Constructing the minimum and the maximum for a group of dates(phase)

Description

Constructs a dataframe containing the output of the MCMC algorithm corresponding to the minimum and the maximum of a group of dates (phase)

Usage

CreateMinMaxGroup(data, position, name ="Phase", add=NULL, exportFile=NULL)

Arguments

Value

A dataframe containing the minimum and the maximum of the group of dates included in the phase of interest. These values may be added to an already existing file "add" if given.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

    data(Events)
    Temp = CreateMinMaxGroup(Events, c(2,4), "Phase2")
    Temp = CreateMinMaxGroup(Events, c(3,5), "Phase1", Temp)

Bayesian credible interval

Description

Computes the shortest credible interval at the desired level.

Usage

CredibleInterval(a_chain, level = 0.95)

Arguments

Details

A (100 * level) % credible intervalgives the shortest interval, whose posterior probability is equal to the desired level. This interval is approximated by constructing the shortest interval such that N*(1-level) elements of the sample are outside the interval.

Value

Returns a vector of values containing the level of confidence and the endpoints of the shortest credible interval.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events); attach(Events)

  CredibleInterval(Event.1)
  CredibleInterval(Event.12, 0.50)

Test for the existence of a hiatus between two parameters

Description

Finds if it exists a gap between two dates that is the longest interval that satisfies : P(a_chain < IntervalInf < IntervalSup < b_chain | M) = level

Usage

DatesHiatus(a_chain, b_chain, level=0.95)

Arguments

Value

Returns the endpoints of the longest hiatus between two parameters

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events); attach(Events)
  DatesHiatus(Event.1, Event.12)
  DatesHiatus(Event.1, Event.12, level = 0.5)

Events

Description

Contains the output of the MCMC algorithm for four events modelled by ChronoModel.

Usage

data(Events)

Format

A data frame with 30000 observations on the following 5 variables.

iter

a numeric vector corresponding to iteration number

Event.1

a numeric vector containing the output of the MCMC algorithm for the parameter Event 1

Event.12

a numeric vector containing the output of the MCMC algorithm for the parameter Event 12

Event.2

a numeric vector containing the output of the MCMC algorithm for the parameter Event 2

Event.22

a numeric vector containing the output of the MCMC algorithm for the parameter Event 22

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

data(Events)
summary(Events)

Importing a CSV file containing the output of the MCMC algorithm

Description

Use of the read.csv with th default values for CSV files extracted from ChronoModel software

Usage

  ImportCSV(file, dec = '.', sep=',', comment.char='#', header = TRUE)

Arguments

Value

Returns a dataframe containing a representation of the data in the file.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events)
  write.csv(Events, "data.csv", row.names=FALSE)
  ImportCSV("data.csv")
  ImportCSV("data.csv", dec = '.', sep=',', comment.char='#', header = TRUE)

Plot of a marginal posterior density

Description

This function draws the density of a one-parameter and adds summary statistics.

Usage

MarginalPlot(a_chain, level = 0.95, title = "Marginal posterior density",
  colors = T, GridLength = 1024)

Arguments

Details

The density is estimated using density() function with n=GridLength.

Value

Draws a plot of the estimated marginal posterior density for the one-parameter and adds the mean and the credible interval at the desired level

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events); attach(Events)

  MarginalPlot(Event.1, 0.95)
  MarginalPlot(Event.1, 0.50)

  MarginalPlot(Event.2, 0.95, title="Marginal density plot of Event 2")
  MarginalPlot(Event.2, 0.95, colors = FALSE)

Bayesian test for anteriority / posteriority between two parameters

Description

This function estimates the posterior probability that event 'a' is older than event 'b' using the output of the MCMC algorithm. This provides a bayesian test for checking the following assumption: "Event a is older than event b"

Usage

MarginalProba(a_chain, b_chain)

Arguments

Details

For a given output of MCMC algorithm, this function estimates the posterior probability of the event 'a' < 'b' by the relative frenquency of the event "the value of event 'a' is lower than the value of event 'b'" in the simulated Makov chain.

