Giunti and Laveder	The Power of Confidence Intervals
Bityukov and Krasnikov	Uncertainties and discovery potential in planned experiments
Cooper-Sarkar	The ZEUS NLO QCD fit to determine parton distributions and $\alpha_s$
Kjaer	Exact optimization of likelihood analyses in a unified Bayesian-Frequentist Monte Carlo Framework: The "K2-filter"
Kjaer	Optimal statistical treatment of parameterized systematic errors in a unified Bayesian-Frequentist Monte Carlo Framework.
Kjaer	Statistically regularized deconvolution of unbinned spectra containing event-by-event resolution functions in a unified Bayesian-Frequentist Monte Carlo Framework.
Kahrimanis	Objectively derived default prior depends on stopping rule; Bayesian treatment of nuisance parameters is defended
Sharafiddinov	Mass of the Neutrino and Evolution of the Universe.
Wolter	Measurement of physical quantities in the Bayesian framework using neural networks to fit the probabilitydistributions
Redin	Advanced Statistical Techniques in muon g-2 experiment at BNL
Aslan and Zech	Comparison of different goodness-of-fit tests
Roe and Woodroofe	BooNE Neutrino Oscillations
Wang	Diagnose bad fit to multiple data sets
Vaiciulis	Support Vector Machines in Analysis of Top Quark Production
Sina and Seo	Low Count Poisson Statistics and Cosmic-ray Spectral Studies
Yabsley	Statistical practice at the Belle experiment, and some questions
Angelini et al.	Jet reconstruction through a general purpose clustering algorithm
Rolke and Lopez	Bias-Corrected Confidence Intervals For Rare Decays
Blobel and Kleinwort	A new method for the high-precision alignment of track detectors
Blobel	An unfolding method for high energy physics experiments
Kinoshita	Estimating Goodness-of-Fit for Unbinned Maximum Likelihood Fitting

Signorelli et al.	Strong Confidence limits and frequentist treatment of systematics.
Bock and Wittek	Multidimensional event classification in images from gamma ray air showers
Parodi et al.	How to include the information coming from $B^0_s$ oscillations in CKM fits
Hakl and Richter-Was	Application of Neural Networks optimized by Genetic Algorithms to Higgs boson search
Punzi	Limits setting in difficult cases and the Strong Confidence approach.
Karlen	Credibility of Confidence Intervals
Demortier	Bayesian treatments of systematic uncertainties
Conrad et al.	Coverage of Confidence Intervals calculated in the Presence of Systematic Uncertainties.
Hill and DeYoung	Application of Bayesian statistics to muon track reconstruction in AMANDA
Raja	Confidence limits and their errors
Towers	Overview of Probability Density Estimation methods (PDE's)
Towers	How to optimise the signal/background discrimination of a MV analysis (hint: reduce the number of variables)

Stump	New Generation of Parton Distributions and Methods of Uncertainty Analysis
Bluemlein & Boettcher	Polarized Parton Distributions and their Errors
Reisert	The H1 NLO QCD fits to determine $\alpha_s$ and parton distribution functions.

C. Giunti	INFN, Sez. di Torino, and Dip. di Fisica Teorica, Univ. di Torino, I-10125 Torino, Italy
M. Laveder	Dip. di Fisica "G. Galilei", Univ. di Padova, and INFN, Sez. di Padova, I-35131 Padova, Italy
The Power of Confidence Intervals
We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter bounded to be non-negative. We show that the confidence intervals (upper limits) obtained with a (biased) method that near the boundary has large power in testing the parameter against larger alternatives and small power in testing the parameter against smaller alternatives are physically more significant. Considering the recently proposed methods with correct coverage, we show that the physical significance of upper limits is smallest in the Unified Approach and highest in the Maximum Likelihood Estimator method. We illustrate our arguments in the specific cases of a bounded Gaussian distribution and a Poisson distribution with known background.

