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According to van Fraassen, inference to the best explanation (IBE) is incompatible with Bayesianism. To argue to the contrary, many philosophers have suggested hybrid models of scientific reasoning with both explanationist and probabilistic elements. This paper offers another such model with two novel features. First, its Bayesian component is imprecise. Second, the domain of credence functions can be extended., Author(s): Namjoong Kim [sup.1] Author Affiliations: (1) grid.256681.e, 0000 0001 0661 1492, Department of philosophy, Gyeongsang National University, , Jinjoodaero 501, Inmoon 1 hogwan 404, 52828, Jinju-si, Gyeongsangnamdo, Republic of [...]

Features involving the taste, smell, touch, and sight of products, as well as attributes such as safety and confidence, are not easily measured in product research without respondents actually experiencing [...]

Business analytics has evolved from being a novelty used by a select few to an accepted facet of conducting business. Recommender systems form a critical component of the business analytics [...]

In this paper we use Bayes estimates of a multinomial probit model with fully flexible substitution patterns to forecast consumer response to ultra-low-emission vehicles. In this empirical application of the [...]

We investigate whether partners in a brand alliance should be similar or dissimilar in brand image to foster favorable perceptions of brand fit. Using a Bayesian nonlinear structural equation model [...]

Disaggregate demand in the marketplace exists on a grid determined by the package sizes offered by manufacturers and retailers. Although consumers may want to purchase a continuousvalued amount of a [...]

Social learning can occur when information is transferred from existing customers to potential customers. It is especially important when the information that is conveyed pertains to experience attributes, i.e., attributes [...]

Online advertising campaigns often consist of multiple ads, each with different creative content. We consider how various creatives in a campaign differentially affect behavior given the targeted individual s ad [...]

We reanalyze endogenous sample selection in the context of customer scoring, targeting, and influencing decisions. Scoring relies on ordered lists of probabilities that customers act in a way that contributes [...]

This paper considers the history of keywords used in Marketing Science to develop insights on the evolution of marketing science. Several findings emerge. First, 'pricing' and 'game theory' are the [...]

Most ads in practice receive no more than a single eye fixation. This study investigates the limits of what ads can communicate under such adverse exposure conditions. We find that [...]

The development of progress plans for each identified technical performance parameter (TPP) is a critical element of technical performance measurement. The measured values of TPPs are referred to as technical [...]

For high-dimensional data sets with complicated dependency structures, the full likelihood approach often leads to intractable computational complexity. This imposes difficulty on model selection, given that most traditionally used information criteria require evaluation of the full likelihood. We propose a composite likelihood version of the Bayes information criterion (BIC) and establish its consistency property for the selection of the true underlying marginal model. Our proposed BIC is shown to be selection-consistent under some mild regularity conditions, where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size. Simulation studies demonstrate the empirical performance of this new BIC, especially for the scenario where the number of parameters increases with sample size. Technical proofs of our theoretical results are provided in the online supplemental materials. KEY WORDS: Consistency; Model selection; Pseudo-likelihood; Variable selection.

Copulas have proven to he very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a 'vine' in the graphical models literature, where each copula is entitled a 'pair-copula.' We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are Bayesian model averages over the distribution of the lag structure of the Markov process. Using a simulation study we show that the selection approach is reliable and can improve the estimates of both conditional and unconditional pairwise dependencies substantially. We also show that a vine with selection outperforms a Gaussian copula with a flexible correlation matrix. The advantage of the pair-copula formulation is further demonstrated using a longitudinal model of intraday electricity load. Using Gaussian. Gumbel, and Clayton pair-copulas we identify parsimonious decompositions of intraday serial dependence, which improve the accuracy of intraday load forecasts. We also propose a new diagnostic for measuring the goodness of lit of high-dimensional multivariate copulas. Overall, the pair-copula model is very general and the Bayesian method generalizes many previous approaches for the analysis of longitudinal data. Supplemental materials for the article are also available online. KEY WORDS: Bayesian model selection; Copula diagnostic; Covarianee selection; D-vine; Goodness of fit; Inhomogeneous Markov process; Intraday electricity load; Longitudinal copulas.

In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist perspective. We show that the mixed-model formulation of penalized splines can help obtain, at least approximately, confidence bands with either Bayesian or frequentist properties. Simulations and data analysis support the proposed methods. The R package ConfBands accompanies the article. KEY WORDS: B-spline; Bayesian penalized spline; Confidence band; Mixed model; Penalization.