Value

Returns the posterior probability of the following assumption: "Event a is older than event b"

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events); attach(Events)

  # Probability that Event.1 is older than Event.12
  MarginalProba(Event.1, Event.12)
  # Probability that Event.1 is older than Event.2
  MarginalProba(Event.1, Event.2)

  # Probability that the beginning of the phase 1 is older than the end of the phase 1
  # Should always be 1 for every phase
  data(Phases); attach(Phases)

  MarginalProba(Phase.1.alpha, Phase.1.beta)

Marginal summary statistics

Description

Gives a list of summary statistics resulting from the output of the MCMC algorithm for a one-parameter.

Usage

MarginalStatistics(a_chain, level = 0.95, max_decimal = 0)

Arguments

Details

The 100*level % HPD (highest posterior density) region is estimated using HDR function from Package 'hdrcde'.

Value

A matrix of values corresponding to the following summary statistics

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

References

Hyndman, R.J. (1996) Computing and graphing highest density regions. American Statistician, 50, 120-126.

Examples

  data(Events); attach(Events)
  
  MarginalStatistics(Event.1)
  MarginalStatistics(Event.2, level = 0.90)
  

Bayesian credible intervals for a series of dates

Description

Estimation of the shorest credible interval for each variables of simulated Markov chain.

Usage

MultiCredibleInterval(data, position, level = 0.95)

Arguments

Value

Returns a matrix of values containing the level of confidence and the endpoints of the shortest credible interval for each variable of the MCMC chain. The name of the resulting rows are the positions of the corresponding columns in the CSV file.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events)
  MultiCredibleInterval(Events, c(2,4,3), 0.95)

Plot of the endpoints of credible intervals or HPD intervals of a series of dates

Description

Draws a plot of segments corresponding to the endpoints of the intervals (CI or HPD) of each selected date.

Usage

MultiDatesPlot(data, position, level = 0.95,  intervals = c("CI", "HPD"), 
title = "Plot of intervals")

Arguments

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Events)
  MultiDatesPlot(Events, c(2,4,3), level = 0.95, intervals ="CI", title = "Plot of CI intervals")
  MultiDatesPlot(Events, c(2,4,3), level = 0.95, intervals ="HPD", title = "Plot of HPD intervals")

Bayesian highest posterior density regions for a series of MCMC chains

Description

Estimation of the highest posterior density regions for each variables of simulated Markov chain. This function uses the "hdr" function oincluded in the package "hdrcde.

Usage

MultiHPD(data, position, level=0.95)

Arguments

Value

Returns a matrix of values containing the level of confidence and the endpoints of each interval for each variable of the MCMC chain. The name of the resulting rows are the positions of the corresponding columns in the CSV file.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

References

Hyndman, R.J. (1996) Computing and graphing highest density regions. American Statistician, 50, 120-126.

Examples

  data(Events)
  MultiHPD(Events, c(2,4,3), 0.95)

Plot of the marginal posterior densities of several phases

Description

Draws a plot with the marginal posterior densities of the minimum and the maximum of the dates included in each phase. No temporal order between phases is required.

Usage

MultiPhasePlot(data, position_minimum, position_maximum = position_minimum+1,
level = 0.95,  title = "Phases marginal posterior densities")

Arguments

Value

Draws a plot with the marginal posterior densities of the minimum and the maximum of the dates included in each phase and adds the time range of each phase.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  # Data extracted from ChronoModel software
  data(Phases)
  
  # List of the name of the phases 
  names(Phases)
  
  # Stipulating position_maximum
  MultiPhasePlot(Phases, c(4,2), c(5,3), title = "Succession of phase 1 and phase 2")
  
  # In this case, equivalent to 
  MultiPhasePlot(Phases, c(4,2), title = "Succession of phase 1 and phase 2")

Phase Time Range for multiple phases

Description

Computes the shortest interval that satisfies : P(PhaseMin < IntervalInf < IntervalSup < PhaseMax | M) = level

Usage

MultiPhaseTimeRange(data, position_minimum, position_maximum = position_minimum+1,
 level = 0.95, max_decimal = 0)

Arguments

Details

For each i, MultiPhaseTimeRange computes the time range interval for the phase defined by its minimum position_minimum[i] and its maximum position_maximum[i]. The default value of position_maximum corresponds to CSV files exported from ChronoModel software.