S.I. Bityukov	Institute for High Energy Physics, Protvino
N.V. Krasnikov	Institute for Nuclear Research, Moscow
Uncertainties and discovery potential in planned experiments
Several criteria used by physicist to quantify the ratio of signal to background are compared. The approach for taking into account the uncertainty in estimations of signal and background is proposed

A.M.Cooper-Sarkar (Oxford U.)	on behalf of the ZEUS Collaboration
The ZEUS NLO QCD fit to determine parton distributions and $\alpha_s$
A next-to-leading order QCD fit was performed on the $e^+p$ deep inelastic scattering data collected by the ZEUS experiment over the years 1996-1997, together with fixed taarget data. The gluon and quark densities of the proton have been extracted. Experimental systematic errors take into account point to point correlations. This allows a correct evaluation of experimental uncertainties in the extracted parton densities. A combined fit for the strong coupling constant,$\alpha_s(M^2_Z)$, and the gluon and quark densities was performed yielding $\alpha_s(M^2_Z) = 0.117\pm0.003\pm0.004$

Niels Kjaer	CERN, CH - 1211 Geneva 23, Switzerland
Jorgen D'Hondt	IIHE (ULB-VUB), Pleinlaan 2, BE-1050 Brussels, Belgium
Exact optimization of likelihood analyses in a unified Bayesian-Frequentist Monte Carlo Framework: The "K2-filter"
This paper presents a generalization of the Kalman filter process control to a situation where the stochastic parts are not analytically computable and only available as Monte Carlo generated events. In a Monte Carlo framework where the exact Matrix elements, Pi(x), are known on an event-by-event basis the maximum likelihood technique provides the optimal analysis. To O(1/n), where n is the number of events the information content can be computed as: I = 1/error^2 = sum_i gi^2, where gi = -dln(Pi(x))/dx\|x0 gi is thus exactly computable from the generation information. When the measurement result, E(x), is close to the reference point, x0, gi contains all the needed information for the estimation of E(x). On the analysis level this paper shows that the error is given by: I = 1/error^2 = sum_i [ gi^2 - (ai-gi)^2 ] , where ai = -dln(Li(x))/dx\|x0 is the information on the analysis level. Therefore, any likelihood analysis is optimized by maximizing I. The optimization is explicitly linear in ai, which leads to solutions of simple linear equations as in other Kalman filter cases. The optimization procedure assumes an initial analysis. Any set of parameters used in the initial analysis can be optimized and the analysis output can be optimized as a function of any observable simultaneously extracting all information content of the observables. The analyses can be optimized for any value of x0 through reweighting of the Monte Carlo events, leading to the final likelihood curves being integrals of ai(x0)dxO. Generalizing the optimization procedure to simultaneous measurements of several observables is shown to give complications which rise only linearly as a function of the number of observables. The Bayesian optimization procedure itself is controlled using a Frequentist's approach, which is simply applying the Jackknife in case of uncorrelated events. This procedure is shown to give exact estimations of any potential overtraining in the optimization procedure. Finally, several examples and recommendations for practical use are given

Niels Kjaer	CERN, CH - 1211 Geneva 23, Switzerland
Optimal statistical treatment of parameterized systematic errors in a unified Bayesian-Frequentist Monte Carlo Framework.
This paper describes a method to explicitly incorporate systematic errors in the statistical part of a likelihood analysis. In Monte Carlo based likelihood analyses systematic errors can be interpreted as uncertainties in the underlying Monte Carlo Model. Often, these uncertainties can be reliable parameterized giving parameters, s, in the simulation, which are either controlled by the information from the data itself or limited by external information from other data. In this case it is shown that the optimal way to treat systematic errors is to simultaneously estimate the observables of interest and the systematic parameters themselves. In the K2-filter approach this is done using an event-by-event analysis with optimal observables for both the observables of interest and s. Even though events contain no explicit information on the systematic s, the measurement will often depend on a combination of s and other observables. The practical implementation of the proposed procedure is simply to generate events according to the a priori known distribution of s. If the measurement does not depend on s this causes no harm, while if it does depend on s, the Monte Carlo sample can be used to extract the correlations with s. This is then transformed into multi-dimensional likelihood curve for the observables and s. The simultaneous measurements can hence be done using classical techniques. An a priori knowledge of s can be folded into the likelihood, and experiments can be combined directly taking the systematic correlations into account.

