Detection of Oestrus by Monitoring Boar Visits Tage Ostersen Advanced Herd Management 22/ Slide 1/30 1 Background 2 Data 3 Duration of Visits 4

Transcription

1 Detection of Oestrus by Monitoring Boar Visits Tage Ostersen Advanced Herd Management 22/ Slide 1/30 1 Background 2 Data 3 Duration of Visits 4 Break 5 Frequency of Visits 6 Combining Frequency and Duration of Boar Visits 7 Conclusion Slide 2/30

2 Background 1 European legislation 70 % of Danish sows are group housed a third of these are fed by ESF Non productive day are expensive Manual oestrus detection is dicult when sows are group housed Slide 3/30 Background 2 Slide 4/30

3 Background 3 Slide 5/30 Purpose of Monitoring Visits to a Boar Less work input for farmer Fewer non productive days - i.e. lower cost per reproduction cycle Need of a detection method with short response time - in time to inseminate the sow Slide 6/30

4 Raw Data Slide 7/30 Characteristics of the Raw Data The frequency of visits increases around oestrus The duration of some visit are prolonged around oestrus The duration of visits seem to vary more around oestrus If the duration is accumulated per hour the change is more distinct If the duration is accumulated per 6 hours the number of observations decline steeply Need of a detection method that can detect both the change in duration and in frequency Slide 8/30

5 Overview 3 parts - duration, frequency and combination Duration Multiprocess DLM Detection method: Recognizes "patterns" Frequency DGLM - generalized because frequency is Poisson distributed Detection method: Recognizes outliers Combination Slide 9/30 Denition of the Model Describing Duration Y t is the logarithmical transformed cumulated seconds near the boar per observation hour t denotes the observation hour. Hours, where the sow did not visits the boar are excluded Observation equation : Y t = µ t + v t, where v t N(0, V ) System equation : µ t = µ t 1 + w t, where w t N(0, W ) Slide 10/30

6 Denition of the Model Describing Duration Y t is the logarithmical transformed cumulated seconds near the boar per observation hour t denotes the observation hour. Hours, where the sow did not visits the boar are excluded Observation equation : Y t = µ t + v t, where v t N(0, V ) System equation : µ t = µ t 1 + w t, where w t N(0, W ) NB: A DLM lters raw data provides an estimate of the underlying level (µ t ) and the variance (V ) by means of a Kalman lter Slide 10/30 The Multiprocess DLM (class II) Idea: Instead of one model have multiple models Apply a mixture of the models mixed so that the most appropriate model weighs the most Consider model combinations at time t 2to t Slide 11/30

7 The Multiprocess DLM (class II) Idea: Instead of one model have multiple models Apply a mixture of the models mixed so that the most appropriate model weighs the most Consider model combinations at time t 2to t Present case: 4 models Normal model Outlier model Level shift model Oestrus model 4 models entail 64 model combinations, when considering the last three observations (4 3 = 64) Slide 11/30 Updating Equations of a simple Multiprocess DLM - 1 The model combinations are stated by (ijk) =(M t 2, M t 1, M t ) Prior for θ t at time t a t (ijk) =m t 1(ij) R t (ijk) =C t 1(ij)+W t (k) Slide 12/30

8 Updating Equations of a simple Multiprocess DLM - 1 The model combinations are stated by (ijk) =(M t 2, M t 1, M t ) Prior for θ t at time t a t (ijk) =m t 1(ij) R t (ijk) =C t 1(ij)+W t (k) One step forecast at time t f t (ijk) =a t (ijk) Q t (ijk) =R t (ijk)+v t (k) Slide 12/30 Updating Equations of a simple Multiprocess DLM - 2 Posterior for µ t at time t m t (ijk) =a t (ijk)+a t (ijk) e t (ijk) C t (ijk) =A t (ijk) V t (ijk) A t (ijk) =R t (ijk) Q 1 t (ijk) e t (ijk) =Yt f t (ijk) Slide 13/30

9 Updating Equations of a simple Multiprocess DLM - 3 Posterior model probability p t (ijk) =f (Y t f t (ijk), Q t (ijk)) pt 1(ij) p(k),where f is the density function of a normal distribution and c t i j is a normalizing constant so that k p t(ijk) =1. c t Model Probability Var = 1 Var = 2.25 Var = Slide 14/30 Updating Equations of a simple Multiprocess DLM - 4 Posterior mixture distribution at time t m t C t = i = i j j k m t(ijk) p t (ijk) k (C t(ijk)+(m t m t (ijk)) 2 ) p t (ijk) Slide 15/30

10 Updating Equations of a simple Multiprocess DLM - 5 Model collapsing p t (jk) = i p t(ijk) m t (jk) = i m t(ijk)p t (ijk)/p t (jk) C t (jk) = i (C t (ijk)+(m t m t (ijk)) 2) pt(ijk) p t (jk) Slide 16/30 Updating Equations of a simple Multiprocess DLM - 6 Updating equations of the multiprocess DLM is almost the same as normal DLM Dierences 64 simultaneous models Weighted according to prior transition probability and probability according to forecasted level and variance Can recognize specic patterns Slide 17/30