Value

Returns a matrix of values containing the level of confidence and the endpoints of the shortest time range associated with the desired level

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  # Data extracted from ChronoModel software
  data(Phases)
  
  # List of the name of the phases 
  names(Phases)
  
  # Stipulating position_maximum
  MultiPhaseTimeRange(Phases, c(4,2), c(5,3))
  
  # In this case, equivalent to 
  MultiPhaseTimeRange(Phases, c(4,2))

Gap/Hiatus between a succession of phases (for phases in temporal order constraint)

Description

This function finds, if it exists, the gap between two successive phases. This gap or hiatus is the longest interval [IntervalInf, IntervalSup] that satisfies : P(Phase1Max < IntervalInf < IntervalSup < Phase2Min | M) = level for each successive phase.

Usage

MultiPhasesGap(data, position_minimum, position_maximum = position_minimum+1,
 level = 0.95, max_decimal = 0)

Arguments

Details

For each i, MultiPhasesGap computes the gap interval for the phase defined by its minimum position_minimum[i] and its maximum position_maximum[i]. The default value of position_maximum corresponds to CSV files exported from ChronoModel software.

Value

Returns a matrix of values containing the level of confidence and the endpoints of the gap for each pair of successive phases

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  # Data extracted from ChronoModel software
  data(Phases)
  
  # List of the name of the phases 
  names(Phases)
  
  # Stipulating position_maximum
  MultiPhasesGap(Phases, c(4,2), c(5,3))
  
  # In this case, equivalent to 
  MultiPhasesGap(Phases, c(4,2))

Transition range for a succession of phases (for phases in temporal order constraint)

Description

Finds if it exists the shortest interval [TransitionRangeInf, TransitionRangeSup] that satisfies : P(TransitionRangeInf < Phase1Max < Phase2Min < TransitionRangeSup | M) = level for each phase

Usage

MultiPhasesTransition(data, position_minimum, position_maximum = position_minimum+1, 
level = 0.95, max_decimal = 0)

Arguments

Details

For each i, MultiPhasesTransition computes the transition interval for the phase defined by its minimum position_minimum[i] and its maximum position_maximum[i]. The default value of position_maximum corresponds to CSV files exported from ChronoModel software.

Value

Returns a matrix of values containing the level of confidence and the endpoints of the transition interval for each pair of successive phases

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  # Data extracted from ChronoModel software
  data(Phases)
  
  # List of the name of the phases 
  names(Phases)
  
  # Stipulating position_maximum
  MultiPhasesTransition(Phases, c(4,2), c(5,3))
  
  # In this case, equivalent to 
  MultiPhasesTransition(Phases, c(4,2))

Successive Phases Density Plots (for phases in temporal order constraint)

Description

This functions draws a plot of the densities of several successive phases and adds several statistics (mean, CI, HPDR)

Usage

MultiSuccessionPlot(data, position_minimum, position_maximum = position_minimum+1,
 level = 0.95, title = "Characterisation of a succession of phases")

Arguments

Details

Curves represent the density of the minimum (oldest dates) and the maximum (youngest dates) of the dates included in each phase. Curves of the same color refer to the same phase. When there is only one curve of one color, it means that there is only one event in the corresponding phase and then the minimum equals the maximum. Time range intervals are symbolised by segments above the curves drawn using the same color as the one of the curves of the associated phase. Transition and gap range intervals are represented by two-coloured segments using the colors of successive phases. If the gap between the successive phases does not exist, a cross is drawn instead of a segment.