Niels Kjaer	CERN, CH - 1211 Geneva 23, Switzerland
Statistically regularized deconvolution of unbinned spectra containing event-by-event resolution functions in a unified Bayesian-Frequentist Monte Carlo Framework.
A recursive Bayesian algorithm is applied to update a generator function in the case having a set of events having individual Bayesian resolution functions. The recursive process is locally regularized by computing the statistical significance of the proposed update from the data themselves. The significance is evaluated in a Frequentist's framework using the Jackknife estimator. The algorithm is stopped when all proposed updates have significances which are below a regularization parameter. The choice of this parameter to be one standard deviation is shown to give a deconvoluted spectrum which is optimal and information conserving at the level of one standard deviation. The output of the algorithm is formally a Monte Carlo generator function, with a full covariance matrix, which ensures full usage of the spectral information after deconvolution. Only localized information and features are retained by applying the algorithm, which explains why it is possible to obtain information conservation. The algorithm is extendable to any number of dimensions, but relies on the concept of locality, which is only uniquely defined in 1-d. With an additional required definition of locality the algorithm is shown also to be information conserving in 2-d deconvolution problems at the level of one standard deviation. This rapidly converging algorithm is unique since it correctly deals with event-by-event resolution functions and does not produce any artificial features which other unbinned algorithms are prone to do.

George Kahrimanis	Southern University at Baton Rouge
Objectively derived default prior depends on stopping rule; Bayesian treatment of nuisance parameters is defended
Previous attempts (mine, too) for defining objective priors have been ineffectual, on account of both unsure derivation and implausible results. In a fresh approach, the existence of a default prior probability density is established in a special case: if the experimental error, as a random variable, is known to be independent of the true value. This finding is extended to the generic case. The resulting prior is the same as the one proposed by Balasubramanian (1996). Consequently, prejudice can be eliminated in Bayesian analysis. This assessment calls for a review of comparison between Bayesian and classical methods. Only the Bayesian method is suitable for obtaining results from atypical data sets. Still, the comparison between classical and Bayesian results can point out for us that the sensitivity of an experiment may need enhancement in a certain range. (Alternatively, one can compute a classical goodness of fit, in this way also testing the plausibility of the model.) Although useful, the classical approach has certain severe side effects, such as coupling of the background with the measured signal even if no events are recorded, and the counterintuitive lowering of upper limits in the presence of systematic uncertainties. Remedies have existed for years, though not yet endorsed by everybody: these side effects have been suppressed by means of a mixed approach, in which the background and/or the systematic uncertainties are treated in a Bayesian fashion. Such mixing is defended again here, with the rationale that normally our beliefs regarding systematic variables and the background are far from controversial (unlike beliefs concerning the estimated variables) therefore a Bayesian treatment is suitable. This view becomes more defensible in view of the possibility of objective Bayesian procedures.

Rasulkhozha S. Sharafiddinov	Institute of Nuclear Physics, Uzbekistan Academy of Sciences
Mass of the neutrino and evolution of the universe.
Our study of elastic scattering of unpolarized and longitudinal polarized electrons and their neutrinos by a spinless nuclei [1,2] shows clearly that the neutrino electric charge [2] connected with its nonzero rest mass arise as a consequance of the availability of compound structures of the physical mass and charge. Having the fact that the force of the Newton attraction of the two neutrinos must be less than the force of their Coulomb repulsion, we can establish the new restrictions on the neutrino mass and charge. Some considerations and logical confirmations of the existence of intraneutrino interratio between the forces of different nature have been listed which must explain the violation of chiral symmetry as well as the steadity of the Universe in the dependence of the ultimate structures of elementary particles charges and masses. [1] R.B.Begzhanov and R.S.Sharafiddinov, Mod.Phys.Lett. A15(2000)557 [2] R.S.Sarafiddinov, Spacetime & Substance, 4(2000)176

Marcin Wolter	Tufts University, Boston, USA Institute of Nuclear Physics, Krakow, Poland
Measurement of physical quantities in the Bayesian framework using neural networks to fit the probability distributions
A Bayesian approach to the reconstruction of particle properties is presented. As an illustration, the algorithm is applied to the measurement of the Higgs boson mass. Monte Carlo events generated with various Higgs masses are used to determine the probability distribution for each Higgs boson mass. The probability is a function of measured quantities, in this example energies of b-tagged jets as well as the the angle between them. The probability distributions are fitted using neural networks and the final Higgs mass probability distribution is obtained as a product of the single event distributions. The proposed method offers advantages compared with the traditional approach based on the invariant mass distribution. The miscalibration of the measured quantities is automatically corrected by the probability distributions. Also the Higgs mass resolution can be superior due to the fact that well reconstructed events enter the final distribution with higher weight than the events with worse mass resolution.