We develop a class of models for inference about abundance or density using spatial capture-recapture data from studies based on camera trapping and related methods. The model is a hierarchical model composed of two components: a point process model describing the distribution of individuals in space (or their home range centers) and a model describing the observation of individuals in traps. We suppose that trap- and individual-specific capture probabilities are a function of distance between individual home range centers and trap locations. We show that the models can be regarded as generalized linear mixed models, where the individual home range centers are random effects. We adopt a Bayesian framework for inference under these models using a formulation based on data augmentation. We apply the models to camera trapping data on tigers from the Nagarahole Reserve, India, collected over 48 nights in 2006. For this study, 120 camera locations were used, but cameras were only operational at 30 locations during any given sample occasion. Movement of traps is common in many camera-trapping studies and represents an important feature of the observation model that we address explicitly in our application. Key words: abundance, Bayesian analysis; binomial point process; camera trapping; carnivore surveys; data augmentation; density estimation; hierarchical model; Markov chain Monte Carlo; spatial capturerecapture; tigers; trapping array; trapping grid.

Using data generated from laboratory experiments, we test and compare the empirical accuracy of two models that focus on judgment errors associated with processing information from random sequences. We test for regime-shifting beliefs of the type theorized in Barberis et al. (Barberis, N., A. Shleifer, R. Vishny. 1998. A model of investor sentiment. J. Financial Econom. 49(3) 307-343) and for beliefs in the 'law of small numbers' as modeled in Rabin (Rabin, M. 2002. Inference by believers in the law of small numbers. Quart. J. Econom. 117(3) 775-816). In our experiments, we show subjects randomly generated sequences of binary outcomes and ask them to provide probability assessments of the direction of the next outcome. Inconsistent with regime-shifting beliefs, we find that subjects are not more likely to predict that the current streak will continue the longer the streak. Instead, consistent with Rabin (2002), subjects are more likely to expect a reversal following short streaks and continuation after long streaks. Results of a 'test-of-fit' analysis based on structural estimation of each model also favor the model in Rabin. To provide more insight on Rabin, we use an additional experimental treatment to show that as the perception of the randomness of the outcome-generating process increases, subjects are more likely to predict reversals of current streaks. Key words: decision analysis; inference; experimental economics; behavioral finance History: Received October 5, 2006; accepted April 14, 2009, by George Wu, decision analysis. Published online in Articles in Advance August 27, 2009., 1. Introduction Experimental research by cognitive psychologists provides a multiplicity of evidence showing that cognitive biases have profound effects on belief formation and revision. Translating the wide variety of documented [...]

A methodology is proposed to efficiently model a random set via a multistage hierarchical Bayesian model. We define a NonOverlapping Random Disk Model (NORDM), which is similar in spirit to the well-known Poisson--Boolean model. This model is formulated in a conditional setting that facilitates Bayesian sampling of important parameters in the model. This framework can accommodate any object, not just those with disk shapes, although the model can be easily extended to include any known compact convex set instead of the disc (e.g., polygons or ellipses). We further propose a growth model that is conceptually simple and allows straightforward estimation of parameters, without the need for tedious calculations of hitting or inclusion probabilities. The model is applied to severe storm cell development as obtained from weather radar. KEY WORDS: Growth model; Hierarchical Bayesian estimation; Nonoverlapping random disc model; Poisson-Boolean model.

Bayesian model-based classifiers, both unsupervised and supervised, have been studied extensively, and their value and versatility have been demonstrated on a wide spectrum of applications within science and engineering. A majority of the classifiers are built on the assumption of intrinsic discreteness of the considered data features or on their discretization prior to the modeling. On the other hand, Gaussian mixture classifiers have also been utilized to a large extent for continuous features in the Bayesian framework. Often, the primary reason for discretization in the classification context is the simplification of the analytical and numerical properties of the Bayesian models. However, the discretization can be problematic due to its ad hoc nature and the decreased statistical power to detect the correct classes (or clusters) in the resulting procedure. Here, we introduce an unsupervised classification approach for fuzzy feature vectors that utilizes a discrete model structure while preserving the continuous characteristics of data. This goal is achieved by replacing the ordinary likelihood by a binomial quasi-likelihood to yield an analytical expression for the posterior probability of a given clustering solution. The resulting model can also be justified from an information-theoretic perspective. Our method is shown to yield highly accurate clusterings for challenging synthetic and empirical data sets and to perform favorably compared to some alternative approaches. Index Terms--Bayesian clustering, fuzzy modeling, quasi-likelihood, continuous data.

