Evaluating forecast performance with state dependence

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

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State selected ion–molecule reactions by a TESICO technique. IX. Vibrational state dependence of the cross sections in the reaction C2H+2(ν2)+D2(H2)

The Journal of Chemical Physics ◽

10.1063/1.447618 ◽

1984 ◽

Vol 81 (12) ◽

pp. 5666-5671 ◽

Cited By ~ 17

Author(s):

K. Honma ◽

Tatsuhisa Kato ◽

Kenichiro Tanaka ◽

Inosuke Koyano

Keyword(s):

Cross Sections ◽

Vibrational State ◽

State Dependence ◽

Ion Molecule Reactions ◽

The Cross

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A copula-based multivariate hidden Markov model for modelling momentum in football

AStA Advances in Statistical Analysis ◽

10.1007/s10182-021-00395-8 ◽

2021 ◽

Author(s):

Marius Ötting ◽

Roland Langrock ◽

Antonello Maruotti

Keyword(s):

Markov Model ◽

Hidden Markov Models ◽

Markov Models ◽

Hidden Markov ◽

State Dependence ◽

Change Points ◽

Sports Fans ◽

Modelling Framework ◽

State Dependent ◽

Different Levels

AbstractWe investigate the potential occurrence of change points—commonly referred to as “momentum shifts”—in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state dependence of the variables, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.

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