6,630 research outputs found
Bayesian Inference of Arrival Rate and Substitution Behavior from Sales Transaction Data with Stockouts
When an item goes out of stock, sales transaction data no longer reflect the
original customer demand, since some customers leave with no purchase while
others substitute alternative products for the one that was out of stock. Here
we develop a Bayesian hierarchical model for inferring the underlying customer
arrival rate and choice model from sales transaction data and the corresponding
stock levels. The model uses a nonhomogeneous Poisson process to allow the
arrival rate to vary throughout the day, and allows for a variety of choice
models. Model parameters are inferred using a stochastic gradient MCMC
algorithm that can scale to large transaction databases. We fit the model to
data from a local bakery and show that it is able to make accurate
out-of-sample predictions, and to provide actionable insight into lost cookie
sales
Decision Forest: A Nonparametric Approach to Modeling Irrational Choice
Customer behavior is often assumed to follow weak rationality, which implies
that adding a product to an assortment will not increase the choice probability
of another product in that assortment. However, an increasing amount of
research has revealed that customers are not necessarily rational when making
decisions. In this paper, we propose a new nonparametric choice model that
relaxes this assumption and can model a wider range of customer behavior, such
as decoy effects between products. In this model, each customer type is
associated with a binary decision tree, which represents a decision process for
making a purchase based on checking for the existence of specific products in
the assortment. Together with a probability distribution over customer types,
we show that the resulting model -- a decision forest -- is able to represent
any customer choice model, including models that are inconsistent with weak
rationality. We theoretically characterize the depth of the forest needed to
fit a data set of historical assortments and prove that with high probability,
a forest whose depth scales logarithmically in the number of assortments is
sufficient to fit most data sets. We also propose two practical algorithms --
one based on column generation and one based on random sampling -- for
estimating such models from data. Using synthetic data and real transaction
data exhibiting non-rational behavior, we show that the model outperforms both
rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25,
2021
Nonparametric Regression and the Detection of Turning Points in the Ifo Business Climate
Business climate indicators are used to receive early signals for turning points in the general business cycle. Therefore methods for the detection of turning points in time series are required. Estimations of slopes of a smooth component in the data can be calculated with local polynomial regression. A change in the sign of the slope can be interpreted as a turning point. A plug-in method is used for data-based bandwidth choice. Since in practice the identification of turning points at the actual boundary of the time series is of special interest, this situation is discussed in more detail. The nonparametric approach is applied to the Ifo Business Climate to demonstrate the application of the nonparametric approach and to analyze the time lead of the indicator.Nonparametric regression, slope estimation, turning points, business climate indicators
Nonparametric Bayesian multiple testing for longitudinal performance stratification
This paper describes a framework for flexible multiple hypothesis testing of
autoregressive time series. The modeling approach is Bayesian, though a blend
of frequentist and Bayesian reasoning is used to evaluate procedures.
Nonparametric characterizations of both the null and alternative hypotheses
will be shown to be the key robustification step necessary to ensure reasonable
Type-I error performance. The methodology is applied to part of a large
database containing up to 50 years of corporate performance statistics on
24,157 publicly traded American companies, where the primary goal of the
analysis is to flag companies whose historical performance is significantly
different from that expected due to chance.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS252 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian Fused Lasso regression for dynamic binary networks
We propose a multinomial logistic regression model for link prediction in a
time series of directed binary networks. To account for the dynamic nature of
the data we employ a dynamic model for the model parameters that is strongly
connected with the fused lasso penalty. In addition to promoting sparseness,
this prior allows us to explore the presence of change points in the structure
of the network. We introduce fast computational algorithms for estimation and
prediction using both optimization and Bayesian approaches. The performance of
the model is illustrated using simulated data and data from a financial trading
network in the NYMEX natural gas futures market. Supplementary material
containing the trading network data set and code to implement the algorithms is
available online
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