Value

Returns a plot of all densities and adds several summary statistics

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  # Data extracted from ChronoModel software
  data(Phases)
  
  # List of the name of the phases 
  names(Phases)
  
  # Stipulating position_end
  MultiSuccessionPlot(Phases, c(4,2), c(5,3), title = "Succession of phase 1 and phase 2")
  
  # In this case, equivalent to 
  MultiSuccessionPlot(Phases, c(4,2), title = "Succession of phase 1 and phase 2")

Plot of the marginal posterior densities of the duration of a phase

Description

This function draws the marginal posterior densities of the time elapsed between the minimum and the maximum of the dates included in a phase, and adds summary statistics (mean, CI)

Usage

PhaseDurationPlot(PhaseMin_chain, PhaseMax_chain, level=0.95, 
title = "Duration of the phase", colors = T, GridLength=1024)

Arguments

Value

A plot with the marginal posterior densities of the duration of a phase and adds several summary statistics (mean, Credible interval, Time range)

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases); attach(Phases)

  PhaseDurationPlot(Phase.1.alpha, Phase.1.beta, 0.95, "Duration of Phase 1")
  PhaseDurationPlot(Phase.2.alpha, Phase.2.beta, 0.95, "Duration of Phase 2",colors = FALSE)

Plot of the marginal posterior densities of a phase

Description

This function draws the marginal posterior densities of the minimum and the maximum of the dates included in the phase

Usage

PhasePlot(PhaseMin_chain, PhaseMax_chain, level = 0.95,
  title = "Characterisation of a phase", colors = T,
  GridLength = 1024)

Arguments

Value

A plot with the marginal posterior densities of the minimum and the maximum of the dates included in the phase and adds several summary statistics (mean, Credible interval, Time range)

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases); attach(Phases)

  PhasePlot(Phase.1.alpha, Phase.1.beta, 0.95, "Densities of Phase 1")
  PhasePlot(Phase.2.alpha, Phase.2.beta, 0.95, "Densities of Phase 2",colors = FALSE)

Summary statistics for a phase

Description

Estimation of several summary statistics of the minimum, the maximum and the duration of the dates included in the phase.

Usage

PhaseStatistics(PhaseMin_chain, PhaseMax_chain, level = 0.95,
  max_decimal = 0)

Arguments

Details

The summary statistics are those given by MarginalStatistics function. The time range is given by PhaseTimeRange function. The duration is computed as follow duration = maximum - minimum at each iteration of the MCMC output.

Value

Returns a list of values corresponding to the summary statistics:

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases); attach(Phases)
  PhaseStatistics(Phase.1.alpha, Phase.1.beta, 0.95, 0)
  PhaseStatistics(Phase.2.alpha, Phase.2.beta, 0.95, 0)

Phase Time Range

Description

Computes the shortest interval [IntervalInf ; IntervalSup ] that satisfies : P(PhaseMin_chain =< IntervalInf < IntervalSup =< PhaseMax_chain | M) = level.

Usage

PhaseTimeRange(PhaseMin_chain, PhaseMax_chain, level = 0.95,
  max_decimal = 2)

Arguments

Value

A vector of values containing the desired level of confidence and the endpoints of the shortest time range associated with this desired level.

Examples

  data(Phases); attach(Phases)
  PhaseTimeRange(Phase.1.alpha, Phase.1.beta, 0.95)
  PhaseTimeRange(Phase.2.alpha, Phase.2.beta, 0.95, 0)

Phases

Description

Contains the output of the MCMC algorithm for all the phases (beginning and end) of two successive phases modelled in ChronoModel. Phase 1 is assued to be older than Phase 2.

Usage

data(Phases)

Format

A data frame with 30000 observations on the following 5 variables.

iter

a numeric vector corresponding to iteration number

Phase.1.alpha

a numeric vector containing the output of the MCMC algorithm for the beginning of the phase "Phase 1"

Phase.1.beta

a numeric vector containing the output of the MCMC algorithm for the end of the phase "Phase 1"

Phase.2.alpha

a numeric vector containing the output of the MCMC algorithm for the the beginning of the phase "Phase 2"

Phase.2.beta

a numeric vector containing the output of the MCMC algorithm for the end of the phase "Phase 2"

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases)
  attach(Phases)
  PhasePlot(Phase.1.alpha, Phase.1.beta)
  PhaseTimeRange(Phase.1.alpha, Phase.1.beta)

  PhasesGap(Phase.1.beta, Phase.2.alpha)
  PhasesTransition(Phase.1.beta, Phase.2.alpha)

Gap or Hiatus between two successive phases (for phases in temporal order constraint)

Description

This function finds, if it exists, the gap between two successive phases. This gap or hiatus is the longest interval [IntervalInf ; IntervalSup] that satisfies : P(Phase1Max_chain < IntervalInf < IntervalSup < Phase2Min_chain | M) = level.

