A. Dawid. Statistical theory: the prequential approach. Journal of the Royal Statistical Society, Series A, 147:278--292, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....representations from a combination of prior representations, prior data, expert guidance, anomaly detection, and performance feedback. Our view of the role of learning in intelligent agent design fits naturally into a recently developed interpretation of probability called prequential theory (Dawid, 1984; Dawid 2 The requirement that the influence graph be acyclic may be too restrictive for generic object modeling applications. While the semantics of undirected links is less clear (cf. Jensen, 1996) thus making the Machine Learning MCMC Issue 7 7 1 01 and Vovk, 1999) Prequential ....

Dawid, A. P. (1984). "Statistical Theory, the Prequential Approach." Journal of the Royal Statistical Society A 147: 278-292.

....issue is discussed in more detail in Section 2. In our earlier work [15] we demonstrated empirically that marginal likelihood can be in practice a poor model selection criterion for classification domains, and that model selection criteria based on prequential (predictive sequential) approaches [5, 6, 7, 19] or cross validation [23, 9] lead to more accurate predictive models. In this paper we extend and elaborate our previous work in two ways. First, instead of constraining ourselves to simple variants of the Naive Bayes model, here we change the model family to consist of more complex finite mixture ....

.... intuitively appealing (and in many cases conceptually convenient) to think of the data D as a random sample from some true but unknown probability distribution, it should be pointed out that the model selection problem can also be formalized without such an assumption, as demonstrated in, e.g. [5, 20, 18]. Given a set F = fM 1 ; Mmg of possible models, and a data sample D, in the (unsupervised) model selection problem, the task is to choose a model M 2 F so that the resulting predictive distribution P (X 1 ; XnjD; M) Z P (X 1 ; XnjD; M; P ( jD; M)d (1) yields more ....

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A.P. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society A, 147:278--292, 1984.

....upon a particular data source (AbdelGhaly et al. 1986, Brocklehurst and Littlewood, 1992) These tools will be used to compare the accuracy of the new model with that of the older parametric models. Basically there are two main tools: the u plot and the prequential likelihood ratio (PLR) (Dawid, 1984). The PLR is a very general and powerful means of comparing the accuracy of sequences of predictions coming from two competing prediction systems while the u plot detects bias in a series of model predictions. In fact it does this in a very general way which has been used successfully to ....

Dawid, A.P. (1984) `Statistical Theory: The Prequential Approach', Journal Royal Statistical Society, Series A,147, 278-292.

....that the theoretical arguments against the use of marginal likelihood are also meaningful in practice. However, since we have to solve the problem in practice we also consider alternatives to the unsupervised marginal likelihood model selection score. This includes Dawid s prequential approach [ Dawid, 1984 ] empirical crossvalidation methods [ Stone, 1974 ] and the supervised marginal likelihood approximation discussed in [ Kontkanen et al. 1998 ] As opposed to the unsupervised marginal likelihood, these criteria can be easily modified for different loss functions. Dawid s prequential ....

.... likelihood P (v N j u N ; M ) which are generally different from the (unsupervised) maximum likelihood parameters (see the discussion in [ Friedman et al. 1997 ] Prequential Approaches In Dawid s prequential (predictive sequential) approach for statistical validation of models [ Dawid, 1984 ] alternative models are compared by measuring their cumulative loss, so the validation score is computed through a sequential updating of the predictive distribution. From the rules of probability theory it follows that Gamma log P (DjM) Gamma log N Y i=1 P (x i jx i Gamma1 ) ....

A.P. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society A, 147:278--292, 1984.

....loss of an algorithm over a sequence of m trials is P m t=1 (y t Gamma y t ) 2 : A critical aspect of this model is that when the algorithm is making its prediction y t for the tth instance x t , it has access to pairs (x s ; y s ) only for s t. We adopt a worst case outlook, following [Daw84, Vov90, LW91, LLW91, FMG92, MF92, CFH 93] and many others, assuming nothing about the environment of the predictor, in particular the pairs (x 1 ; y 1 ) x m ; y m ) Our results can be loosely interpreted as having the following message: To the extent that the environment is ....

A. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society (Series A), pages 278--292, 1984.

....be a security intermediate between D and E (cf. the end of Section 4 of Shiryaev (1994) This paper is part of a general program of providing more parsimonious foundations for probability theory and its applications. In the most complete form this program is described in Shafer (1995) see also Dawid (1984, 1985) and Vovk (1993a, 1993b) Acknowledgments The research described in this publication was made possible in part by Grant No. MRS300 from the International Science Foundation and Russian Government. It was finished while the author was a Fellow at the Center for Advanced Study in the ....

Dawid, A.P. (1984): "Statistical Theory. The Prequential Approach" (with Discussion), J. R. Statist. Soc. A, 147, 278--292.

....and Dawid [15] no assumptions are made about true distributions; it is entirely competitive on line. Competitive on line statistics is concerned with, of course, the on line performance of statistical procedures. Many procedures, like the RR, can be used in both batch and on line setting. Dawid s [19] prequential approach to statistics recommends using on line performance as a measure of quality of batch algorithms; therefore, competitive on line results also provide a justification for the use of the corresponding algorithms in the batch setting (provided the philosophy of prequential ....