Sergei I. Redin

Budker Institute of Nuclear Physics, Novosibirsk, Russia
Yale University, USA.

Advanced Statistical Techniques in muon g-2 experiment at BNL

In our muon g-2 experiment we intend to measure the muon g-2 value to about 0.3 ppm (parts per million) accuracy. There are two quantities in this experiment which have to be measured precisely: one is magnetic field in muon storage ring, measured by system of NMR probes in terms of frequency of proton spin resonance (omega_p) and another is frequency of g-2 oscillations in time distribution of electrons emerging from muon decays (omega_a).

Technically, omega_a is to be found by chi-squared optimization of parameters of a fit function approximating time distribution (histogram) of decay electrons. This is a standard data analysis technique in high energy physics, however precision requirement in our experiment is exceptionally high. By this reason all statistical properties of fitted distribution, such as statistical errors and correlations among parameters, must be well understood, all statistical tests must be well justified and all possible systematic effects must be extensively studied, etc.

A simple procedure which was developed in our g-2 experiment to calculate analytically statistical errors and correlations of parameters is given. In a course of these studies it was found that correlation between frequency and phase of g-2 oscillations can be used to improve statistical error of omega_a by use of information on phase, which we posess in our experiment. An appropriate equation was derived.

Similar procedure was developed for analytical estimation of systematic shift of omega_a due to presence of small unidentified background. This allowed us to study number of possible sources of systematic errors including such a fundamental systematic effect as finite binwidth, which might be important for any distribution in physics and elsewhere.

Some of omaga_a stability checks in g-2 experiment are based on a set-subset comparison. These are, in particular, checks for stability with respect to change of (1) the histogram fit start time and (2) energy threshold of decay electrons. For the first case it was shown that difference in omega_a should be within square root of [ sigma^2(subset) - sigma^2(full set) ] for one standard deviation. As a matter of fact, this set-subset formula is valid for any distribution no matter of how many parameters it has and whether or not they correlate to each other. We have proved this theorem ourself, though it might be found somewhere in literature.

For the case of energy threshold change, this theorem is not applied since some parameters of g-2 distribution (phase and amplitude of g-2 oscillations) depend on average energy and hence depend on energy threshold. Nonetheless procedure, developed for the first case allowed us to derive formula for this situation too. The formula contains sigma, phase and amplitude for both subset and full set.

B. Aslan and G. Zech	Universit�t Siegen, Germany
Comparison of different goodness-of-fit tests
Various procedures of distribution free goodness-of-fit test and tests of the uniform distribution, respectively, have been extracted from literature. In addition, we have constructed several new tests. We have investigated the power of the selected tests with respect to different slowly variing distortions of experimental distributions which could opccur in physics applications. None of the tests is optimum for all kind of distortions. The application of most goodness-of-fit tests is restricted to one dimension. We discuss the possibility to extend binning free tests to two or more dimensions.

Byron P. Roe and Michael B. Woodroofe	University of Michigan, Ann Arbor, MI 48109, U.S.A.
BooNE Neutrino Oscillations
For neutrino oscillations, the probability of oscillation is given by p_phi,Delta-m^2(E) =sin^2 2phi sin^2(1.27Delta-m^2 L/E), where phi and Delta-m^2 are parameters to be determined. E is the neutrino energy and L is the length of the neutrino path. The mini-BooNE experiment has an incoming nu_mu beam and searches for nu_mu-->nu_e. If the results of the LSND experiment are due to neutrino oscillations, the number of events expected would be of the order of one hundred to a few hundred. The process can be modelled as a marked Poisson process with the energy of the events as "marks". The likelihood can be written as L = (product_k=1 ^n =N[theta(e)g(e,x) + bh(e,x)])times exp(-Lambda)de_1de_2... where Lambda = int_0^infty int_0^1 N[theta(e)g(e,x) + bh(e,x)]dxde. x represents parameters of event shape. Here theta g represents the signal and bh represents the background. g and h are normalized to 1. g is a function of one of the parameters, Delta-m^2, and theta is a function of both parameters. Appropriate methods for maximizing the likelihood and setting frequentist confidence intervals or limits will be discussed.