Usage

PhasesGap(Phase1Max_chain, Phase2Min_chain, level = 0.95,
  max_decimal = 0)

Arguments

Value

Returns a vector of values containing the level of confidence and the endpoints of the gap between the successive phases

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases); attach(Phases)
  PhasesGap(Phase.1.beta, Phase.2.alpha, 0.95)
  PhasesGap(Phase.1.beta, Phase.2.alpha, 0.50)

Transition range between two successive phases (for phases in temporal order constraint)

Description

Finds if it exists the shortest interval [TransitionRangeInf , TransitionRangeSup ] that satisfies : P(TransitionRangeInf < Phase1Max_chain < Phase2Min_chain < TransitionRangeSup | M) = level

Usage

PhasesTransition(Phase1Max_chain, Phase2Min_chain, level = 0.95,
  max_decimal = 0)

Arguments

Value

Returns a vector of values containing the level of confidence and the endpoints of the transition interval between the successive phases

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases); attach(Phases)
  PhasesTransition(Phase.1.beta, Phase.2.alpha, 0.95)
  PhasesTransition(Phase.1.beta, Phase.2.alpha, 0.50)

Density Plots of two successive phases (for phases in temporal order constraint)

Description

Plot of the densities of the minimum and the maximum of the dates included in each phase and adds several summary statistics (mean, CI, HPDR)

Usage

SuccessionPlot(Phase1Min_chain, Phase1Max_chain, Phase2Min_chain,
  Phase2Max_chain, level = 0.95,
  title = "Characterisation of several phases", GridLength = 1024)

Arguments

Details

Curves represent the density of the minimum (oldest dates) and the maximum (youngest dates) of the dates included in each phase. Curves of the same color refer to the same phase. Time range intervals are symbolised by segments above the curves drawn using the same color as the one of the curves of the associated phase. Transition and gap range intervals are represented by two-coloured segments using the colors of the both phases in succession. If the gap between the successive phases does not exist, a cross is drawn instead of a segment.

Value

Plot of the densities of the minimum and the maximum of the dates included in each phase

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

Examples

  data(Phases); attach(Phases)
  SuccessionPlot(Phase.1.alpha, Phase.1.beta, Phase.2.alpha, Phase.2.beta, 0.95)

Plot of the activity of events

Description

A statistical graphic designed for the archaeological study of rhythms of the long term that embodies a theory of archaeological evidence for the occurrence of events.

Usage

TempoActivityPlot(data, position, level=0.95,  count = TRUE, 
title = "Activity plot")

Arguments

Value

It calculates the cumulative frequency of specified events by calculating how many events took place before each date in a specified range of dates.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr>, Thomas S. Dye <TSD@tsdye.com> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

References

Dye, T.S. (2016) Long-term rhythms in the development of Hawaiian social stratification. Journal of Archaeological Science, 71, 1–9.

Examples

  data(Events); 
  TempoActivityPlot(Events[1:1000,], c(2:5))
  TempoActivityPlot(Events[1:1000,], c(2:5), count = TRUE)

Plot of the occurence of events

Description

A statistical graphic designed for the archaeological study of rhythms of the long term that embodies a theory of archaeological evidence for the occurrence of events.

Usage

TempoPlot(data, position, level=0.95,  count = TRUE, Gauss=FALSE, title = "Tempo plot")

Arguments

Value

It calculates the cumulative frequency of specified events by calculating how many events took place before each date in a specified range of dates.

Author(s)

Anne Philippe <Anne.Philippe@univ-nantes.fr>, Thomas S. Dye <TSD@tsdye.com> and

Marie-Anne Vibet <Marie-Anne.Vibet@univ-nantes.fr>

References

Dye, T.S. (2016) Long-term rhythms in the development of Hawaiian social stratification. Journal of Archaeological Science, 71, 1–9.

Examples

  data(Events); 
  TempoPlot(Events[1:1000,], c(2:5))
  TempoPlot(Events[1:1000,], c(2:5), count = TRUE)