A Philip Dawid. Statistical theory: the prequential approach. J R Statist Soc A, 147:278--292, 1984.

....observable, rather than uncovering some true underlying structure. This is more in line with the Bayesian way of thinking, where models are mere windows through which to view the world [see Poirier (1988) but have no inherent meaning in terms of characteristics of the real world. See also Dawid (1984) and Geisser and Eddy (1979) Forecasting is conducted conditionally upon the regressors, so we will generate qk dimensional vectors z f ,f =1, q, given which we will predict the observable y. In empirical applications, z f will typically 9 be constructed from some original value r f of which ....

Dawid, A.P. (1984), "Statistical Theory: The Prequential Approach," Journal of the Royal Statistical Society, Ser. A, 147, 278-292.

....assumptions, as does generalized estimating equations. It is obtained by projecting the partial score function onto a collection of Hilbert spaces with inner product specified by conditional moments, conditioned on nested events. We also demonstrate, within a prequential frame of reference (Dawid 1984, 1991) that the estimating function is optimal among the largest collection of estimating functions that can be described by the postulated conditional moments. Just as quasi likelihood can be viewed as a generalization of least squares, projected partial likelihood can be viewed as a ....

....This construction might at first glance seem heuristic and arbitrary: we simply sum the projections of fs j g, which are onto different linear spaces fG j g associated with different inner products fh Delta; Deltai j g. However, this is entirely natural within a prequential frame of reference. In Dawid (1984, 1991) it is argued that if we are to assess the adequacy of the joint distribution P of a sequence of random variables fX j g based on the realization fx j g, all that is relevant is the realization fx j g, together with the associated sequence of conditional distributions fP j g; P j ( Delta) ....

Dawid, A.P. (1984). Statistical theory: the prequential approach (with discussion). J. R. Statist. Soc. A, 147, 278-292.

....and Dawid [14] no assumptions are made about true distributions; it is entirely competitive on line. Competitive on line statistics is concerned with, of course, the on line performance of statistical procedures. Many procedures, like the RR, can be used in both batch and on line setting. Dawid s [18] prequential approach to statistics recommends using on line performance as a measure of quality of batch algorithms; therefore, competitive on line results also provide a justi cation for the use of the corresponding algorithms in the batch setting (provided the philosophy of prequential ....

A Philip Dawid. Statistical theory: the prequential approach. J R Statist Soc A, 147:278-292, 1984.

....the true model and seeks only as small a predictive error as possible. In practice, this often leads to consistency, indicating how strong the criterion of good prediction is. The prequential approach has been developed 5 in a series of papers by A. P. Dawid and co authors, see for instance Dawid (1992, 1984), Seillier Moiseiwitsch and Dawid (1993) amongst many others. Most recently Skouras and Dawid (1998) study the eciency of point prediction systems. A key point made by Dawid in these works is that the performance of a method must be assessed independently of the method to avoid con ict of ....

Dawid, A. P (1984) Statistical theory: The prequential approach. J. Roy. Statist. Soc. Ser. B, 147, 278-292.

....been a prominent feature of the Bayesian forecasting literature (Harrison and Stevens, 1976; West and Harrison, 1997) and recent advances in Markov Chain Monte Carlo (Gelman, Carlin, Stern and Rubin, 1995) have increased the pace of progress. The closely related prequential Bayesian literature (Dawid, 1984) also features density forecasts prominently. Interest in forecasts of various sorts creates a derived demand for methods of evaluating forecasts. In parallel with the historical emphasis on point forecasts, most literature has focused on the evaluation of point forecasts (Diebold and Lopez, ....

Dawid, A.P. (1984), "Statistical Theory: The Prequential Approach," Journal of the Royal 24 Statistical Society, Series A, 147, 278-292.

.... For previous work on model selection in the context of nonparametric regression estimation, see, for example, Barron [1] for complexity regularization) and Vapnik [5] for structured risk minimization) In this paper, we estimate the model dimension using prequential model selection due to Dawid [2] and Rissanen [4] Prequential model selection is a data driven methodology for selecting between rival models on the basis of their predictive abilities. For a given set of observations, as illustrated below, the predictive ability of a model is measured by the model s accumulated prediction ....

A. P. Dawid, "Statistical theory: The prequential approach," J. R. Statist. Soc. A, vol. 147, part 2, pp. 278-292, 1984.

....domains, the unsupervised marginal likelihood model selection score does not perform well in supervised model selection tasks. As an alternative to the unsupervised marginal likelihood model selection score, we consider several other model selection criteria, including Dawid s prequential approach (Dawid, 1984), empirical crossvalidation methods (Stone, 1974; Geisser, 1975) and the supervised marginal likelihood approximation discussed in (Kontkanen, Myllymaki, Silander, Tirri, 1998) As opposed to the unsupervised marginal likelihood, these criteria can be easily modified for different loss ....

