Benchmarking segmentation results using a Markov model and a Bayes information criterion

2003 ◽  
Author(s):  
Fionn D. Murtagh ◽  
Xiaoyu Qiao ◽  
Danny Crookes ◽  
Paul Walsh ◽  
P. A. M. Basheer ◽  
...  
Keyword(s):  
Markov Model ◽  
Information Criterion ◽  
Bayes Information Criterion

scholarly journals Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect

Risks ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 5
Author(s):  
Karim Barigou ◽  
Stéphane Loisel ◽  
Yahia Salhi
Keyword(s):  
Life Insurance ◽  
Cross Validation ◽  
Cohort Effect ◽  
Information Criterion ◽  
Mortality Forecasting ◽  
Hand Model ◽  
Regularization Techniques ◽  
Bayes Information Criterion ◽  
The One ◽  
Regularized Model

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Standard single population models typically suffer from two major drawbacks: on the one hand, they use a large number of parameters compared to the sample size and, on the other hand, model choice is still often based on in-sample criterion, such as the Bayes information criterion (BIC), and therefore not on the ability to predict. In this paper, we develop a model based on a decomposition of the mortality surface into a polynomial basis. Then, we show how regularization techniques and cross-validation can be used to obtain a parsimonious and coherent predictive model for mortality forecasting. We analyze how COVID-19-type effects can affect predictions in our approach and in the classical one. In particular, death rates forecasts tend to be more robust compared to models with a cohort effect, and the regularized model outperforms the so-called P-spline model in terms of prediction and stability.

Optimal Order of Markov Models Applied to Bankchecks

1997 ◽  
Vol 11 (05) ◽  
pp. 789-800 ◽  
Author(s):  
C. Olivier ◽  
T. Paquet ◽  
M. Avila ◽  
Y. Lecourtier
Keyword(s):  
Markov Model ◽  
Structural Properties ◽  
Conditional Probability ◽  
Akaike Information Criterion ◽  
Markov Models ◽  
Information Criterion ◽  
Optimal Order ◽  
Structural Representation ◽  
Akaike Criterion

The aim of this study is to show that the optimal order of Markov Model of cursive words can be rigorously stated in order to fit the structural properties of the observed data using Akaike information criterion. The method has been tested on French Postal check amounts up to order 4. An original structural representation of cursive words based on graphemes is used. The conditional probability to have a word model given an observed sequence of graphemes is computed independently of the length of the sequence. The recognition results obtained confirm the optimal order found using Akaike criterion.

scholarly journals A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores

2017 ◽  
Author(s):  
Lekha Patel ◽  
Nils Gustafsson ◽  
Yu Lin ◽  
Raimund Ober ◽  
Ricardo Henriques ◽  
...  
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Continuous Time ◽  
Hidden Markov ◽  
Super Resolution ◽  
Information Criterion ◽  
Switching Behavior ◽  
Time Signal ◽  
Full Characterization ◽  
Continuous Time Process

AbstractFluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.

Bid and Ask spreads for the cap and floor contracts under the Liouville fractional Vasicek model

2020 ◽  
Vol 39 (1) ◽  
Author(s):  
Farshid Mehrdoust
Keyword(s):  
Interest Rate ◽  
Information Criterion ◽  
Rate Model ◽  
Vasicek Model ◽  
Bayes Information Criterion ◽  
Interest Rate Model ◽  
Newton Raphson

This paper presents bid and ask formulas for cap and floor contracts prices byusing Wang transform under a Liouville fractional Vasicek (LfVasicek) interest rate model. To do this, the parameters of the model are calibrated by using the Newton-Raphson (NR) method. Then the standard and Liouville fractional versions of the Vasicek model are compared by the Bayes information criterion (BIC). Finally, we obtain the bid-ask boundaries for interest rate amount and cap and foor prices.

scholarly journals Estimasi Parameter Model Poisson Hidden Markov Pada Data Banyaknya Kedatangan Klaim Asuransi Jiwa