Ming-Jer Wang	Institute of Physics, Academia Sinica, Taipei, Taiwan
Diagnose bad fit to multiple data sets
Determining parameter uncertainties on parton distributions using global fits to data sets is becoming an important research area due to the increase of the measurement precision in hadron collider experiments. Before extracting a set of reliable parameter uncertainties, one needs to make sure that a consistent data set has been established. For this reason, new criterion for tests of goodness of fit to multiple data sets had been proposed to detect inconsistent data set in a global fit of parton distribution function. This method did indicate that the combined CTEQ5 data set is not internally consistent. In the present study, we propose to examine the inconsistent experimental data set which is identified by parameter-fitting criteria, using pull distribution and residual plot in order to allocate uncorrected systematic shift in the data. Seven classes of pull distributions were postulated for seven possible distortions. Only five of them could be clearly identified. This provides us a basis for the diagnosis purpose. If the residual uncertainty is not available, we still could examine the residual plot against physical variable instead of pull distribution. In addition, detailed systematic pattern might be revealed by this residual plot also.

Anthony Vaiciulis	University of Rochester, Rochester, NY, USA
Support Vector Machines in Analysis of Top Quark Production
Multivariate data analysis techniques have the potential to improve physics analyses in many ways. The common classification problem of signal/background discrimination is one example. A comparison of a conventional method and a Support Vector Machine algorithm is presented here for the case of identifying top quark signal events in the dilepton decay channel amidst a large number of background events.

Ramin Sina and Eun-Suk Seo	Institute for Physical Sciences and Technology, University of Maryland
Low Count Poisson Statistics and Cosmic-ray Spectral Studies
The Cosmic-ray spectrum above 10 GeV can be described as power law which steepens at about 1 PeV (Commonly referred to as the "Knee" in the spectrum) and hardens again at about 1 EeV (the "Ankle" in the spectrum). At about 30 EeV, the spectrum is expected to die off due to interactions with the cosmic microwave background. However several experiments have reported significant flux above this maximum energy. Although the origin of the ultra high energy part of the spectrum is still a mystery, cosmic-ray particles with energies below 1 PeV are believed to be accelerated by supernova shocks, with the maximum energy proportional to the charge of the cosmic-ray particle. To test the supernova shock acceleration model, it is essential to use detectors with good charge resolution to separate protons from heavier nuclei. Such detectors must be placed above the atmosphere. Since the flux below the Knee falls off by a factor of approximately 500 with every decade of energy, therefore, these detectors will have a very limited statistics near the maximum energies expected from supernovae shocks, i.e. about 1 PeV. The currently operating ground-based experiments also suffer from small statistics in their highest energy range. In this paper we will discuss the statistical techniques needed to measure spectral features with low count Poisson statistics.

B.D. Yabsley	Virginia Polytechnic Institute and State University
Statistical practice at the Belle experiment, and some questions
The Belle collaboration operates a general-purpose detector at the KEKB asymmetric-energy e+ e- collider, performing a wide range of measurements in beauty, charm, tau and 2-photon physics. In this paper, the treatment of statistical problems in past and present Belle measurements is reviewed. The adoption of a uniform method in the future requires the development of standard tools. Early results from a tool to calculate frequentist confidence intervals from multiple measurements in the Unified Approach, under the simplifying assumption of Gaussian errors, are presented, and compared with more exact calculations. A number of open questions, including the preferred method of treating systematic errors, are also discussed.

L. Angelini, P. De Felice, L. Nitti, M. Pellicoro, S. Stramaglia	Department of Physics and I.N.F.N. - Bari
Jet reconstruction through a general purpose clustering algorithm.
A general purpose algorithm for data mining [1], based on the synchronization property of extended spatio-temporal chaotic systems, has been properly modified and tailored to reconstruct jets in high energy particle physics. Comparison with standard approaches will be presented. [1] L. Angelini et al., P.R.L. 85 (554) 2000.

Wolfgang Rolke and Angel Lopez	University of Puerto Rico - Mayaguez
Bias-Corrected Confidence Intervals For Rare Decays
When we find limits for rare decays we usually first search for a cut combination with a high signal to noise ratio. Unfortunately this introduces a bias in the signal rate, making it appear higher than it really is. We will discuss a method based on the bootstrap algorithm which corrects for this "cut selection" bias. We will present the results of a mini Monte Carlo study that first shows the presence of this type of bias, and then also shows that our method is quite effective in correcting for it, yielding confidence intervals with the correct coverage.