We present a statistical approach for identifying residues in DNA sequences for which diversity may be maintained by natural selection. Bayesian generalized linear models (GLMs) are used to describe patterns of mutation in a DNA sequence alignment. Posterior distributions of key quantities, such as probabilities of nonsynonymous and synonymous mutations per site, are studied. Inference in this class of models is achieved through customary Markov chain Monte Carlo methods. Model selection is dealt with by means of a minimum posterior predictive loss approach. We describe how information on the evolutionary process underlying the sequences can be formally incorporated into the models through structured priors. The proposed methodology was designed to analyze several DNA sequences encoding the vaccine candidate apical membrane antigen-1 (AMA-1) of the human malaria parasite Plasmodium falciparum. The study of genetic variability in antigen sequences is relevant to determining whether a particular antigen is a viable target for a vaccine construct. Using a simulation study, we first compare the GLM-based approach to existing methods for delecting sites under selection that are based on stochastic models of sequence evolution. We then apply the proposed models to the AMA-1 sequence data, which allows us to identify residues with the greatest disparities between nonsynonymous and synonymous changes. Recent experimental evidence suggests that several of these residues are immunologically relevant, indicating that the proposed models may be used predictively to identify functionally significant residues in antigens for which experimental results are not yet available. KEY WORDS: Bayesian generalized linear model; DNA sequence data: Malaria antigens; Model comparison; Mutation count data: Natural selection: Structured priors.

We investigate a solution to the problem of multisensor scene understanding by formulating it in the framework of Bayesian model selection and structure inference. Humans robustly associate multimodal data as appropriate, but previous modeling work has focused largely on optimal fusion, leaving segregation unaccounted for and unexploited by machine perception systems. We illustrate a unifying Bayesian solution to multisensory perception and tracking, which accounts for both integration and segregation by explicit probabilistic reasoning about data association in a temporal context. Such an explicit inference of multimodal data association is also of intrinsic interest for higher level understanding of multisensory data. We illustrate this by using a probabilistic implementation of data association in a multiparty audiovisual scenario, where unsupervised learning and structure inference is used to automatically segment, associate, and track individual subjects in audiovisual sequences. Indeed, the structure-inference-based framework introduced in this work provides the theoretical foundation needed to satisfactorily explain many confounding results in human psychophysics experiments involving multimodal cue integration and association. Index Terms--Sensor fusion, audiovisual, multimodal, detection, tracking, graphical models, model selection, Bayesian inference, speaker association.

We develop a Bayesian capture-recapture model that provides estimates of abundance as well as time-varying and heterogeneous survival and capture probability distributions. The model uses a state-space approach by incorporating an underlying population model and an observation model, and, here is applied to photo-identification data to estimate trends in the abundance and survival of a population of bottlenose dolphins (Tursiops truncatus) in northeast Scotland. Novel features of the model include simultaneous estimation of time-varying survival and capture probability distributions, estimation of heterogeneity effect for survival and capture, use of separate data to inflate the number of identified animals to the total abundance, and integration of separate observations of the same animals from right and left side photograph. A Bayesian approach using Markov chain Monte Carlo methods allows for uncertainty in measurement and parameters, and simulations confirm the model's validity. KEY WORDS: Abundance; Logits; Photo-identification; Survival; Trends.

Genomic alterations have been linked to the development and progression of cancer. The technique of comparative genomic hybridization (CGH) yields data consisting of ffluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data. We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Because the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation--based inference. Publicy available data on pancreatic adenocarcinoma, glioblastoma multiforme, and breast cancer are analyzed, and comparisons are made with some widely used algorithms to illustrate the reliability and success of the technique. KEY WORDS: Amplifications'. Cancer; Copy number; Deletions; DNA; Genomic aterations; Intensity ratios; MCMC; Tumor.

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors for the regression parameters and independent exponential priors on their variances. A connection with the inverse-Gaussian distribution provides tractable full conditional distributions. The Bayesian Lasso provides interval estimates (Bayesian credibleintervals) that can guide variable selection. Moreover, the structure of the hierarchical model provides both Bayesian and likelihood methods for selecting the Lasso parameter. Slight modifications lead to Bayesian versions of other Lasso-related estimation methods, including bridge regression and a robust variant. KEY WORDS: Empirical Bayes; Gibbs sampler: Hierarchical model; Inverse Gaussian; Linear regression; Penalized regression; Scale mixture of normals.