11 Fitting a Multiprocess DLM to Boar Visit Data Unknown variance - constant? Discount factor to estimate W Oestrus seems to be characterized by higher level and higher variance The time distance between two observations should inuence the belief in oestrus Slide 18/30 Fitting a Multiprocess DLM to Boar Visit Data Unknown variance - constant? Discount factor to estimate W Oestrus seems to be characterized by higher level and higher variance The time distance between two observations should inuence the belief in oestrus p t (ijk) =f (Y t f t (ijk), Q t (ijk)) pt 1(ij) p(k) c t Slide 18/30

12 Fitting a Multiprocess DLM to Boar Visit Data M(α 1 ) Normal model with observational variance factor C k = 1, discount factor δ k = 0.99 and xed transition probability π = π N M(α 2 ) Outlier model with observational variance factor C k = 20, discount factor δ k = 0.99 and xed transition probability π = π O M(α 3 ) Level shift model with observational variance factor C k = 1, discount factor δ k = 0.01 and xed transition probability π = π L M(α 4 ) Oestrus model with observational variance factor C k = 20, discount factor δ k = 0.99 and xed transition probability π = 0 Slide 19/30 ResultsofMultiprocessDLM Log seconds pr. hour Raw data and filtered mean (Sow no 18) (a) Model probability P(M α4 ) Date (b) Slide 20/30

13 ResultsofMultiprocessDLM-2 sensitivity = True Positive True Positive+False Negative specicity = True Negative True Negative+False Positve One alarm during a block means the the whole block is dened as an alarm-block Model Block of 24 hours Block of 72 hours Total TP Total TN Total FP Total FN Sensitivity Specicity Slide 21/30 BREAK Slide 22/30

14 Denition of the Model Describing Frequency Y t is number of visits per 6 hours There is a diurnal pattern of the visits high activity 5 a.m. to 5 p.m. low activity 5 p.m. to 5 a.m. Slide 23/30 Denition of the Model Describing Frequency Y t is number of visits per 6 hours There is a diurnal pattern of the visits high activity 5 a.m. to 5 p.m. low activity 5 p.m. to 5 a.m. Observation equation : (Y t η t, V t ) P(λ η t )=P(eη t ), where : η t = F tθ t System equation : θ t = G t θ t 1 + w t, where w t (0, W ) Slide 23/30

15 Denition of the Model Describing Frequency Y t is number of visits per 6 hours There is a diurnal pattern of the visits high activity 5 a.m. to 5 p.m. low activity 5 p.m. to 5 a.m. Observation equation : (Y t η t, V t ) P(λ η t )=P(eη t ), where : η t = F tθ t System equation : θ t = G t θ t 1 + w t, where w t (0, W ) F high t = ( 1 0 ) F low t = ( 0 1 ) G t = ( ) Slide 23/30 Monitoring the Frequency of Boar Visits oestrus indicator = observed frequency forecasted frequency forecasted frequency Visits per 6 hours Raw data, 1 step forecast and filtered mean (Sow no 18) Oestrus Indicator Observered Frequency Forecasted Frequency Forecasted Frequency Date (a) (b) Slide 24/30

16 Results of DGLM Model Block of 24 hours Block of 72 hours Total TP Total TN Total FP Total FN Sensitivity Specicity Slide 25/30 Combining Frequency and Duration of Boar Visits Bayes Theorem is a way of reversing probabilities Idea: Utilize the probability of oestrus from the multiprocess DLM as a prior probability of oestrus Assume that the test result of the frequency model is independent of the duration model P(oestrus +) = P(+ oestrus) P(+) = P(oestrus) sensitivity P(M α4 ) sensitivity P(M α4 )+(1 specicity) (1 P(M α4 )) Slide 26/30

17 Combining Frequency and Duration of Boar Visits Results Slide 27/30 Combining Frequency and Duration of Boar Visits Results Block of 24 hours Model Combined Duration Frequency Total TP Total TN Total FP Total FN Sensitivity Specicity Slide 28/30

18 Combining Frequency and Duration of Boar Visits Results Block of 24 hours Model Combined Duration Frequency Total TP Total TN Total FP Total FN Sensitivity Specicity Error Rate Slide 28/30 Conclusion 87 % of the sows entering oestrus are detected Signicantly fewer false alarms than earlier attempts The combined model is not signicantly more ecient than duration alone The number of false alarms is still too high Slide 29/30

19 Conclusion 87 % of the sows entering oestrus are detected Signicantly fewer false alarms than earlier attempts The combined model is not signicantly more ecient than duration alone The number of false alarms is still too high Other information about oestrus in the individual sow should be included Farrowing rate of the herd Pregnancy test of the individual sow Activity measurements? Day of reproduction cycle Visual observations? Slide 29/30 Questions? Slide 30/30