In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation with an optimal rate. We also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of estimation accuracy and computation time.

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Familial clustering of schizophrenia (SCZ), bipolar disorder (BPD), and major depressive disorder (MDD) was systematically reported (Aukes, M. F. Genet Med 2012, 14, 338-341) and any two or even three of these disorders could co-exist in some families. In addition, evidence from symptomatology and psychopharmacology also imply that there are intrinsic connections between these three major disorders. A total of 56,569 single nucleotide polymorphism (SNPs) on chromosome 5 were genotyped by Affymetrix Genome-Wide Human SNP array 6.0 on 119 SCZ, 253 BPD (type-I), 177 MDD patients and 1000 controls. Associated SNPs and flanking genes was screen out systematically, and cadherin pathway genes (CDH6, CDH9, CDH10, CDH12, and CDH18) belong to outstanding genes. Unexpectedly, nearly all flanking genes of the associated SNPs distinctive for BPD and MDD were replicated in an enlarged cohort of 986 SCZ patients (P ≤ 9.9E-8). Considering multiple bits of evidence, our chromosome 5 analyses implicated that bipolar and major depressive disorder might be subtypes of schizophrenia rather than two independent disease entities. Also, cadherin pathway genes play important roles in the pathogenesis of the three major mental disorders.

Familial clustering of schizophrenia (SCZ), bipolar disorder (BPD), and major depressive disorder (MDD) was systematically reported (Aukes et al, Genet Med 2012, 14, 338-341) and convergent evidence from genetics, symptomatology, and psychopharmacology imply that there are intrinsic connections between these three major psychiatric disorders, for example, any two or even three of these disorders could co-exist in some families. A total of 60, 838 single-nucleotide polymorphisms (SNPs) on chromosome 3 were genotyped by Affymetrix Genome-Wide Human SNP array 6.0 on 119 SCZ, 253 BPD (type-I), 177 MDD patients and 1,000 controls. The population of Shandong province was formed in 14 century and believed that it belongs to homogenous population. Associated SNPs were systematically revealed and outstanding susceptibility genes (CADPS, GRM7,KALRN, LSAMP, NLGN1, PRICKLE2, ROBO2) were identified. Unexpectedly, flanking genes for the associated SNPs distinctive for BPD and/or MDD were replicated in an enlarged cohort of 986 SCZ patients. The evidence from this chromosome 3 analysis supports the notion that both of bipolar and MDD might be subtypes of schizophrenia rather than independent disease entity.Also, a similar finding was detected on chromosome 5, 6, 7, and 8 (Chen et al. Am J Transl Res

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