neural network literature (Wahba, 1990; Moody, 1992; MacKay, 1995; Ripley, 1996). This paper suggests Bayesian measure... |

172 | The eective number of parameters: an analysis of generalization and regularization in nonlinear learning systems
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(Show Context)
Citation Context ...ns and these methods clearly cannot be directly applied (Gelfand and Dey, 1994). The most ambitious attempts to tackle this problem appear in the smoothing and neural network literature (Wahba, 1990; =-=Moody, 1992-=-; MacKay, 1995; Ripley, 1996). This paper suggests Bayesian measures of complexity and fit that can be combined to compare models of arbitrary structure. In the next section we use an information theo... |

149 | Network Information Criterion - Determining the Number of Hidden Units for an Arti cial Neural Network
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- 1994
(Show Context)
Citation Context ... right, say to assess the degrees of freedom of estimators, and as a contribution to model choice: for example, criteria such as BIC (Schwarz, 1978), AIC (Akaike, 1973), TIC (Takeuchi, 1976) and NIC (=-=Murata et al., 1994-=-) all trade off model fit against a measure of the effective number of parameters in the model. However, the foregoing discussion suggests that such measures of complexity may not be unique and will d... |

147 |
Scale mixtures of normal distributions
- Andrews, Mallows
- 1974
(Show Context)
Citation Context ...d denotes Student’s tdistribution with d degrees of freedom). A well-known alternative to the direct fitting of many symmetric but non-normal error distributions is through scale mixtures of normals (=-=Andrews and Mallows, 1974-=-). From page 210 of Carlin and Louis (2000), we have the alternate td-formulation model 5, ( wi ∼ 1 d χ2 d = gamma 2 yi ∼ normal µi; 1 wiτ ( d ) ; d ; 2 ) : Unlike our other examples the form of the l... |

135 | G.: A correspondence between bayesian estimation on stochastic processes and smoothing by splines - Kimeldorf, Wahba - 1970 |

106 | Improper priors, spline smoothing and the problem of guarding against model errors in regression - Wahba - 1978 |

105 | Analysis of Multivariate Probit Models - Chib, Greenberg - 1998 |

98 | An asymptotic equivalence of choice of model by crossvalidation and Akaike’s criterion - Stone - 1977 |

90 | Bayes factors and model uncertainty
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Citation Context ...RJMCMC) in varying dimension models (Green, 1995). Moreover, RJMCMC methodology helps us to account for model uncertainty using Bayesian model averaging techniques (see Draper, 1995, Chatfield, 1995, =-=Kass and Raftery, 1995-=-, Cairns, 2000). However, this methodology is demanding in both the design stage and the implementation. 3 Distributions for claim counts In this section we focus on three popular distributions for mo... |

83 | How biased is the apparent error rate of a prediction rule - Efron - 1986 |

77 | Generalized linear models, 2nd edn - McCullagh, Nelder - 1989 |

71 |
Expected information as expected utility
- Bernardo
- 1979
(Show Context)
Citation Context ...efined (up to a multiplicative constant) as −2log{p.y|θ/} (Kullback and Leibler, 1951; Burnham and Anderson, 1998) and can be interpreted as a measure of ‘surprise’ (Good, 1956), logarithmic penalty (=-=Bernardo, 1979-=-) or uncertainty. Suppose that we have an estimator ˜θ.y/ of the pseudotrue parameter θt . Then the excess of the true over the estimated residual information will be denoted dΘ{y; θ t ; ˜θ.y/} =−2log... |

67 |
Bayes estimates for the linear model (with discussion
- Lindley, Smith
- 1972
(Show Context)
Citation Context ... exponential, or logistic or t4; wherezij = (xij − ¯xj)/sd(xj) are the standardised covariates. The ridge regression approach assumes a further restriction that the βj for j =1, 2, 3 are exchangable (=-=Lindley and Smith, 1972-=-) and therefore we have βj ∼ N(0,φ−1 ). We use ‘non-informative’ priors with prior precision equal to 10−3 for the independent regression and for φ in ridge regression we use gamma prior with paramete... |

63 | Bayes and Empirical Bayes Methods for Data Analysis, 2 nd Edition. Boca Raton - Carlin, Louis - 2000 |

61 | Model choice: a minimum posterior predictive loss approach - Gelfand, Ghosh - 1998 |

61 | Predictive model selection - Laud, Ibrahim - 1995 |

52 | A 1960 Statistical Theory and Methodology - Brownlee |

49 |
Model selection and inference
- Burnham, Anderson
- 1998
(Show Context)
Citation Context ...r Linde 2.3. True and estimated residual information The residual information in data y conditional on θ may be defined (up to a multiplicative constant) as −2log{p.y|θ/} (Kullback and Leibler, 1951; =-=Burnham and Anderson, 1998-=-) and can be interpreted as a measure of ‘surprise’ (Good, 1956), logarithmic penalty (Bernardo, 1979) or uncertainty. Suppose that we have an estimator ˜θ.y/ of the pseudotrue parameter θt . Then the... |

49 | On Measuring and Correcting the Effects of Data Mining and Model Selection - Ye - 1998 |

38 | Hierarchical generalized linear model (with discussion - Lee, Nelder - 1996 |

