Performs calculations to estimate the break-point locations when their initial values are given. Negative binomial distribution is used to model the over-dispersed discrete (count) data. This function supports for the simulation of break-point locations in the CE algorithm based on the four parameter beta distribution or truncated normal distribution. User can select either BIC or AIC to select the optimal number of break-points.

1 2 | ```
CE.NB.Init(data, init.locs, eps = 0.01, rho = 0.05, M = 200, h = 5, a = 0.8, b = 0.8,
distyp = 1, penalty = "BIC", var.init = 1e+05, parallel = FALSE)
``` |

`data` |
data to be analysed. A single column array or a dataframe. |

`init.locs` |
Initial break-point locations. |

`eps` |
the cut-off value for the stopping criterion in the CE method. Default value is 0.01. |

`rho` |
the fraction which is used to obtain the best performing set of sample solutions (i.e., elite sample). Default value is 0.05. |

`M` |
sample size to be used in simulating the locations of break-points. Default value is 200. |

`h` |
minimum aberration width. Default is 5. |

`a` |
a smoothing parameter value. It is used in the four parameter beta distribution to smooth both shape parameters. When simulating from the truncated normal distribution, this value is used to smooth the estimates of the mean values. Default is 0.8. |

`b` |
a smoothing parameter value. It is used in the truncated normal distribution to smooth the estimates of the standard deviation. Default is 0.8. |

`distyp` |
distribution to simulate break-point locations. Options: 1 = four parameter beta distribution, 2 = truncated normal distribution. Default is 1. |

`penalty` |
User can select either BIC or AIC to obtain the number of break-points. Options: "BIC", "AIC". Default is "BIC". |

`var.init` |
Initial variance value to facilitate the search process. Default is 100000. |

`parallel` |
A logical argument specifying if parallel computation should be carried-out (TRUE) or not (FALSE). By default it is set as ‘FALSE’. In WINDOWS OS systems "snow" functionalities are used, whereas in Unix/Linux/MAC OSX "multicore" functionalities are used to carryout parallel computations with the maximum number of cores available. |

The negative binomial (NB) distribution is used to model the discrete (count) data. NB model is preferred over the Poission model when over-dispersion is observed in the count data. A performance function score (BIC or AIC) is calculated for each of the solutions generated by the statistical distribution (four parameter beta distribution or truncated normal distribution) with respect to the user provided initial locations. Finally, a list containing a vector of break-point locations, number of break-points, BIC/AIC values and log-likelihood value is returned in the console.

A list is returned with following items:

`No.BPs` |
The number of break-points |

`BP.Loc` |
A vector of break-point locations |

`BIC/AIC` |
BIC/AIC value |

`ll` |
Loglikelihood of the optimal solution |

Priyadarshana, W.J.R.M. <mjayawardana@swin.edu.au>

Priyadarshana, W. J. R. M. and Sofronov, G. (2012a) A Modified Cross- Entropy Method for Detecting Multiple Change-Points in DNA Count Data, In Proc. of the IEEE Conference on Evolutionary Computation (CEC), 1020-1027, DOI: 10.1109/CEC.2012.6256470.

Priyadarshana, W. J. R. M. and Sofronov, G. (2012b) The Cross-Entropy Method and Multiple Change-Points Detection in Zero-Inflated DNA read count data, In: Y. T. Gu, S. C. Saha (Eds.) The 4th International Conference on Computational Methods (ICCM2012), 1-8, ISBN 978-1-921897-54-2.

Rubinstein, R., and Kroese, D. (2004) The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning. Springer-Verlag, New York.

Schwarz, G. (1978) Estimating the dimension of a model, The Annals of Statistics, 6(2), 461-464.

`CE.NB`

for CE with Negative binomial,

`CE.ZINB`

for CE with zero-inflated negative binomial,

`CE.ZINB.Init`

for CE with zero-inflated negative binomial with initial locations,

`profilePlot`

to obtain mean profile plot.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | ```
#### Simulated data example ###
segs <- 6 # Number of segements
M <- c(1500, 2200, 800, 2500, 1000, 2000) # Segment width
#true.locations <- c(1501, 3701, 4501, 7001, 8001) # True break-point locations
seg <- NULL
p <- c(0.45, 0.25, 0.4, 0.2, 0.3, 0.6) # Specification of p's for each segment
for(j in 1:segs){
seg <- c(seg, rnbinom(M[j], size =10, prob = p[j]))
}
simdata <- as.data.frame(seg)
rm(p, M, seg, segs, j)
#plot(data[, 1])
## Not run:
## CE with the four parameter beta distribution with BIC as the selection criterion ##
##Specification of initial locations
init.locations <- c(1400, 3400, 4650, 7100, 8200)
obj1 <- CE.NB.Init(simdata, init.locs = init.locations, distyp = 1, penalty = BIC, parallel = TRUE)
obj1
profilePlot(obj1, simdata) # To obtain the mean profile plot
## CE with truncated normal distribution with BIC as the selection criterion ##
obj2 <- CE.NB.Init(simdata, init.locs = init.locations, distyp = 2, penalty = BIC, parallel = TRUE)
obj2
profilePlot(obj1, simdata) # To obtain the mean profile plot
## End(Not run)
``` |

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