....likelihood P (v N j u N ; M ) which are generally different from the (unsupervised) maximum likelihood parameters (see the discussion in (Friedman et al. 1997) 2.2. 2 Prequential Approaches In Dawid s prequential (predictive sequential) approach for statistical validation of models (Dawid, 1984), alternative models are compared by measuring their cumulative loss, so the validation score is computed through a sequential updating of the predictive distribution. From the rules of probability theory it follows that Gamma log P (DjM ) Gamma log N Y i=1 P (x i jx i Gamma1 ) N X ....

Dawid, A. (1984). Statistical theory: The prequential approach. Journal of the Royal Statistical Society A, 147, 278--292.

....where the proposed methods may be of potential interest include problems of prediction from long time series with a rapidly growing parameter space, and methods for monitoring model adequacy. As an example of the latter category, consider the prequential method for model criticism proposed by Dawid (1984, 1991) Implementation of this approach requires computing the probability of each observation under its foward predictive distribution (conditional on previous observations) Forward predictive distributions associated with individual data items may be easily computed as a by product of our ....

Dawid, A. P. (1984) Statistical theory: the prequential approach (with discussion). J. Roy. Statist.

....in the case that a fixed function is to be learned from noise free examples, we show that if the distributions on the domain generating the examples change by at most O(ffl 2 = d log(1=ffl) then any consistent algorithm learns to within accuracy ffl. 1 Introduction In prediction models [7, 11] like that studied in this paper, learning proceeds in trials, where in the tth trial, the algorithm (1) is given x t chosen from some set X , 2) is required to output a prediction y t 2 f0; 1g, and (3) discovers y t 2 f0; 1g. We will consider two models for problems like these, both introduced ....

A. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society (Series A), pages 278--292, 1984.

....data compression which have been explored in the information theory literature. We then give applications of these results to the theory of pattern recognition [Vap82] and PAC learning [Val84] We take the extreme position, as advocated by Dawid and Vovk in the theory of Prequential Probability [Daw84, Dawarb, Dawara, Vov90a] Rissanen in his theory of stochastic complexity [Ris78, RL81, Ris86, Yam91] and Cover, Lempel and Ziv, Feder and others in the theory of universal prediction and data compression of individual sequences [FMG92, MF92, Cov65, CS77, Han57, Vov92] that no assumptions ....

A. P. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society, Series A, pages 278--292, 1984.

....that if the distributions on the domain generating the examples change by at most O(ffl 2 = d log(1=ffl) then any consistent algorithm learns to within accuracy ffl. For a list of the typographical symbols used, please consult Latex, by Leslie Lamport. 1 Introduction In prediction models [Daw84, HLW94] like that studied in this paper, learning proceeds in trials, where in the tth trial, the algorithm (1) is given x t chosen from some set X, 2) is required to output a prediction y t 2 f0; 1g, and (3) discovers y t 2 f0; 1g. The focus of these models differs from those like the PAC model ....

A. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society (Series A), pages 278--292, 1984.

....a sequence of probability forecasts, produced through some statistical estimation procedure, should provide a good long run representation of the actual outcome of those forecasts. Indeed, this idea lies at the heart of Phil Dawid s theory of prequential assessment, as represented for example by Dawid (1984) as well as Dawid and Seillier Moiseiwitsch (1993) The real difficulty lies in the specification of an appropriate probability framework for this comparison. Traditionally, frequentists have used the probability framework of independent replications of some experiment under identical conditions. ....

Dawid, A.P. (1984). Statistical theory: the prequential approach (with discussion). J.R. Statist. Soc. A 147, 278--292.

....and, therefore, satisfy both Prequential Principles. Keywords: FARTHINGALE; FORECASTING; GOODNESS OF FIT; LIMIT THEOREMS OF PROBABILITY THEORY; MARTINGALE; PERFECT INFORMATION GAME; STRONG PREQUENTIAL PRINCIPLE; WEAK PREQUENTIAL PRINCIPLE 1 INTRODUCTION The prequential approach to Statistics (Dawid, 1984, 1991, 1992a, 1992b) is based on the idea that we can judge the quality of an inference method by converting it into a forecasting system, and assessing the empirical success of the sequence of one step ahead forecasts that it implies. In this context, it is natural to impose what we here term ....

Dawid, A. P. (1984) Statistical theory: the prequential approach (with discussion) . J. R. Statist. Soc. A, 147, 278--292.

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A. Dawid. Statistical theory: the prequential approach. Journal of the Royal Statistical Society, Series A, 147:278--292, 1984.

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A. Philip Dawid. Statistical theory: the prequential approach. Journal of the Royal Statistical Society A, 147:278--292, 1984.

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Dawid, A.P. (1984), "Statistical Theory: the Prequential Approach," Journal of the Royal Statistical Society, Ser. A, 147, 278-292.

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A.P. Dawid. Statistical Theory: The Prequential Approach. J. R. Statist. Soc. A, 147:278--292, 1984.

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Dawid, A.P. (1984), "Statistical Theory: the Prequential Approach," Journal of the Royal Statistical Society, Ser. A, 147, 278-292.

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