35 | Science and Statistics - Box - 1976 |

30 | MCMC Methods for Computing Bayes Factors: A Comparative Review - Han, Carlin - 2001 |

29 | A likelihood-based method for analysing longitudinal binary responses - Fitzmaurice, Laird - 1993 |

29 | Performing Likelihood Ratio Tests with MultiplyImputed Data Sets.” Biometrika - Meng, Rubin - 1992 |

28 | The direct use of likelihood for significance testing - Dempster - 1997 |

28 |
Distribution of informational statistics and criterion of model fitting
- Takeuchi
- 1976
(Show Context)
Citation Context ...ed model, both in its own right, say to assess the degrees of freedom of estimators, and as a contribution to model choice: for example, criteria such as BIC (Schwarz, 1978), AIC (Akaike, 1973), TIC (=-=Takeuchi, 1976-=-) and NIC (Murata et al., 1994) all trade off model fit against a measure of the effective number of parameters in the model. However, the foregoing discussion suggests that such measures of complexit... |

20 | Counting degrees of freedom in hierarchical and other richly parameterised models - Hodges, Sargent - 1998 |

18 | Random-Effects Models for Longitudinal Data Using Gibbs Sampling - Gilks, Wang, et al. - 1993 |

16 |
Empirical Bayes estimates of agestandardised relative risks for use in disease mapping
- Clayton, Kaldor
- 1987
(Show Context)
Citation Context ... of pD and DIC to compare alternative prior and likelihood structures. 8.1. The spatial distribution of lip cancer in Scotland We consider data on the rates of lip cancer in 56 districts in Scotland (=-=Clayton and Kaldor, 1987-=-; Breslow and Clayton, 1993). The data include observed (yi) and expected (Ei) numbers of cases for each county i (where the expected counts are based on the age- and sex-standardized national rate ap... |

10 |
The Surprise Index for the Multivariate Normal Distribution
- Good
- 1956
(Show Context)
Citation Context ...n data y conditional on θ may be defined (up to a multiplicative constant) as −2log{p.y|θ/} (Kullback and Leibler, 1951; Burnham and Anderson, 1998) and can be interpreted as a measure of ‘surprise’ (=-=Good, 1956-=-), logarithmic penalty (Bernardo, 1979) or uncertainty. Suppose that we have an estimator ˜θ.y/ of the pseudotrue parameter θt . Then the excess of the true over the estimated residual information wil... |

10 | Bayesian model choice: what and why - Key, Pericchi, et al. - 1999 |

7 | Splines from a Bayesian Point of View - Linde - 1995 |

6 |
Limiting behaviour of posterior distributions when the model is incorrect
- Berk
- 1966
(Show Context)
Citation Context ...value θt (Sawa, 1978) which specifies a likelihood p.Y|θt / that minimizes the Kullback–Leibler distance Et [log{pt.Y/}=p.Y|θt/]from pt .Y/. Having observed data y, under reasonably broad conditions (=-=Berk, 1966-=-; Bunke and Milhaud, 1998) p.θ|y/ converges to θt as information on the components of θ increases. Thus Bayesian analysis implicitly relies on p.Y|θt / being a reasonable approximation to pt .Y/, and ... |

6 | 2001: Bayesian Varying-coefficient Models using Adaptive Regression Splines
- Biller, Fahrmeir
(Show Context)
Citation Context ...odels for diagnostic probabilities in screening studies (Erkanli et al., 1999), longitudinal binary data using Markov regression models (Erkanli et al., 2001), spline models with Bernoulli responses (=-=Biller and Fahrmeir, 2001-=-), multistage models for treatment usage which combine to form a total DIC (Gelfand et al., 2000), complex spatial models for Poisson counts (Green and Richardson, 2000), pharmacokinetic modelling (Ra... |

6 |
Diagnostics for Smoothing Splines
- Eubank
- 1985
(Show Context)
Citation Context ...594 D. J. Spiegelhalter, N. G. Best, B. P. Carlin and A. van der Linde of freedom’ n − tr.H/. In this class of models this measure of complexity coincides with pD. Interest in regression diagnostics (=-=Eubank, 1985-=-; Eubank and Gunst, 1986) and cross-validation to determine the smoothing parameter τ=λ (Wahba (1990), section 4.2) also drew attention to the diagonal entries of the hat matrix as leverage values. Li... |

6 | Bayesian neural networks with correlating residuals
- Vehtari, Lampinen
- 1999
(Show Context)
Citation Context ...a total DIC (Gelfand et al., 2000), complex spatial models for Poisson counts (Green and Richardson, 2000), pharmacokinetic modelling (Rahman et al., 1999) and structures of Bayesian neural networks (=-=Vehtari and Lampinen, 1999-=-). The following examples illustrate the use of pD and DIC to compare alternative prior and likelihood structures. 8.1. The spatial distribution of lip cancer in Scotland We consider data on the rates... |

6 | Comparing hierarchical models for spatio-temporally misaligned data using the deviance information criterion - Zhu, Carlin - 2000 |

5 | Evaluation of highly complex modeling procedures with Binomial and Poisson data. Unpublished manuscript - Ye, Wong - 1997 |