Volker Blobel Claus Kleinwort	Inst. f. Experimentalphysik Hamburg Deutsches Elektronensynchrotron DESY
A new method for the high-precision alignment of track detectors
Track detectors in high energy physics experiments require an accurate determination of a large number of alignment parameters. A method has been developed, which allows the determination of up to several thousand alignment parameters in a simultaneous linear least squares fit of an arbitrary number of tracks. The method is general for problems where global parameters (e.g. from alignment) and independent sets of local parameters (e.g track parameters like angles and curvatures) appear simultaneously. Constraints between global parameters can be incorporated. The huge matrix system of the normal equations is reduced to the size corresponding to the global parameters, which allows the exact determination of the global parameters. A program has been developed which allows a certain fraction of outliers in the data. The sensitivity of the method is demonstrated in an example of the alignment of a 56-plane drift chamber and a 2-plane silicon tracker. In this example about 1000 alignment parameters incl. local drift velocity values are determined in a fit of 50 thousand tracks from ep-interactions and field-on and field-off cosmics.

Volker Blobel	Inst. f. Experimentalphysik Hamburg
An unfolding method for high energy physics experiments
Finite detector resolution and limited acceptance require to apply unfolding methods to distributions measured in high energy physics experiments. Information on the detector resolution is usually given by a set of Monte Carlo events. Based on the experience with a widely used unfolding program (RUN) a modified method has been developed. The first step of the method is a maximum likelihood fit of the Monte Carlo distributions to the measured distribution in one, two or three dimensions; the finite statistic of the Monte Carlo events is taken into account by the use Barlows method with a new method of solution. A clustering method is used before to combine bins in sparsely populated areas. In the second step a regularization is applied to the solution, which introduces only a small bias. The regularization parameter is determined from the data after a diagonalization and rotation procedure.

Kay Kinoshita	University of Cincinnati
Estimating Goodness-of-Fit for Unbinned Maximum Likelihood Fitting
An unbinned maximum likelihood fit has the advantage that it maximizes the use of available information to obtain the shape of a distribution in the face of limited statistics. Measurements made recently by Belle using this method include sin$2\phi_1$ and B and D meson lifetimes. However, this method has one difficulty in that there has been no method for evaluating goodness-of-fit for the result. We derive a formal estimate of goodness-of-fit for this method.

Giovanni Signorelli a,b) Donato Nicolo' b) Giovanni Punzi a,b)	a) Istituto Nazionale di Fisica Nucleare e Universita' PISA b) Scuola Normale Superiore di PISA
Strong Confidence limits and frequentist treatment of systematics.
Calculation of Confidence Limits using the Strong Confidence paradygm is described. Application to standard problems like Gaussian and Poisson with background are discussed and compared to other methods. Prescriptions to introduce systematic uncertainties in a pure frequentist way are suggested. The computation of the limits for the CHOOZ neutrino oscillation experiment in this framework is illustrated.

Rudy Bock and Wolfgang Wittek	CERN and MPI,Munich
Multidimensional event classification in images from gammaray air showers.
Exploring signals from outer space has become a science under fast expansion: astroparticle physics. Among earthbound observations, the technique of gamma ray Cherenkov telescopes using the atmosphere as calorimeter is a particularly recent technique. Events in such telescopes appear as 2-dimensional images (100 - 1000 pixels), and the image characteristics have to be used to discriminate between the interesting gammas and the dominating charged particles, mostly protons. Present techniques of analysis express the images in terms of several parameters; the goal is to find some test statistic(s) which allow(s) to optimize the classification. Among optimization techniques, the following have been used or are under investigation - cut sequences in the image parameters - Classification and Regression Trees (CART, commercial products) - Linear Discriminant Analysis (LDA) - Composite Probabilities (under development) - Kernel methods - Artificial Neural Networks The methods and some early tentative results will be briefly presented, remaining problems will be discussed.

F. Parodi P. Roudeau A. Stocchi A. Villa	Genova University LAL-Orsay CERN/LAL-Orsay Milano University
How to include the information coming from $B^0_s$ oscillations in CKM fits
In this paper we discuss how to include the information coming from the searches for $B^0_s$ oscillations in CKM fits, starting from the standard output (amplitude spectrum) of the LEP Oscillation Working Group. The adopted method (Likelihood ratio) is compared with other proposed methods.