In this article we consider the relationship of covariates to the time to caries of permanent first molars. This involves an analysis of multivariate doubly interval-censored data. To describe this relationship. We suggest an accelerated failure time model with random effects, taking into account that the observations are clustered, Indeed, up to four permanent molars per child enter into the analysis, implying up to four caries times for each child. Each distributional part of the model is specified in a flexible way as a penalized Gaussian mixture with an overspecified number of mixture components. A Bayesian approach with the Markov chain Monte Carlo methodology is used to estimate the model parameters, and a software package in the R language has been written that implements it. KEY WORDS: Clustered data; Density smoothing, Gaussian Markov random field; Markov chain Carlo; Regression; Survival data.

Zellner's g prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this article we study mixtures of g priors as an alternative to default g priors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular. We present theoretical properties of the mixture g priors and provide real and simulated examples to compare the mixture formulation with fixed g priors, empirical Bayes approaches, and other default procedures. KEY WORDS: AIC; Bayesian model averaging; BIC; Cauchy; Empirical Bayes; Gaussian hypergeometric functions; Model selection; Zellner-Siow priors.

Beta distributions with both parameters equal to 0, 1/2, or 1 are the usual choices for 'noninformative' priors for Bayesian estimation of the binomial parameter. However, as illustrated by two examples from the Bayesian literature, care needs to be taken with parameter values below 1, both for noninformative and informative priors, as such priors concentrate their mass close to 0 and/or 1 and can suppress the importance of the observed data. These examples concern the case of no successes (or failures) and illustrate the informativeness of the Jeffreys prior usually recommended as the 'consensus prior.' In particular, the second example suggests that when the binomial parameter is known to be very small, an informative prior from the beta(1, b) family (b > 1) seems appropriate, while a beta(a, b) with a < 1 can be too informative. It is thus argued that sensitivity analysis of an informative prior should be based on a consensus posterior corresponding to the Bayes-Laplace prior rather than the Jeffreys prior. KEY WORDS: Bayesian inference; Binomial distribution; Noninformative priors; Prior families.

In this paper, we present a modulated Poisson process model to describe and analyze arrival data to a call center. The attractive feature of this model is that it takes into account both covariate and time effects on the call volume intensity, and in so doing, enables us to assess the effectiveness of different advertising strategies along with predicting the arrival patterns. A Bayesian analysis of the model is developed and an extension of the model is presented to describe potential heterogeneity in arrival patterns. The proposed model and the methodology are implemented using real call center arrival data. Key words: call center; advertising strategy; modulated Poisson process; Bayesian analysis; heterogeneity, 1. Introduction and Background Forecasting call volume data that is based on a specific advertisement or promotion plan poses a challenging problem for call centers. The need for optimal scheduling [...]

We propose Bayesian parametric and semiparametric partially linear regression methods to analyze the outcome-dependent follow-up data when the random time of a follow-up measurement of an individual depends on the history of both observed longitudinal outcomes and previous measurement times. We begin with the investigation of the simplifying assumptions of Lipsitz, Fitzmaurice, Ibrahim, Gelber, and Lipshultz, and present a new model for analyzing such data by allowing subject-specific correlations for the longitudinal response and by introducing a subject-specific latent variable to accommodate the association between the longitudinal measurements and the follow-up times. An extensive simulation study shows that our Bayesian partially linear regression method facilitates accurate estimation of the true regression line and the regression parameters. We illustrate our new methodology using data from a longitudinal observational study. KEY WORDS: Bayesian cubic smoothing spline; Latent variable; Partially linear model.

The direct simulation method, which has enabled exact Bayesian inference for discrete mixture distributions, is used for continuous mixture distribution models. This method is compared with the particle filters and Gibbs sampler by using simulated data and real datasets.

A general formulation is provided for Bayesian model-based clustering, where the subset labels are exchangeable up to covariate effects. The statistical performance of the optimal clustering is compared with methods like hierarchical clustering, which are model-based but ad hoc in their detailed definition.

This paper presents a newly developed simulation-based approach for Bayesian model updating, model class selection, and model averaging called the transitional Markov chain Monte Carlo (TMCMC) approach. The idea behind TMCMC is to avoid the problem of sampling from difficult target probability density functions (PDFs) but sampling from a series of intermediate PDFs that converge to the target PDF and are easier to sample. The TMCMC approach is motivated by the adaptive Metropolis--Hastings method developed by Beck and Au in 2002 and is based on Markov chain Monte Carlo. It is shown that TMCMC is able to draw samples from some difficult PDFs (e.g., multimodal PDFs, very peaked PDFs, and PDFs with flat manifold). The TMCMC approach can also estimate evidence of the chosen probabilistic model class conditioning on the measured data, a key component for Bayesian model class selection and model averaging. Three examples are used to demonstrate the effectiveness of the TMCMC approach in Bayesian model updating, model class selection, and model averaging. DOI: 10.1061/(ASCE)0733-9399(2007)133:7(816) CE Database subject headings: Bayesian analysis; Simulation; Markov chains; Monte Carlo method.