2020 ◽  
Vol 1 (2) ◽  
pp. 65
Author(s):  
Vieri Koerniawan ◽  
Nurtiti Sunusi ◽  
Raupong Raupong
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Life Insurance ◽  
Expectation Maximization ◽  
Numerical Solutions ◽  
Likelihood Function ◽  
Hidden Markov ◽  
Information Criterion ◽  
Model Parameters ◽  
Insurance Data

The Poisson hidden Markov model is a model that consists of two parts. The first part is the cause of events that are hidden or cannot be observed directly and form a Markov chain, while the second part is the process of observation or observable parts that depend on the cause of the event and following the Poisson distribution. The Poisson hidden Markov model parameters are estimated using the Maximum Likelihood Estimator (MLE). But it is difficult to find analytical solutions from the ln-likelihood function. Therefore, the Expectation Maximization (EM) algorithm is used to obtain its numerical solutions which are then applied to life insurance data. The best model is obtained with 2 states or m = 2 based on the smallest Bayesian Information Criterion (BIC) value of 338,778 and the average predicted number of claims arrivals is 0.385 per day.

scholarly journals Calibration of the Hargreaves–Samani method for the calculation of reference evapotranspiration in different Köppen climate classes

2015 ◽  
Vol 47 (2) ◽  
pp. 521-531 ◽  
Author(s):  
Javier Almorox ◽  
Jürgen Grieser
Keyword(s):  
Reference Evapotranspiration ◽  
Information Criterion ◽  
Absolute Error ◽  
Climatic Data ◽  
The Standard Model ◽  
Bayes Information Criterion ◽  
Maximum Air Temperature ◽  
Monteith Equation

The Penman–Monteith equation (FAO-56) is accepted as the standard model for estimating reference evapotranspiration (ETo). However, the major obstacle to using FAO-56 widely is that it requires numerous climatic data. The Hargreaves–Samani (HS) method is frequently used for the calculation of ETo since it is based on measurements of daily minimum and maximum air temperature alone. Those are commonly recorded at many meteorological stations throughout the world. It is the objective of this paper to evaluate the quality of HS and calibrate the coefficients of this method for different climates as represented by the Köppen classification. Estimated values are compared with Penman–Monteith ETo values in terms of the coefficient of efficiency Ceff as well as the root mean square error, the mean absolute error and the Bayes information criterion. The Penman–Monteith equation for ETo (FAO-56) is based on physics and known to provide best estimates of ETo. The results of our work show that the correlation between long-term monthly means of HS and FAO-56 can be improved significantly by introducing climate-class specific coefficients.

Fitting multi-population mortality models to socio-economic groups

2020 ◽  
pp. 1-29
Author(s):  
Jie Wen ◽  
Andrew J.G. Cairns ◽  
Torsten Kleinow
Keyword(s):  
Goodness Of Fit ◽  
Information Criterion ◽  
Age Effects ◽  
Period Effects ◽  
Mortality Models ◽  
Bayes Information Criterion ◽  
The Common ◽  
Population Mortality ◽  
Index Of Multiple Deprivation ◽  
Special Case

Abstract We compare results for 12 multi-population mortality models fitted to 10 distinct socio-economic groups in England, subdivided using the Index of Multiple Deprivation. Using the Bayes Information Criterion to compare models, we find that a special case of the common age effect (CAE) model fits best in a variety of situations, achieving the best balance between goodness of fit and parsimony. We provide a detailed discussion of key models to highlight which features are important. Group-specific period effects are found to be more important than group-specific age effects, and non-parametric age effects deliver significantly better results than parametric (e.g. linear) age effects. We also find that the addition of cohort effects is beneficial in some cases but not all. The preferred CAE model has the additional benefit of being coherent in the sense of Hyndman et al. ((2013) Demography50(1), 261–283); some of the other models considered are not.

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