Frantisek Hakl Elzbieta Richter-Was	Institute of Computer Science, Czech Academy of Science, Prague, Czech Republic Institut fyziki Jadrovej, Jagelonian University, Krakow, Poland
Application of Neural Networks optimized by Genetic Algorithms to Higgs boson search
Our contribution describe an application of a neural network approach to SM (standard model) and MSSM (minimal supersymetry standard model) Higgs search in the associated production $t\bar{t}H$ with $H \rightarrow b\bar{b}$. This decay channel is considered as a discovery channel for Higgs scenarios for Higgs boson masses in the range 80 - 130 GeV. Neural network model with a special type of data flow is used to separate $t\bar{t}jj$ background from $H \rightarrow b\bar{b}$ events. Used neural network combine together a classical neural network approach and linear decision tree separation process. Parameters of these neural networks are randomly generated and population of predefined size of those networks is learned to get initial generation for the following genetic algorithm optimization process. A genetic algorithm principles are used to tune parameters of further neural network individuals derived from previous neural networks by GA operations of crossover and mutation. The goal of this GA process is optimization of the final neural network performance. Our results show that NN approach is applicable to the problem of Higgs boson detection. Neural network filters can be used to emphasize difference of $M_{bb}$ distribution for events accepted by filter (with better $\frac{signal} {background}$ ate) and $M_{bb}$ distribution for original events (with original $\frac{signal}{background}$ rate) under condition that there is no loss of significance. This improvement of the shape of $M_{bb}$ distribution can be used as a criterion of existence of Higgs boson decay in considered discovery channel.

Giovanni Punzi	Scuola Normale Superiore and INFN-Pisa
Limits setting in difficult cases and the Strong Confidence approach.
Examples of difficult situations in the practice of limits setting are examined, including measurements affected by significant systematic uncertainties. Fully frequentist solutions to these problems are described, based on the concept of Strong Confidence, a localized application of the standard Confidence Level concept possessing many desirable properties from a physicist's viewpoint.

Dean Karlen	Carleton University
Credibility of Confidence Intervals
Classical confidence intervals are often misinterpreted by scientists and the general public alike. The confusion arises from the two different definitions of probability in common use. Likewise, there is general dissatisfaction when confidence intervals are empty or they exclude parameter values for which the experiment is insensitive. In order to clarify these issues, the use of a Bayesian probability to evaluate the credibility of a classical confidence interval is proposed.

Luc Demortier	The Rockefeller University
Bayesian treatments of systematic uncertainties
We discuss integration-based methods for incorporating systematic uncertainties into upper limits, both in a Bayesian and a hybrid frequentist-Bayesian framework. For small systematic uncertainties, we show that the relevant integral can be expressed as a convolution. We derive the correct form of this convolution, examine its properties, and present several examples.

Jan Conrad, Olga Botner, Allan Hallgren and Carlos P. de los Heros	High Energy Physics Division, Uppsala University
Coverage of Confidence Intervals calculated in the Presence of Systematic Uncertainties.
We present a Monte Carlo implementation of Highland \& Cousins method to include systematic uncertainties into confidence interval calculation. Different ordering schemes and different types of paramtrizations of systematic uncertainties are considered. Using this implementation we perform measurements of the coverage for different assumptions on the size and shape of the systematic uncertainties. We illustrate the effect of including systematic uncertainties in a limit calculation with a real example taken from the field of high energy neutrino astrophysics

Gary Hill Tyce DeYoung	University of Wisconsin Santa Cruz Institute for Particle Physics
Application of Bayesian statistics to muon track reconstruction in AMANDA
The AMANDA neutrino telescope detects neutrinos by observing Cherenkov light from secondary leptons produced in charged current neutrino interactions. At lower energies, a background of penetrating muons approximately 10^6 times as numerous as neutrino-induced muons is rejected by looking for muons travelling upward through the earth. A comparison of maximum likelihood and Bayesian approaches to track reconstruction will be presented, and the implications of each approach for background rejection will be discussed.

Sherry Towers	State University of New York at Stony Brook
Overview of Probability Density Estimation methods (PDE's)
Probability Density Estimation techniques are gaining popularity in particle physics. I will give an overview of these powerful methods, and a comparison of their performance relative to those of neural networks.

Sherry Towers	State University of New York at Stony Brook
How to optimise the signal/background discrimination of a MV analysis (hint: reduce the number of variables)
As particle physics experiments grow more complicated with each passing decade, so too do the analyses of data collected by these experiments. Multivariate analyses involving dozens of variables are not uncommon in this field. I will show how the use of many variables in a multivariate analysis can actually degrade the ability to distinguish signal from background, rather than improve it.