Adverse effects of trademark dilution and factors influencing this trend are examined. Its impact is measured using a hierarchical Bayes associative network model.

A long-term HIV-1 dynamic model by considering drug potency, drug exposure, and drug susceptibility was proposed and HIV-1 dynamic parameters were estimated. A large between-subject variation in estimated viral dynamic parameters was observed, even after accounting for variations in drug exposure and drug susceptibility and it is suggested that the characteristics of HIV-1 dynamics are host-dependent.

This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom selection. Mortality rates in patient discharge records are widely used to infer hospital quality. However, hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others. In this situation the assumption of random admission leads to spurious inference about hospital quality. This study controls for hospital selection using a model in which distance between the patient's residence and alternative hospitals are key exogenous variables. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator, and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals. The study uses data on 74,848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia. It finds the smallest and largest hospitals to be of the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study's selection model. KEYWORDS: Bayesian inference, hospital quality, simultaneous equations, MCMC, Medicare, pneumonia, mortality.

Information about the structure of a causal system can come in the form of observational data--random samples of the system's autonomous behavior--or interventional data--samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people's ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision-making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints. Keywords: Causal reasoning; Decision making; Bayesian networks; Bayesian models; Rational inference; Hypothesis testing; Active learning; Observational learning; Interventions; Structure learning; Web experiments; Human experimentation; Computer simulation

Before a logistic regression model is used to describe the relationship between a binary response variable and predictors, the fit of the model should be assessed. The nature of any model deficiency may indicate that some aspect of the model should be reformulated or that poorly fitting observations need to be considered separately. We propose graphical methodology based on a Bayesian framework to address issues such as this. Publicly available software allows diagnostic plots to be constructed quickly and easily for any model of interest. These plots are more intuitive and meaningful than traditional graphical diagnostics such as residual plots. KEY WORDS: Bayesian methodology; Diagnostic plot; Marginal model plot; Model criticism; Posterior predictive distribution.

This article suggests a method for variable and transformation selection based on posterior probabilities. Our approach allows for consideration of all possible combinations of untransformed and transformed predictors along with [...]

A sequential discovery sampling procedure is to randomly sample and audit one record at a time until either a first record containing a major fault is discovered or a pre-determined maximum number of successive fault-free records has been sampled. If a major fault is discovered, the sampling is terminated and the account is rejected. If no major fault is discovered, the account is accepted and the auditor provides a confidence interval and associated confidence level for the tree proportion of records in the account containing major faults. A dynamic programming model incorporating the auditor's degree of belief regarding the existence of records in the account containing major faults, sampling costs and the value of discovery of a major fault is presented. The implied confidence level associated with the optimal maximum sample size of the dynamic programming model provides valuable supplementary information for an auditor in the provision of the confidence level for the required confidence interval. Journal of the Operational Research Society (2002) 53, 119-122. DOI: 10.1057/palgrave/jors/2601270 Keywords: discovery sampling; dynamic programming; Bayesian model

We observe n events occurring in (0, T] taken from a Poisson process. The intensity function of the process is assumed to be a step function with multiple changepoints. This [...]

Michael Henderson is a Graduate Student, Statistics Department, University of Georgia, Athens, GA 30602-1952. Mary C. Meyer is Assistant Professor, Department of Statistics, University of Georgia, Athens, GA 30602-1952 (E-mail: mmeyer@stat.uga.edu)., ********** The simple problem of providing a confidence interval for the estimate of a binomial parameter can prove to be quite interesting. There are a suprising variety of competing intervals [...]

Two red deer populations in Scotland are used to test culling rates based on a Bayesian calibration of a wildlife management model. The two samples demonstrate the need to incorporate different variables in management models to maintain stability for dissimilar populations.

We present a model of entry and exit with Bayesian learning and price competition. A new product of initially unknown quality is introduced in the market, and purchases of the product yield information on its true quality. We assume that the performance of the new product is publicly observable. As agents learn from the experiments of others, informational externalities arise. We determine the Markov Perfect Equilibrium prices and allocations. In a single market, the combination of the informational externalities among the buyers and the strategic pricing by the sellers results in excessive experimentation. If the new product is launched in many distinct markets, the path of sales converges to the efficient path in the limit as the number of markets grows.