Daniel R. Stump	Michigan State University
New Generation of Parton Distributions and Methods of Uncertainty Analysis
A new generation of parton distribution functions, CTEQ6 in the sequence of CTEQ global analyses, is presented. This analysis significantly extends previous analyses because it includes a full treatment of available correlated systematic errors for the data sets, and provides a systematic treatment of uncertainties of the resulting distribution functions. The properties of the new parton distributions are shown. Methods for computing uncertainties of physical predictions based on the CTEQ6 analysis are described.

Johannes Bluemlein and Helmut Boettcher	DESY Zeuthen
Polarized Parton Distributions and their Errors
A QCD analysis of the world data on polarized deep inelastic scattering is presented in leading and next-to-leading order. New parametrizations are derived for the quark and gluon distributions and the value of alpha_s(M_Z) is determined. Emphasis id put on the derivation of fully correlated 1sigma error bands for these distributions, which are directly applicable to determine experimental errors of other polarized observables. The error calculation based on Gaussian error propagation through the evolution equations is discussed in detail.

Pekka Sinervo	University of Toronto
Estimating the Significance of Data
A review of what is commonly known as "signal significance" in the observation of new phenomena in experimental particle physics data will be provided. The statistical concepts underlying definitions of signal significance will be summarized and specific recent examples of their uses will be discussed.

Rajendran Raja	Fermi National Accelerator laboratory
Confidence Limits and their errors
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use especially in cases of limited statistics. We introduce the concept of statistical errors of confidence limits and argue that not only should limits be calculated but also their errors in order to represent the results of the analysis to the fullest. We show that comparison of two different limits from two different experiments becomes easier when their errors are also quoted. Use of errors of confidence limits will lead to abatement of the debate on which method is best suited to calculate confidence limits.

Fred James	CERN
Overview of Bayesian and Frequentist Principles
A summary of the principles forming the basis for Bayesian and Frequentist methodologies, including: 1. How probability is defined and used. 2. Point estimation (how the "best estimate" is defined). 3. Interval estimation (how intervals are constructed to contain a given confidence or credibility). 4. Hypothesis testing (how to compare two or more hypotheses). 5. Goodness-of-fit (how to measure whether data are compatible with a single given hypothesis). 6. Decision making (how to make optimal decisions)

Fred James	CERN
The relation of goodness-of-fit to confidence intervals
Confidence intervals are by convention defined so that they contain a given "confidence", which is either coverage probability for frequentist intervals or Bayesian probability content for Bayesian credibility intervals. Alternatively, one could imagine defining intervals (or more generally regions in parameter space) which contain all parameter values which give good fits to the data. This latter definition may be closer to what physicists expect. Especially when the complement of a confidence interval (an exclusion region) is published, the reader may interpret that as the ensemble of parameter values excluded because they don't fit to the data. Why are exclusion regions not calculated that way? Should they be?

Fred James	CERN
Comment on a paper by Garzelli and Giunti
In a paper "Bayesian View of Solar Neutrino Oscillations" [hep-ph/0108191 v3], Garzelli and Giunti list eight reasons for using Bayesian inference (which they call "only a few facts"). I will show that one can just as easily interpret those "facts" to arrive at the opposite conclusion. The goal of this exercise is not to show that Bayesian inference is right or wrong, but to show that this very general way of reasoning does not lead to unambiguous conclusions. I propose a different procedure, based on finding the method with the properties appropriate to the way the results will be used or interpreted.

Burkard Reisert	Max-Planck-Institut f\"ur Physik, Munich. on behalf of the H1 Collaboration
The H1 NLO QCD fits to determine $\alpha_s$ and parton distribution functions.
A dedicated NLO QCD fit to the H1 $e^+p$ neutral current cross sections (1994-97) and the BCDMS $\mu p$ data allowed the strong coupling constant $\alpha_s$ and the gluon distribution to be simultaneously determined. Correlated, uncorrelated and statistical errors of the measurements are treated by the fit to obtain an error band for the gluon distribution. The variation of input parameters to the fit gives rise to additional uncertainties for the gluon and $alpha_s$. A fit to the neutral and charged current cross sections including the latest $e^-p$ and $e^-p$ measurements is in preparation aiming for the extraction of the full set of parton density functions.